information sharing in a supply chain

J Intell Manuf (2012) 23:1083–1101 DOI 10.1007/s10845-010-0430-3

Impact of information sharing in hierarchical decision-making framework in manufacturing supply chains

Nurcin Celik · Sai Srinivas Nageshwaraniyer · Young-Jun Son

Received: 14 November 2009 / Accepted: 25 June 2010 / Published online: 22 July 2010 © Springer Science+Business Media, LLC 2010

Abstract This paper presents a comprehensive framework for the analysis of the impact of information sharing in hier- archical decision-making in manufacturing supply chains. In this framework, the process plan selection and real-time resource allocation problems are formulated as hierarchical optimization problems, where problems at each level in the hierarchy are solved by separate multi-objective genetic algo- rithms. The considered multi-objective genetic algorithms generate near optimal solutions for NP-hard problems with less computational complexity. In this work, a four-level hier- archical decision structure is considered, where the decision levels are defined as enterprise level, shop level, cell level, and equipment level. Using this framework, the sources of information affecting the achievement of best possible deci- sions are then identified at each of these levels, and the extent of their effects from sharing them are analyzed in terms of the axis, degree and the content of information. The generality and validity of the proposed approach have been successfully tested for diverse manufacturing systems generated from a designed experiment.

Keywords Multi-objective optimization · Supply chain · Information sharing · Shop floor control · Hierarchical decision-making

Introduction

In today’s global and competitive market circumstances, hav- ing an efficient supply chain has become more significant

N. Celik · S. S. Nageshwaraniyer · Y.-J. Son (B) Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA e-mail: [email protected]

than ever. Many industries in various sectors have launched initiatives to enhance the efficacy of their supply chain man- agement, and massive amounts of savings were achieved as a result of such pioneering works. For example, Kurt Salmon Associates Inc. (1993) has estimated that potential savings can add up to around $30 billion per year for the gro- cery industry. For the healthcare industry, Computer Science Corp. (1996) estimated that savings would be about $11 bil- lion per year (48% of the process costs) when the informa- tion is helped flow in the right direction at right time in the supply chain. Later, according to Premier Alliance (2004), “The Supply Chain Collaborative Breakthrough Series” initiative, which is established by members of Premier Inc. (an alliance of 1,500 hospitals and health systems), saved more than $46 million over a 3 year period by enabling the sharing of the data among various echeclons of the sup- ply chains. Procter & Gamble (manufacturer) and Wal-mart (retailer) have disclosed their new supply chain integration initiative with an aggressive goal of sharing information via their channel partnership. The partnership started with a sim- ple desire to improve business relationships, and was gradu- ally enhanced by sharing information and knowledge about their respective markets. This sharing in turn enabled more effective execution of such concepts as category manage- ment, continuous replenishment, and process coordination, which collectively helped make the supply chain more effi- cient (Grean and Shaw 2002; Siems 2005). The mutual bene- fits that Procter & Gamble and Wal-mart obtained out of this initiative reached more than billion dollars.

While many other instances of such initiatives as the ones mentioned above exist in the industry and related research works are available in the literature on informa- tion sharing in the supply chain (Legner and Schemm 2008; Chen et al. 2007), their focuses are mostly on the shar- ing of demand information between various echelons in an

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aggregated manner (especially between retailers and their upstream suppliers). Furthermore, most of these studies lack the ability to quantify the magnitudes of benefits although the said benefits have been the center point for their discussions. In order to understand the actual benefits of the information sharing within a supply chain, the effect of this sharing should be analyzed in conjunction with a particular control system (e.g. hierarchical structure, heterarchical structure, or hybrid structure) governing the supply chain. In this paper, we pres- ent a coherent and comprehensive framework for analyzing the impact of information sharing in and across various deci- sion levels (e.g. enterprise level, shop level, cell level, and equipment level) of the hierarchical, supply chain control sys- tems. In particular, we consider a two-echelon supply chain, where the hierarchical process plan selection from a set of alternatives and real-time resource allocation are considered. In this work, the primitive process plan for each level of deci- sion is assumed to be available when a part production order is submitted. These primitive process plans contain a com- plete set of possible production alternatives including the ones affected by the shop, cell, machine, and tool selections. When the manufacturing system starts to operate, succinct decisions have to be made on these primitive process plans to determine which processes will be performed in which sequence. First, the final serialized process plan is derived from the primitive process plan considering the system sta- tus. The making of these decisions is called the “linearization of process plans”. Then, resource-allocated process plans are generated by assigning the most appropriate resources (i.e., shops, cells, machines and tools) to these linearized process plans and sent out to the manufacturing system to be executed.

Our particular objective in this study is three-fold. The first objective is to refine a four-level hierarchical decision- making framework to be used for the linearization of process plans and real-time resource allocation in a supply chain sys- tem, where the four levels are enterprise level, shop level, cell level, and equipment level. The sources of information affecting each decision level in the hierarchy are then iden- tified in each of these levels. This four-level hierarchical framework is constructed as a mechanism to enable opti- mal or near optimal decision-making within the considered supply chain. This optimal decision-making is enabled via the multi-objective genetic algorithm, which is embedded into our four-level hierarchical decision-making framework mentioned above.

The second objective is to develop a novel approach to investigate various roles of information sharing in manu- facturing supply chains in a quantitative manner using a test-bed developed in this work in conjunction with intelli- gent decision-making algorithms. This investigation aims to determine the magnitude of the impact of sharing of informa- tion on linearization of process plans and real-time resource

allocation, where the overall goal is to increase efficiency by decreasing the total cost of production and lead-time to enhance its re-configurability. This is a unique study, which allows us to simultaneously manage near optimal decision- making via the considered four-level hierarchical decision framework, operations based on the generated (linearized) process plans and resource allocations, and automatic feed- back that is used to check systems performance based on these decisions. Given updated system status and require- ments, the linearization and resource allocation of the process plans will be regenerated if the values are beyond the allowed threshold range, while specifically balancing the benefits of such updates against the cost of schedule disruption. While illustrated from the perspective of a single facility, the pro- posed approach will permit modeling of large supply chain instances with external suppliers and multistage fabrication- assembly systems.

To this end, the critical aspects of the information to be shared when developing models to help decision-making in supply chain systems are analyzed in detail. These critical aspects are classified in three main categories, including (1) the axis of shared information, (2) the degree of shared infor- mation, and (3) the content of shared information. The axis of shared information can be either vertical, where the informa- tion is shared among various hierarchical levels (i.e., cells) within a single echelon (i.e., manufacturing facility) or hori- zontal, where the information is shared across multiple ech- elons of the supply chain (see Fig. 1). The content of shared information refers to the actual information that is shared between various members of supply chain and customers, and can be defined both for vertical or horizontal axises. The degree of information shared can be divided into three aggre- gated levels for both axises: no information sharing, partial information sharing, and full information sharing. In the case of information sharing via the horizontal axis, no informa- tion sharing defines the situation where the supplier only has information on the orders received from the manufacturer and must utilize historical data to augment the order information when preparing demand forecasts. With partial information

Fig. 1 Information sharing among supply chain members

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sharing, the demand distribution faced by the retailer and the retailer’s inventory policy are known. Finally, with full information sharing, the supplier also receives instantaneous information on the retailer’s demand. In the case of infor- mation sharing via the vertical axis, no information sharing defines the situation where only shop-level aggregated infor- mation is known and the operations planning framework has no detailed information regarding various cells of a shop floor or specific machines within these cells. In this case, strategies can only be determined at the strategic level in a highly aggregated manner. With partial information sharing, the cell level information is known and shared within the same shop floor. Hence, the planning can be performed at the tactical level. Lastly, with full information sharing, all the information generated from the smallest element of the shop floor, which is considered as machine in this study, is known and shared among other decision levels. Therefore, accurate predictions as well as the decision tasks can be generated for the operational level within this echelon of the supply chain.

The accuracy of the information that is shared in differ- ent dimensions mentioned above (i.e., capacity of machines employed in the manufacturing process, shop floor layouts, and maximum safety stock of the average on hand inven- tory) is essential in generating feasible decisions in supply chain systems. Distortion of this information could lead to congestion and problems such as excessive work-in-process inventory, back order costs, and increase in cycle time. The consequences arising from faults at the shop floor level may have detrimental effects on the performance of entire sup- ply chain organization. Therefore, the impact of distortion of information during the hierarchical decision-making has also been studied, and solutions to mitigate the losses arising from lack of or inaccuracy in information sharing have been discussed in this research.

The third objective is to develop an accurate representa- tion of a manufacturing supply chain involving a production facility and a retailer facility as a simulated test-bed, where realistic manufacturing scenarios can be mimicked to investi- gate alternative “what-if” scenarios. These what-if scenarios entail different shop, cell, and equipment configurations. This test-bed is built in a great detail to allow for tracking even very small structural changes (e.g. tool conditions, remain- ing processing time at a machine) within the system and how sharing of different information would affect the system per- formance in a greater scale.

The remainder of this paper is organized as follows. Section “Background and Literature Survey” summarizes a background and literature survey related to this study. Section “Proposed Approach for the Impact Analysis of Informa- tion Sharing” gives an overview of the proposed approach for the impact analysis of information sharing. Section “Considered Manufacturing Supply Chain” presents the

details of the manufacturing supply chain system considered in this work. In Section “Mathematical Formulation of the Problem”, we first describe a generic mathematical formula- tion of the linearization of process plans and resource allo- cation problem for each level of the production system and then explore ways of employing various parameters incor- porating shop level, cell level and equipment level informa- tion into this mathematical formulation. Section “Details of the Multi-Objective Genetic Algorithm” explains the pro- posed four level hierarchical decision-making framework and its near optimal decision capability using multi-objective genetic algorithm. Section “Experiment and Results” sum- marizes the designed experiments together with the results obtained from our case study. Lastly, in Section “Conclusion and Future Work”, the conclusions are drawn and the future aspects of this study are discussed.

Background and literature survey

Information sharing in supply chain systems

When information is shared in inter-organizational networks, it can result in a more efficient flow of goods and services, reduced inventory level, and lower costs, which benefits the overall network (Venkateswaran and Son 2004). Information sharing has also been found to reduce the bullwhip effect (order variability) and to add value to the chain (Chen et al., 2000; Lee et al. 1997). For example, Wal-Mart shares point-of-sale information with their suppliers and transmits orders electronically to the relevant supplier when inventory for an item falls to a predetermined minimum level of stock (Lancioni et al., 2000). This inter-organizational information sharing reduces carrying costs of inventory, facilitates quick response for inventory replenishment, and allows suppliers to better plan their production schedules, and reduces lead times (Stevenson, 1994; Baganha and Cohen 1998; Sherali et al. 2008).

While benefits of inter-organizational information shar- ing has been widely studied (Chen et al. 1998; Lee et al. 2000), it is difficult for firms to reap these benefits unless they have a better grasp of the antecedents of inter-organi- zational information sharing that influence its effectiveness. This is an area in which firms need guidance so that they can effectively channel resources to their knowledge and infor- mation sharing activities. The ability of managers to coordi- nate the complex network of business relationships that exist between parties involved in the supply network is critical to the success of a firm (Lambert and Cooper, 2000).

The network patterns, which can have one or more stages, create varying levels of complexity, and hence differing envi- ronments for information sharing. Further, location of the firm(s) within a network creates different information needs

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and consequences due to the distortion in the flow of informa- tion. Managing the flow of information effectively requires close attention to the coordination mechanism established among the member firms in a network. The degree of coor- dination is likely to affect the nature and amount of informa- tion that is shared across the network. Similarly, the degree to which the partner firms perceive a match in their goals may impact the nature and amount of information they are willing to share with each other (Samaddar et al., 2006).

Lee et al. (1997) explain the importance of mitigation of detrimental impact of distortion of information in the form of inbound orders, from downstream members to upstream members, in a supply chain. They consider a series of compa- nies in a supply chain, and each of the companies orders from its immediate upstream member. They claim that the distor- tion is amplified in the upstream direction of the supply chain as a demonstrative of the “bull whip” effect. They analyzed demand signal processing, rationing game, order batching, and price variations as four sources of the “bull whip” effect. In particular, there is an amplification and larger variance in the distortion of information from downstream to upstream members. Sterman (1989) attributes the increase in amplifi- cation and variance of information distortion to several “mis- perceptions of feedback”.

As mentioned earlier, a great percentage of the literature examines the impact of information sharing in the supply chain in a highly aggregated manner without considering the possibility that the organizations may benefit much from the information sharing in a detailed level. However, shar- ing of information horizontally among the partners of sup- ply chain (i.e., demand, work-in-process levels, replenish- ment time and amount) and then sharing the elements of this information vertically within a production facility (using hierarchical decision-making process proposed in this work) may help organizations work in their highest efficiency. Sim- ilarly, sharing of data originated from the production floor (i.e., cell, and equipment related data) with various members of the facility may enhance the productivity and efficiency level leading to minimized lead times, work-in-process, cost and therefore, maximized profit. In this work, we intend to develop a coherent and comprehensive framework for ana- lyzing the impact of information sharing among various deci- sion levels of manufacturing supply chains.

Hierarchical decision-making

In a hierarchical decision-making system, the commands typ- ically flow from top to down, and feedback information flow from bottom to up, and the relationships among the modules are limited to master-slave relationships between parent and child nodes in a tree shaped hierarchy (Bongaerts et al. 2000). One common decision area considered in the literature within this natural hierarchy is process planning. Process planning

is the task of planning the various processes or operations to be made on raw materials to transform it into the desired part. The output of this task is a plan that contains the routes, pro- cesses, process parameters, machines, tools and set-ups to be used for manufacturing parts (Ma et al. 2000; Nau and Chang 1983). While computer aided hierarchical process planning has advanced significantly in its duty of creating the prim- itive process plans with alternatives, human intervention is still needed as decision mechanisms to finalize process plans by serializing the process plans after considering alternate sequences of the operation to be performed, and then allo- cate the resources based on this final process plan. These decisions are quite important as they are essential for pro- duction and determine the efficiency of production (Joshi et al. 1986). Other approaches (Dilts et al. 1991) have used the hierarchical decision-making architectures to operational decisions via off-line schedulers at different levels of the hier- archy. In these approaches, when a disturbance occurs, it is fed back to the appropriate level in the hierarchy (e.g., the cell scheduler), and only after the schedule has been adapted, the new schedule triggers a new flow of commands that forms the reaction to the disturbance. The resulting response time is low leading to a low robustness (Bongaerts et al. 2000).

In this study, we propose a multi-objective genetic algo- rithmic approach to be used as a decision aid for hierarchical linearization of process plans and real-time (on-line) resource allocation inside a production facility of a two-echelon sup- ply chain and help analyze the effect of information shar- ing in manufacturing systems. Real-time resource allocation decisions at each level determine which resources will be utilized for the production. For instance, our considered pro- duction facility comprises two shop floors, each divided into cell areas that are comprised of machines and tools. Here, our resource allocation decisions take into consideration the resource availabilities (e.g., shops, cells, machines and tools) as well as the part routing through these resources. Follow- ing the assignment of jobs to a specific cell at an aggregated level, the machines are allocated to specific operations within these jobs based on the processing cost and times of these operations in a more detailed level. This hierarchical nature of allocating resources at a lower level after allocating resources at a higher level applies to all levels of decision-making.

Meta-heuristics

Process plans that are selected without considering the resource availability (which is imminent in the operation plan of the whole production unit) tend to violate feasibility con- straints and lead to losses. Efforts to find the optimal or near optimal solution for this problem have been spent mainly on two different approaches. In the first approach, the linear- ization of process plans (selection) and resource allocation problems are combined and formulated as a single problem

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(Moon et al. 2002; Yan et al. 2003). The second approach is comprised of two steps, where the first step (Aldakhilallah and Ramesh 1999; Sormaz and Khoshnevis 2003) involves the generation of numerous process plans that achieve the predetermined level of performance criteria in the process- planning problem. Then, in the second step, optimization of the scheduling problem is performed with respect to each of the alternate process plans generated above, where each imposes different feasibility constraints.

The search space for the combined linearization of pro- cess plans (selection) and resource allocation problems is exhaustive, which makes it difficult for deterministic opti- mization methods like integer programming or mixed inte- ger programming to arrive at an optimal solution. The said search space grows even bigger and makes the problem even harsher to resolve when the problem is formulated in detail for large-scale complex systems such as the considered sup- ply chain system in this research. In order to address these challenges, another type of approaches have emerged through the use of meta-heuristics. Meta-heuristics including genetic algorithms (GA) (Moon and Seo 2005), simulation anneal- ing (SA) (Cai et al. 2009), particle swarm optimizations (PSO) (Guo et al. 2009), and Tabu search (Brandimarte and Calderni, 1995) have been employed to obtain solutions to problems which belong to the class of integrated process planning and scheduling (IPPS). GA, evolutionary algorithm (Li et al. 2009), and symbiotic algorithm (Kim et al. 2003) have all been quite successful in obtaining near optimal solu- tions to variants of IPPS problems. The concept of reaching the optimal solution by a way of evolutionary synthesis of the pool of candidate solutions is common to GA, symbiotic, and evolutionary algorithms. In this study, we have designed a multi-objective genetic algorithm in order to take advan- tage of the method of reaching a near optimal solution via evolution in reasonable short time.

Proposed approach for the impact analysis of information sharing

Figure 2 depicts a hierarchical decision-making framework considered in this research, in which we intend to quantita- tively analyze the impact of information sharing in manufac- turing supply chains. The framework consists of enterprise, shop, cell and equipment levels. There exists a controller (including monitoring, decision-making and execution mod- ules) at each level, where its decision-maker could be based on a separate multi-objective genetic algorithm depending of the complexity of its decisions. Each controller is associ- ated with one resource at the same level, and interacts with the controllers at their immediate lower levels. These inter- actions include (1) the information shared about the status of resources at a lower level by controllers at that level,

(2) the decisions to lower level controllers from higher level controllers, and (3) the feedback information on the perfor- mance of resources at a lower level. After process plan lin- earization and real-time resource allocations are received at the system monitor, they are processed by the decision-mak- ers, and the resulting decisions to the lower level controllers are communicated via the executor. We assume that there is no direct interaction between any two controllers, other than those at successive levels, for the ease of analysis of impact of information sharing. Therefore, in this framework, the execution of decisions is performed in a hierarchical man- ner and thus, the term hierarchical decision-making is rightly suggestive of the way it operates.

Each controller receives information related to utiliza- tion, usability, and performance of each resource at its lower level via its system monitor. The content of this information received by a controller depends on its’ position in the hierar- chical framework, the degree of information sharing allowed between itself and its lower level controllers, and the per- meability of information shared. Allowing high degree of information sharing between controllers in successive levels assumes that there is a possible necessity that can arise for the higher level controller to have detailed information about resources at lower levels before it can send its decisions to the lower level controller. Moreover, the same information will be highly permeable at a particular level if sharing it to a controller at that level will favor the overall speed of decision-making and the overall operational performance in the production facility. For instance, the enterprise level deci- sion-maker can select its primitive process plan and, follow- ing that, it can generate its real-time resource allocations by only using the aggregated level shop information when the information from levels other than the shop level are not permeable at the enterprise level. On the other hand, if the latter is highly permeable at the enterprise level, the same decision-maker can proceed by using even the most detailed data including the ones coming from the tool monitor such as tool availability and remaining life of tool.

The decisions communicated from one controller to another are essentially instructions containing the real-time allocation of the resources associated with its current or next duty. The factors that influence these real-time allocations differ from one level to another based on the structures and duties of resources at each level. The enterprise, shop and cell level instructions contain their corresponding shop, cell and machine allocations based on part handling costs and cycle times. However, machine allocation is based on processing cost in addition to the factors mentioned above. Equipment level instructions contain tool allocations based on process- ing cost, tool handling cost, and cycle time.

The nature of feedback from a controller at a given level to its higher level controller is of two types, namely, regu- lar feedback and event based feedback (see Fig. 3). Regular

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Fig. 2 Overview of the considered four-level decision hierarchy and relationship among controllers

ti : time window for i th decision-making

: regular decision-making points

Time

t1 t2 t3

t1 t2 t3

Events requiring decision-making

Events requiring decision-making

t1 t2

Time

Time

Fig. 3 Occurrence of an event that requires new decision-making

feedback is the feedback communicated to the higher level controller after every fixed interval of time, along with the information required for selection of its associated resource for the next interval. This type of feedback is the norm provided that there does not occur a great deviation from the expected performance of the associated resource in the midst of that interval. However, the dynamic and unpredict- able nature of manufacturing systems due to the concurrent flow of various duties as well as sharing of different types of resources (i.e., sharing of cutters for different types of opera- tions) may cause some events requiring immediate decision- making. These events arise due to a change in the system

cause by external and internal disturbances. External distur- bances could be new orders, change in the current order, new parts arrival, non-arrival of parts at the planned times, and increased end-product demand. Internal disturbances may arise due to temporary/permanent failure of any resource (e.g., breakdown or regular maintenance of tools, machines, transport equipment, conveyor belts and even breakdown of a cell or a shop due to fire or power surge). In the case that an event fails the functioning of a given resource, its controller invokes the controller at its higher level to indicate that all the parts assigned to it have to be allocated to other available resources on the same level. Therefore, the controller invokes

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information about the status of all its lower level resources for replanning the process plan linearization and real-time resource allocations.

Considered manufacturing supply chain

The manufacturing supply chain considered in this study is comprised of two echelons, including a part manufacturing facility and a distribution center. In the part manufacturing facility, parts are produced from the raw material and avail- able workpiece through various sets of operations. In the distribution center, the manufactured parts are sent to its end customers. The manufacturing facility is responsible for the production of a unique product while the distribution center is responsible for distribution of many different product types with varying order amounts. Although only a unique part is manufactured in this facility, there are multiple process plans with varying precedence constraints among which one can be selected to implement depending on the immediate shop floor conditions. In this supply chain, we focus on the line- arization of process plans and real-time resource allocation problems, where primitive process plan of the manufactured part is given.

In this manufacturing environment, we perform control via monitoring and decision-making using the algorithms that we have developed in this study. In order to test the proposed framework, a simulation test-bed is used to mimic the real system and analyze dynamic system behavior when the operational characteristics (e.g., the productivity levels of cells, the sharing of cutters) as well as the physical character- istics (e.g., machine break-downs) of the system are changed. The manufacturing facility considered in our case study (see Fig. 4) consists of three cells, where CELL1 consists of two machines, a turning center and a machining center, a robot and a buffer; CELL2 consists of four machines, a turning center, a machining center, a milling center and a laser cen- ter, two robots and two buffers; and lastly CELL3 consists of three machines, a turning center, a machining center and a milling center, a robot and a buffer. The shop level deci- sion-maker can initiate operation of the shop floor by enter- ing the required production of parts. Based on the output obtained from this decision-maker, which is a shop level production schedule, the cell level decision-maker can be initiated in order to determine which machines should be assigned to which operations. Similarly, based on these cell level schedules, the equipment level decision-makers are then being initiated respectively in order to obtain equipment level (the most detailed) production schedules. All of these hierar- chical production schedules which minimize cycle time for the required production are generated using the embedded multi-objective genetic algorithms. The affect of incorporat- ing real-time data streaming from the actual system on the

performance of system is analyzed within this setting. For the configuration shown in Fig. 4, we suppose that the shop level, cell level and equipment level decision-makers are all con- nected to each other. Each of these decision-makers also has full access to shop level, cell level and equipment level mon- itors where the data regarding the actual system is collected. These decision-makers all have their own decision-making algorithm embedded into them to determine what sequence of operations will produce each unit in each level of produc- tion. The materials are initially stored in the storage system, transported to the work cells by the transportation network, and processed by the machines in the work cell and the final products returned back to the storage area. The information regarding the location of the transporters, location and pro- cessing stage of the materials, and equipment and cell status are monitored by the sensors. For example, the individual transport units are fitted with RFID tags, which are read by strategically placed RFID readers to obtain the current loca- tion and the contents of the transport units. In addition, envi- ronmental sensors (temperature and humidity sensors) are placed within critical work areas. The information from the sensors is reported to the corresponding cell level monitor, and all the cell level monitors report to the shop level moni- tor. The shop level monitor then verifies the progress of the schedule and the plan.

The four-level hierarchical process plan of the manufac- tured part is shown in Table 1, where the naming convention for the separation of jobs, operations, tasks and the selection of cells versus machines is adapted from three-level hier- archical process plan developed in Cho et al. (2006). The part manufactured in our facility mentioned above is com- prised of five jobs, where each job can be assigned to any of the cells depending on its operational requirements and the availability of the cells at the aggregated level. In the detailed level, each of these jobs is separated into its specific oper- ations, where each operation can be assigned to any of the machines considering the type of the process, specifications of the machines including the remaining time of the current operation, the corresponding set-up time of the next opera- tion, machine utilization, and the maintenance schedule. The nodes containing the labels of “f0” through “f11” denote spe- cific machining features. The nodes containing labels of “so” and “jo” denote a “split or” and “joint or”, respectively, where among the nodes in between an “so” and “jo” node, having only one path processed is enough for the entire part to be manufactured. For instance, in Operation 2, the process can be in either the sequence of “f2–f3” or “f2–f4”. The nodes containing labels of “sa” and “ja” denote a “split and” and “joint and”, respectively, where among the nodes in between a “sa” and “ja” node, both paths have to be processed. How- ever, the sequence of which path should be processed first and which one should be the latter is a decision to make. For instance, in Job 4, the process can be in either the sequence

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Sensored Storage and Retrieval System

Sensored Network

Sensored Transporter

CELL I CELL II

Shop Level Decision Maker

Cell Level Executor

Cell Level Monitor Sensored Cells and

Machines CELL III

Transport Monitor

Transport Executor

M

X

X M X M

X

M RFID tags

RFID readers

B U F F E R S

Sensors

Cell Level Decision Maker

Equipment Level Decision Maker

Enterprise Level Decision Maker

Fig. 4 Configuration of the production facility considered in this work

of “f8–f9” or “f9–f8”. It should be noted that although the manufactured part in this facility is unique, it could be pro- cessed via several variations of the detailed process plan due to these special nodes explained above. Moreover, the part production requests (orders) are coming in a random manner, and the processing times of each order varies due to mainly the selection of machines.

Mathematical formulation of the problem

Our main objective in this research is to analyze the impact of information sharing within a supply chain quantitatively. For- mally, given an optimization problem with objectives subject to constraints, we intend to examine the results of the deci- sions that are made with respect to this optimization problem. The decisions here involve the selection of processes from alternatives and real-time allocation of resources for upcom- ing production, where the times at which parts, jobs, opera- tions and tasks are planned to be processed are listed. To this end, we explain the details of these decisions, mathematical formulation of the problems considered in this study (objec- tives and constraints), and how the sharing of information in different axises, degrees, and contents affect the solution of these problems.

Model objectives

The supply chains can operate according to many and con- flicting objectives such as minimizing cycle time, minimiz- ing cost, maximizing customer service levels (by means of maximizing order fill rates and on time delivery rates, or by minimizing stock-out rates and backorder levels), minimizing inventory levels, maximizing resource utiliza-

tion, and increasing supply chain flexibility (by means of volume, product mix, routing and delivery time). Among these, we have considered the two most commonly pos- sessed conflicting ones, which are (1) minimizing cycle time, (2) minimizing cost.

Min Cycle Time

The mathematical formulations for our multi-objective opti- mization problem given in this section are made generic, where the same formulation can be utilized for the decision made by decision-makers at enterprise, shop, cell and equip- ment levels. Eq. (1) presents our first objective, which is min- imization of the cycle time of the manufacturing (Tcyclet i me).

min Tcyclet i me

= ∑

i ∈I

∑

j ∈ J

∑

k∈K (wi j k + pi j k + ti j k + ai j k )xi j k (1)

where

I : Set of orders (number of parts) that need to be processed J: Set of Duties that need to be processed in the order of the process plan considered K : Set of resources in which duties need to be processed wi j k : Waiting time of a part i waiting to be processed for duty j in resource k pi j k : Processing time of part i for duty j in resource k ti j k : Transfer time of part i for duty j to resource k ai j k : Set-up time of part i for duty j to resource k xi j k : Binary decision variable, is “1” if duty j is assigned to resource k for parti and “0” otherwise.

In the formulation given in Eq. (1), a resource can be a shop, a cell, a machine, or a tool corresponding to their duties

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Table 1 Four-level hierarchical process plan of the considered parts in this case study

Level Primitive process plan graph Resource-allocated process plan graph

Enterprise

j1

j2

f1

sa f2 so

f3

f4

jo

ja

f5

f6 f7 sa

f10

f11

ja f0

j3

j5

j4

so f8

f9 jo

s o jo

p1

f1 s o f2

f3

jo

f4

j2j1

p2

Shop α 2

Shop α1 p1

P ar t

p 2

Shop

j1

j2

f1

sa f2 so

f3

f4

jo

ja

f5

f6 f7 sa

f10

f11

jaf0

j3

j5

j4

so f8

f9 jo

so jo

p1

Ce ll 5

Cell 3

Cell 2

Ce ll 1

j 1

j2

j3

j 5

Job

so jo

Cell 4

j4

Cell

j2

s a f 2 s o

f3

f4

j o

j a

f 5

o 2

o 3

Machine A

sa o2

o3

ja Operation

Machine B

Equipment f2 so

f3

f4

jo

o2 t2 t3

t4

f0 – f11: machining features

t1 so t2

t3

jo

Cutter a Cutter b

Cutter cTask

(e.g., part, job, operation, and task) depending on the level at which the value of this objective is being calculated.

Min total cost

Equation (2) shows our second objective, which is minimi- zation of the total cost(Ct ot al ), where the cost is split into two factors: total processing cost and total material handling cost.

min Ct ot al = C pr ocessi ng + Cmat er i al handli ng + Cset −u pchange (2)

Processing cost The processing cost is the cost of using a particular resource over a specific period of time. The total processing cost at a level is determined by aggre- gating the operating costs of all resources for each duty that they are assigned to over the planning horizon. Here, the term “resources” refers to machines or tools whose

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corresponding duties are operations or tasks respectively, depending on the level at which the value of this objective is being calculated. The computation for the processing cost is given in Eq. (3).

C pr ocessi ng = ∑

i ∈I

∑

j ∈ J

∑

k∈K Ci j k .xi j k ∀ l ∈ L (3)

where Ci j k is the cost of using a resource k for processing a part i during duty j, and L is the set of alternative process plans.

Material handling cost The material handling cost is the cost of transporting the parts from one resource to another one. It is encountered when one part is moved from one resource to another resource during the course of the change in the duty to be performed on it. Here, the term “resources” refers to shops, cells and machines whose corresponding duties are parts, jobs and operations, respectively, depend- ing on the level at which the value of this objective is being calculated. The computation for the material handling cost is given in Eq. (4).

Cmat er i al handli ng

= ∑

i ∈I

∑

j ∈ J

∑

k∈K

∑

k′∈K dkk′ .xi j +1k′ .xi j k ∀ l ∈ L (4)

where dkk′ is the distance between resources k and k ′ in the

shop floor layout.

Model constraints

The constraints of our multi-objective optimization problem are summarized in Eqs. (5–11). Equation (5) assigns every duty j to at most a resource k; Eq. (6) ensures that a resource is not assigned to more than one duty at any given time; Eq. (7) assures that the total processing time of duties that are assigned to a resource does not exceed the capacity of that resource; Eq. (8) checks the feasibility of the assigned processing times with respect to the maximum cycle time of the whole process plan. Minimum and maximum limits have been enforced on possible processing times of each resource k for a particular duty to ensure that congestion does not happen due to very fast or slow processing times; Eq. (9) defines the decision variable xi j k as binary where it is “1” if duty j is assigned to resource k for part i and “0” otherwise; Conditions in Eq. (10) specify that the relation between the upper and lower limits of the processing times and ensure that the assigned processing time is always a whole number; and lastly Eq. (11) supplements the binary variable xi j k by giving real-time information of whether part i was assigned to a resource k for a duty j at time ‘t’ or not. ∑

k∈K xi j k ≤ 1 ∀ i ∈ I, and j ∈ J (5)

∑

j ∈ J yi j k ≤ 1 ∀ i ∈ I, k ∈ K , and t ∈ T , (6)

where T is time for which supply chain is functional ∑

i ∈I

∑

j ∈ J xi j k . pi j k ≤ Mk ∀ k ∈ K (7)

pmini j k ≤ pi j k ≤ pmaxi j k ∀ i ∈ I (8) xi j k = {0, 1} ∀ i ∈ I, j ∈ J, and k ∈ K (9) pmini j k , p

max i j k ≥ 0, pmini j k ≤ pmaxi j k (10)

if yi j kt = 1, then ∑

i 1 �=i, i 1∈I yi j kt = 0 ∀ j ∈ J, k ∈ K ,

and t ∈ T (11) where Mk is the capacity of resource k (in arbitrary units of time) and yi j kt is the binary decision variable, where yi j kt becomes “1” if xi j k is “1” at any time t. Here, resource refers to shops, cells, machines or tools depending on the level of decision.

Impact of information sharing on formulation

As mentioned earlier, the impact of information sharing on supply chain performance is analyzed in terms of the axis, degree, and content of the information that is being shared. The axis of information sharing can be horizontal among the supply chain echelons (mainly in the enterprise level) and vertical among the levels of decision hierarchies in each of these echelons. On the other hand, the degree of information sharing can be in three different lanes including no informa- tion sharing, partial information sharing, and full information sharing. In the considered hierarchical decision mechanism (see Section “Proposed Approach for the Impact Analysis of Information Sharing”), the model constraints used by the multi-objective genetic algorithm are revised depending on the information that is received from the lower levels in the hierarchy. For instance, within the manufacturing facility (in the vertical axis) if no information is allowed to be shared, then the decision-maker can only use the parameters that are set for its own level. In such a case, a cell level deci- sion-maker cannot use the equipment level parameters while solving the linearization of process plans and/or real-time resource allocation problems at the cell level. In contrast, if information sharing is fully allowed, then the decision-maker at any level can incorporate all the parameters regarding its own level and all the levels below itself. In that case, a cell level decision-maker can use all of the cell level and equip- ment level parameters while solving its optimization prob- lems in order to achieve results that are more accurate. The parameters and the information they contain are incorpo- rated as constraints in our optimization formulation, whose generic formulation is given in Sections “Model and Objec- tives” and “Model Constraints”. Additional constraints will

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Table 2 Contents of shared information for various degrees of information sharing in vertical axis

Degree of information sharing

No information sharing

Partial information sharing

Full information sharing

Level

Enterprise (Inter-shop) — • Shop capacity • Shop capacity • Shop throughput rate • Shop availability • Feedback on order performance

Shop (Inter-cell) — • Cell capacity • Cell capacity • Cell input rate • Cell availability • Number of parts already in the cell • Feed back on job performance

Cell (Inter-machine) — • Machine utilization • Machine utilization • Machine availability • Machine availability • Specialized labor availability • Machine health index

• Machine durability index • Historical data of Interval between breakdowns • Feed back on operation performance • Time to the next preventive maintenance for each machine k • Specialized labor availability

Equipment (Inter-tool) — • Remaining time of the current task

• Remaining time of the current task • Tool availability

• Tool availability • Remaining tool life • Removal time of the currently used tool • Installation time for the fixture change • Feed back on task performance

be incorporated into this generic formulation depending on the information sharing status of the supply chain that are summarized in Table 2 and detailed further in this section. These constraints are determined from the feedback given by the lower level decision-makers to the higher level deci- sion-makers. The above-mentioned performance objectives are the main factors in determining the feasibility constraints at a level of the hierarchy.

Parameters incorporating shop information at Enterprise level

Shop capacity (SC): specifies the maximum number of parts in a particular shop that are undergoing processing at differ- ent machines within various cells in the same shop, at a time. Each resource k refers to the shops available for selection for carrying an order that it can complete.

∑

i ∈I

∑

j ∈ J yi j kt ≤ SCk , ∀k ∈ K , ∀t ∈ T (12)

Shop throughput rate (STR): We want to allocate parts to shops in such a way that the quantity of parts machined over a period of regular planning is greater than the mini- mum throughput that is fixed by the decision-maker to meet the target production at this level of decision hierarchy. This fixed minimum throughput, for a period of regular planning, expected from shop “k” is denoted by ST Rk and is calculated by the plant manager from a targeted quantity of machined parts per day. This value is estimated from the distribution center’s demand that has to be met by the enterprise.

∑

t ∈Tshopplanni ng

∑

j ∈ J

∑

i ∈I yi j kt ≥ STRk ∀k ∈ K (13)

where Tshopplanni ng is the time interval between regular

planning done for shop

Shop Availability (SA): A part to be machined will be assigned to a shop only if it has not already reached the maximum

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number of parts that it can accommodate in itself.

if ∑

i ∈I ∑

j ∈ J yi j kt = SCk , then S Ak = 0, otherwise 1, ∀k ∈ K , ∀t ∈ T (14)

where S Ak is the binary decision variable where it is “1” if shop k is available and “0” otherwise.

Feedback on part order performance (Or der Tcyclet i me): The value of the above feedback that will be sent by the shop level scheduler to its higher level controller will determine whether the same shop can be utilized for another period of regular planning. Thus, the “Feedback on part order perfor- mance” sets the threshold for the objective performance of any shop k.

Parameters Incorporating Cell Information at Shop Level

Cell capacity (CC): ∑

i ∈I

∑

j ∈ J yi j kt ≤ C Ck , ∀k ∈ K , ∀t ∈ T (15)

In this section, we refer to a cell k as resource k. The constraint that Eq. (15) imposes on the capacity of a cell is analogous to the constraint imposed on the capacity of a shop (see Shop capacity (SC) in Eq. 12) although their reasons of existence differ. Similar to the value of SC, CC’s value can vary over time. The value of SC is largely influenced by the number, capability and cost incurred by the way of transportation and material handling equipment on a shop floor. The value of cell capacity, on the other hand, is relatively largely influenced by the total cycle time of a part in it.

Cell input rate: This is an approximation of the number of parts arriving at a particular cell. It can be estimated using a database containing schedules of those parts that are already in the system and about to arrive at a given cell plus based on historical data on how many parts could be arriving at this cell from outside the system.

C ell i nput r at ek = (number of parts arriving from within the system calculated via schedule of parts) (16)

Cell availability (CA):

if ∑

i ∈I

∑

j ∈ J yi j kt = C Ck

then C Ak = 0, otherwise 1 ∀k ∈ K , ∀t ∈ T (17) where C Ak is the binary decision variable and it is “1” if cell k is available and “0” otherwise. A part to be machined will be assigned to a cell only if it has not already reached the maximum capacity that it can handle at a particular time.

Number of parts already in the cell: The cell will have sensors that will convey the number of parts waiting to be processed

at each of its machines and the number of parts stored in its inventory. This information will be used by the cell level con- troller to optimally allocate resources to the incoming parts so as to minimize their cycle times.

Feedback on job performance ( J obTcyclet i me ): Similar to that of Or der Tcyclet i me, “Feedback on job Performance” serves as an indicator of usability of a particular cell for the next period of regular planning. If the value of J obTcyclet i meis above the threshold set by its master decision-maker, the same cell k could be utilized again in the succeeding period of regular planning.

Parameters incorporating machine information at cell level

Machine utilization (MU): indicates the time for which a machine is busy. Since we have already assumed that a machine will handle only one part at a time, the machine capacity need not be taken into consideration when MU is computed. The resource here is the machine k.

MUk = ∑

t ∈T ∑

i ∈I ∑

j ∈ J yi j kt T

, ∀k ∈ K , 0 ≤ MU ≤ 1 (18)

Machine availability (MA): A part to be machined will be assigned to a machine only if its’ queue has not reached its maximum capacity. The maximum queue length at a machine Qkmax specifies the buffer capacity of a machine k.

if ∑

i ∈I

∑

j ∈ J yi j kt ≤ Qkmax + 1,

then M Ak = 0, otherwise 1, ∀k ∈ K , ∀t ∈ T (19) where M Ak is the binary decision variable and it is “1” if machine k is available and “0” otherwise.

Machine health index (MHI): is an assessment to decide how healthy the machine is. It is calculated with respect to the state when it is most healthy by a human and depends on fac- tors that are specific to the machines functionality. Here,0 ≤ M H Ik ≤ 1.

Machine durability index (MDI): The real-time use of MHI would figure in the calculation of MDI which indicates how likely a machine k is to last before next standard maintenance on it performed.

MDI = MHI ∗ F Tpr ev F Tmax

(20)

where F Tpr ev is the time between the preceding two failures, and F Tmaxis the maximum time between any two successive failures which is calculated from historical data. Thus, the value of MDI is influenced by its own health as assessed by

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the human (MHI) and by factors that could not be imme- diately analyzed but could be foreseen due to most recent

occurrence (

F Tpr ev F Tmax

) .

Historical data of interval between breakdowns (Mean time between failures (MTBF) = λ): is calculated from historical as well as most recent data of failure times (FT) between two successive failures.

Time to the next preventive maintenance (Tnex t mai n,k ): is the time to next preventive maintenance for a machine k, which is normally scheduled before the time the machine is likely to fail as given by λ. However, it is important that real-time information about the durability of the machine k is taken into consideration. The idea is to perform maintenance well before the machine is likely to fail if the machine has been judged not be durable until then.

Tnex t mai n,k = λ(1 + ε1)e−(1−M D I )a (21) where a is a large number, λ(1 + ε1) is the value that makes Tnex t mai n,k possible for taking values greater than λ itself, and ε1 is the value judged appropriate by the human.

Feed back on operation performance (O per at i onTcyclet i me ): As is for shop and cell levels, the O per at i onTcyclet i me serves an indicator of usability of a particular machine for the next period of regular planning, if the value of O per at i onTcyclet i me is above the threshold set by its con- troller it could be utilized again.

Specialized labor availability (L A): determines whether labor is available to perform the preventive maintenance or not.

if labor is available,

then L A = 1, otherwise L A = 0 (22)

Parameters incorporating tool information at equipment level

Remaining time of the current task: defines the time required to finish the current task. This parameter is one of the most significant parameters for an equipment level controller as it usually comprises the largest portion of the time that is needed to complete a specific task.

Tool availability (T ia ): defines whether a tool which is nec- essary for completion of a particular task is currently being used by another machine or not and is defined on a binary scale.

T ia = {

1 if the tool i is available 0 otherwise

(23)

Remaining tool life (T − Tused ): Tool life is the time a tool can be reliably used for its given task (i.e., cutting) before it must be discarded/repaired. The cutting speed is an impor- tant factor that influences the tool wear and tool life. In this study, a tool life equation developed by Taylor’s equation (Hicks 2006) which depends on the cutting speed, is used (see Eq. 24).

V .T n = C (24) where V is the cutting velocity in ft/min, T is the tool life in minutes, n is a constant based on the tool material, and C is a constant based on the tool and work. The remaining tool life is therefore the difference between the tool life and the total time that a particular tool was being used (T − Tused ).

Removal time of the currently used tool (tr emoval ): is the time spent to remove a specific tool from the machine when the next task does not use the same tool. The expected removal time of tools differ by their types although the variations within the same kind are usually very small. For instance, the current task might be turning whereas the next one can be grinding both of which can be performed in the same machine, yet use different tools.

Installation time for the fixture change (ti nst allat i on ): is the time that is spent in order to make a machine ready to operate once the entire required fixtures are determined. It is com- prised of the set up time required for specific fixtures and the time needed for manual manipulation of the fixture (espe- cially when the fixture has some problems and needs repair).

ti nst allat i on = ⎛

⎝thsu + (nt t −nt s )∑

i =1 t it su + nb(nt t tt c) + tR

⎞

⎠ /

nb

(25)

where thsu is time required for the hard setup of a new prod- uct, which includes activities such as fixture qualification, and verification and downloading of the part program, nt t is the number of tools necessary to manufacture the part, nt s is the number of necessary tools that are already set up on the machine, tt c is the time required for automatic tool change, tR is the time required for recovery actions, t

i t su is the setup

time for each cutting tool i, which may include, for example, its installation into a collet and into a machine tool carrousel, and nb is the number of parts assigned to the machine per batch.

Feedback on task performance (T ask Tcyclet i me): The most detailed production schedules (equipment level schedules) for the considered case study are provided by the pro- posed multi-objective genetic algorithm (decision-maker). The “Feedback on task performance” allows us to invoke the decision-maker when needed.

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Details of the multi-objective genetic algorithm

As mentioned earlier, in this study, we proposed a multi- objective genetic algorithmic approach to be used as a deci- sion aid for hierarchical linearization of process plans and real-time resource allocation to parts, inside a production facility of a two-echelon supply chain to help analyze the effect of information sharing in manufacturing systems. Details of the multi-objective genetic algorithms employed by decision-maker at each level are provided in this section.

Representation and initialization

The shop floor and its productions schedule generation struc- ture, which comprise the basis for evaluation of alternate pro- cess plans enabling the achievement of best performances, are outlined earlier in Table 1 and Fig. 2, respectively. The evaluation framework proposed in this work accepts inputs such as shop floor functions and operations in addition to the process plan variations shown in that table. The resources here are the shops, cells, machines and tools that have to be assigned to part manufactures, jobs, operations and tasks at a time. An operation can be a part of a series of functions, and an operation itself may have functions that can replace each other. We already possess the shop floor plan and its related alternate process plans. The fulfillment of this requisite for working on the integrated process planning and scheduling (IPPS) problem allows us to proceed to evaluate the efficacy of the alternate process plans with respect to the performance objectives subject to the constraints that have been explained in Section “Mathematical Formulation of the Problem”. In particular, we focus on the linearization of process plans and real-time resource (shop, cell, machine or tool) allocation problems in a hierarchical manner. Here, it is also assumed that some machines are versatile as far as their ability to per- form more than one operation although not simultaneously. Such machines give the advantage of minimizing cycle time by offering the possibility of handling different part rout- ings. Thus, this will lead to a decrease in the overall batch processing time.

We have a 2 × 6 facility layout from which machines will be chosen and assigned to one among those set of opera- tions that they are capable of performing. This is the job of the Cell Level Decision-Maker (CLDM). The CLDM then deputes instructions to each of the machines in its cell. Based on these instructions, the Equipment Level Decision-Maker (EQLDM) in each of the machines, then chooses tools for all functions in its operation. The tools are also shared among EQLDMs so an EQLDM has to schedule its functions in such a way that the tools it needs for any function that is going to be performed at a certain time are available. In this way, the responsibility of a EQLDM of tool selection and function sequencing is similar to the responsibility of a CLDM of

machine selection and operation sequencing. The Shop-floor Level Decision-Maker (SLDM) handles the responsibility for the design of cells and job sequencing. The design of cells in the 2 × 6 facility layout requires the information of machine selection from a CLDM. The SLDM then evaluates and verifies the machine selection and operation sequencing decisions made by all of its CLDMs to ensure there is no vio- lation of the feasibility constraints. Similarly, a CLDM eval- uates the feasibility of the tool selection and task sequencing decisions made by all of its EQLDMs. There is an Enter- prise Level Decision-Maker (ELDM) that has the respon- sibility of distributing final requests for part manufactures to its SLDMs based on the information input passed on to it by its preceding and succeeding echelons in its supply chain, and based on the feedback received from each of its SLDMs. Thus, the decision-planning and execution follows a hierarchical negotiation process. We analyze the effect of the availability and accuracy of information that has to be shared as part of these negotiation processes on the overall perfor- mances of the enterprise judged by the values of the objective functions mentioned in our mathematical formulation (see Section “Mathematical Formulation of the Problem”). The flow of the process followed by a controller for near optimal process plan linearization and resource allocation is shown in Fig. 5.

In this work, solutions to our mathematical formulation are found using a multi-objective genetic algorithm. The decision-makers at a level of hierarchy passes on instructions consisting of inputs and expected outputs to all the decision- makers in the immediate lower level in the hierarchy. If there is a conflict between the inputs and expected outputs, the decision-makers, which have received the instructions, send feedback to their master decision-maker. The frequency with which these interactions happen between two levels of deci- sion-makers in the hierarchy is significant to the efficiency of the whole supply chain.

Experiment and results

In this section, we demonstrate our proposed framework to analyze the impact of information sharing via a designed experiment on our case study (see Section “Considered Manufacturing Supply Chain”). During the experiment, a detailed simulation model of the considered manufactur- ing system is built using Arena 12.0 simulation package in order to mimic the real system and its dynamic behavior. We have developed the controllers in the hierarchical decision- making framework for the manufacturing system in Fig. 4 using multi-objective genetic algorithm toolbox available in MATLAB. There are two separate multi-objective GA pro- grams designed to serve as the shop level controller and cell level controller. These programs utilize Tournament selec- tion, crossover probability of 0.8 and constraint dependent

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Fig. 5 Process followed by a controller for near optimal process plan linearization and resource allocation

default mutation with probability of 0.2. The programs in these controllers select the optimal linearized process plan and determine the optimal resource allocations at their level for each part that achieved the best values of the conflict- ing objectives that have been mentioned in Section “Model Objectives”. These decisions of optimal linearized process plan and resource allocations serve as parameters for Arena to simulate the model of the system in Fig. 4. The model parameters that are driven by the multi-objective genetic algorithm are incorporated into the simulation using Visual Basic for Application (VBA) script and embedded into the simulation model using VBA blocks. These VBA blocks are executed each time an entity passes through them. Hence a timing entity is used to control the execution of the algorithms in sequence. The simulation model essentially runs through a bulletin board array system which involves a machine-id array. In this machine-id array, the machine ids are repre-

sented in the rows and the parameters of interest (e.g. machine availability or tool conformance) are in the columns. In par- ticular, sections of this simulation use the data that is kept in this array for calculations or write computed/observed values into this array. The results obtained using this simulation, are summarized further in this section.

Partial versus full degree of information sharing on vertical axis at cell level: sharing of machine health information

At the cell level, we have information indices that con- tain real-time information about the status of health of each machine. Machine availability and Historical data of inter- val between breakdowns for each machine indicate whether the machine is on the verge of breakdown. Machine health index, Machine durability index and Time to the next pre- ventive maintenance give signals of whether a machine is

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Fig. 6 Analysis of impact of sharing and non-sharing of machine health information. a Cell input rate-High, Number of parts already in the cell-High, Machine health information shared. b Cell input rate- High, Number of parts already in the cell-High, Machine health infor- mation not shared. c Cell input rate-High, Number of parts already in the cell-Low, Machine health information not shared. d Cell input rate- High, Number of parts already in the cell-Low, Machine health infor- mation shared. e Cell input rate-Low, Number of parts already in the

cell-High, Machine health information shared. f Cell input rate-Low, Number of parts already in the cell-High, Machine health informa- tion not shared. g Cell input rate-Low, Number of parts already in the cell-Low, Machine health information shared. h Cell input rate-Low, Number of parts already in the cell-Low, Machine health information not shared. Objective 1: Cycle time of producing a specific part in a given cell. Objective 2: Cycle cost of of producing a specific part in a given cell

going to breakdown and also indicate whether the machine ought to be scheduled for regular maintenance before the next period of regular planning. The manufacturer is alerted upon the receipt of this information. Based on this alert, he might plan to replace the machines that are on verge of break- down or under maintenance with alternative ones which are available for the same operation. He might also decide to service and use them if the time and cost required for com- pleting the service are reasonably less when compared to time for replacement of the current machine and installation of an identical one. However, since our aim is to demon- strate the impact of partial versus full degree of information sharing at the cell level, we compare the differences result- ing in the cycle time and cost values from using and not using a particular machine for performing a given opera- tion. As partial information sharing at cell level does not include sharing of machine health information, this compar- ison allows us to judge when the sharing of that information

is vital to the efficient functioning of the cell for a given machine.

We have conducted experiments with varying values of Cell input rate and Number of parts already in the cell. Using different combinations of these two indices, Pareto fronts containing cycle times and costs of an incoming part for cases of sharing and non-sharing of machine health information are obtained and shown in Fig. 6a–h. During the experiment, it is assumed that the individuals situated towards the middle of the Pareto front to form the set of possible solutions and the optimal solution is among them. The average cycle times and costs of production are expected to be less when the individ- uals belong to the same set because they physically become closer to each other.

We propose that the need to share machine health infor- mation is dependent on the magnitude of servicing time of a given machine relative to the difference between average cycle times. The servicing time for given machine is the time

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that is taken to complete regular maintenance or perform breakdown service after it stops working. The difference between average cycle times is calculated between two Pareto fronts corresponding to the same values of Cell input rate and Number of parts already in the cell but differing on the fact whether information was shared or not shared. For instance, the difference between the average cycle times of Fig. 6g, h is about 50 units. Next, consider a machine in the same scenario that is likely to breakdown or be scheduled for maintenance at the time that the given part could be undergoing an oper- ation on it. It will be optimal to allocate that machine to the part only if the servicing time for that machine is less than 50 units. If the servicing time is greater than 50 units, then an alternative machine could have been allocated to the part in the first place thereby which the part would incur less cycle time. Thus, given a large servicing time relative to the differ- ences in average cycle times, it is advisable to share informa- tion regarding the machine health. This is because during the planning for a given part appropriate alternative machines can be allocated if it is known that the given machine could stop working at the time the part is to be operated on it.

It is observed that the difference between average cycle times of the Pareto front obtained from sharing and not shar- ing of machine health information decreases when the val- ues of either of the above indices is changed from high to low. It implies that given a machine and its servicing time, as the waiting time in the cell decreases, the sharing of its health information becomes necessary for achieving lower cell cycle times. After obtaining the same type of results for each machine in a given cell, the manufacturer will be able to determine the threshold values of the indices Cell input rate and Number of parts already in the cell corresponding to each machine that indicates the scenarios for which sharing of its health information has to be enabled. Sharing of machine health information also proves to be useful in scenarios where the differences in average cycle times are large. In these sce- narios, it becomes important for the manufacturer to install and operate a machine identical to the one that has stopped working since the cell cycle times are drastically increased by using alterative machines. The purpose of sharing machine health information in these scenarios would be to caution the manufacturer as and when the breakdown or maintenance time is approaching. The manufacturer would then be able to alert his control systems for gearing up to install an identical machine.

Partial versus full degree of information sharing on vertical axis at equipment level: sharing of tool set-up change information

At the equipment level, we have information indices that can be broadly classified into two categories based on the nature of information that they contain. Removal time of

the currently used tool, Installation time for fixture change and Remaining time of the current task belong to the Set-up change information set, as they contain information related to tool set-up change. Tool availability, Remaining tool life and Feedback on task performance form elements of Tool health information set since they serve as indicators of tool health. The differences in the impact of sharing and non-sharing of information related to tool health on the performance of the manufacturing system is judged from an analysis similar to what has been performed for analyzing the impact of sharing and non-sharing of information related to machine health at the cell level. It can be concluded that as the difference in average cycle times resulting from not using or using a given tool decreases; it becomes necessary to share its health information at the time of tool allocation so that the over- all cell cycle time can be minimized. Therefore, we proceed with the experiments to analyze the importance of sharing tool set-up change information. Through these experiments, we intend to list scenarios for which sharing of tool set-up change information could be useful.

The experiments for evaluating the utility of tool set-up change information were performed for various scenarios where each corresponds to a different combination of the values of the indices Cell input rate and Number of parts already in the cell. From Fig. 7a–e, the values of these indi- ces, corresponding to which the results in the graphs have been obtained, increase implying an increase in waiting time of the incoming parts to which tools have to be allocated in advance for performing the required tasks.

We note here that these experiments were conducted without the sharing of tool set-up change information. Upon sharing that information, the whole Pareto front shifts by a certain amount further into the positive quadrant in each of the Fig. 7a–e since we have machines that have the capability to perform different operations and have to incur some set-up change cost and time. In this case, we again have a set of pos- sible solutions that can be obtained via the above mentioned assumption. But it is favorable to the manufacturer to have a set as small as possible or in other words a set with individu- als whose values are precise with respect to each other. This will ensure that his decision of selection of the final optimal solution does not differ from the other individuals in the same set. The size of the resulting set again depends on the tool set-up costs and time as conveyed by the tool set-up change information. However, it is more probable that the set of pos- sible solutions in Fig. 7a is altered via adding appropriate tool set-up time and costs such that the graph with the modi- fied Pareto front has a precise set of possible solutions from which the optimal solution can be chosen. Thus, it is clear that the sharing of tool set-up change information becomes important in the scenario corresponding to Fig. 7a.

The necessity of sharing tool-set up change informa- tion decreases as the values of indices Cell input rate and

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Fig. 7 Analysis of impact of sharing and non-sharing of tool set-up change information. Objective 1: Cycle time of producing a part in a given cell. Objective 2: Cycle cost of producing a part in a given cell

Number of parts already in the cell increase. This can be concluded from the changes in the structure of the Pareto fronts from Fig. 7a–e. They show that as the values of the indices increase, the tool set-up change costs and times have to relatively increase in order that the modified Pareto front resulting from addition of set-up costs and times will yield a more precise set of possible solutions. Thus, in such cases sharing of tool set-up change information that do not modify the existing Pareto front by much, prove unnecessary and the investment expenditure enabling the sharing of that informa- tion becomes wasteful.

In summary, for scenarios where the values of the above- mentioned indices are small or when the expected waiting times and costs are small, it is advisable to enable the shar- ing of the tool set-up change information. This is because the positions of individuals in the Pareto front resulting from not including that information is expected to be altered by a significant amount when their appropriate tool set-up change costs and times are added to them. It means that this informa- tion can significantly influence the selection of the optimal solution for a given part, which is its optimal linearized pro- cess plan containing sequence of tasks, and also machine and tool allocations in the given cell.

Conclusion and future work

In this paper, a comprehensive framework was presented for the analysis of the impact of information sharing in hierarchi- cal decision-making in manufacturing supply chains. In this framework, decisions are made on a four level-hierarchy for a production system of a two echelon supply chain, where the decision levels are enterprise level, shop level, cell level, and equipment level. At each level, a controller has the responsi- bility of deputing duties (e.g., part, job, operation, and task) via instructions containing input information and expected outputs to all the lower level controllers that are under its supervision. Every lower level controller sends frequent feed- back to its master controller so that the master controller can perform regular planning. In this framework, process plan selection and real-time resource allocation problems are

formulated as hierarchical optimization problems, where problems at each level in the hierarchy are solved by separate multi-objective genetic algorithms. These considered multi- objective genetic algorithms generate near optimal solutions for NP-hard problems with less computational complexity.

Using this framework, the sources of information affecting the achievement of best possible decisions were then identi- fied at each of these levels, and the extent of their effects from sharing them were analyzed in terms of the axis, degree and the content of information. The proposed approach has been successfully tested for an exemplary manufacturing system, where partial versus full degree of information sharing on vertical axis was tested at the cell level (mainly on sharing machine health information) and the equipment level (mainly on sharing tool set-up change information).

In our first set of results (cell level), we have observed that the difference between average cycle times of the Pareto front obtained from sharing and not sharing of machine health information decreases when the values of either of the indices mentioned in Section “Experiment and Results” (Cell input rate and Number of parts already in the cell) is changed from high to low. Therefore, given a machine and its servicing time, as the waiting time in the cell decreases, the sharing of its health information becomes more significant in order to achieve lower cell cycle times. In the second set of results (equipment level), when values of the same indices (Cell input rate and Number of parts already in the cell) are small or when the expected waiting times and costs are small, it is advisable to enable the sharing of the tool set-up change information. It has been shown that this information can significantly influence the selection of the optimal solution for a given part, which is its optimal lin- earized process plan containing sequence of tasks, and also machine and tool allocations in the given cell.

Further research is under development for the partial versus full degree of information sharing on vertical axis at the shop level for the manufacturing systems, where there are multiple production facilities conducting the same process. The analysis of the impact of information sharing on horizon- tal level together with vertical level is also being considered as part of the future extension of this study.

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