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International Journal of Production Research Vol. 50, No. 16, 15 August 2012, 4699–4717

Impact of the pull and push-pull policies on the performance of a three-stage supply chain

Santosh Mahapatra*, Dennis Z. Yu and Farzad Mahmoodi

School of Business, Clarkson University, 311, Bertrand H. Snell Hall, Potsdam, NY 13699, USA

(Received 4 January 2011; final version received 23 October 2011)

We investigate the performance of two common operating policies (i.e., pull and push-pull) for a make- to-stock product in an un-capacitated, three-stage supply chain. The pull policy operates based on periodic orders received from the immediate downstream facility. However, in the push-pull policy, while processes upstream of the order decoupling point are managed by the push policy, the downstream processes are managed by the pull policy. Simulation experiments are conducted to examine the impact of each operating policy under a variety of experimental conditions, characterised by demand uncertainty and lead-time variability. Our results indicate that the relative advantage of the two policies is dependent on the type of uncertainty, the level of uncertainty, the inventory control policy and the performance measures of interest. More specifically, while the push-pull policy results in lower inventory, the pull policy yields a better fill rate. This is in contrast to the notion that the pull policy generally results in superior inventory performance. Our findings suggest that firms should carefully consider the level of uncertainty, the inventory control policy and the performance measures of interest when determining the operating policy.

Keywords: pull policy; push-pull policy; demand uncertainty; lead-time variability; operational performance; simulation research

1. Introduction

It is challenging to manage a multi-stage supply chain in an environment characterised by uncertain customer demand and variable manufacturing and distribution lead-times. In such environments, the performance of a multi- stage supply chain is manifested in terms of excess inventory, poor customer service, or both. The push, pull and push-pull (referred to as ‘hybrid’ here thereof) operating policies are the three principal policies utilised to control production and distribution systems (Karmarkar 1990). Whilst in the push policy sourcing and production and distribution processes are purely based on anticipated demand, or forecast, in the pull policy such processes are triggered after the customer order is received (Spearman and Zazanis 1990). Alternatively, in the hybrid policy, processes upstream of the order decoupling point (i.e. point of differentiation) are managed by the push policy, while the processes downstream of the order decoupling point are managed by the pull policy (Pyke and Cohen 1990).

While several studies have examined the push, pull or hybrid policies in a single-stage supply chain, evaluation of the policies in a multi-stage supply chain is rather limited and the insights are either incomplete or case-specific (see Masuchun et al. 2004). This can be attributed to a higher level of operational challenges in multi-stage supply chains than in single-stage chains. As such a comparative assessment of the three policies is difficult because the workings of the three policies are distinctly different, and the criteria for evaluating the performance while accounting for the difference in their workings are not clearly outlined.

To address the knowledge gap, we investigate the performance of two of the three policies (i.e. pull and hybrid policies), while accounting for the basic tenets of the push and pull-based operations. Our study involves a storable product in a three-stage supply chain consisting of a manufacturing plant, a warehouse and retailer(s). We do not analyse the case when the push policy is implemented throughout the supply chain. Such practice is fairly unrealistic since in a typical multi-stage supply chain at least one of the upstream facilities initiates production based on orders from the downstream facilities. The operating policies are carried out independently at the three facilities meaning the information (e.g. forecasts or orders) that triggers actions is generated locally. The decentralised characterisation of the operations is consistent with the ‘push’ or ‘pull’ fundamentals (e.g. Pyke and Cohen 1990, Spearman and

*Corresponding author. Email: [email protected]

ISSN 0020–7543 print/ISSN 1366–588X online

� 2012 Taylor & Francis http://dx.doi.org/10.1080/00207543.2011.637091

http://www.tandfonline.com

Zazanis 1990) and reflects the typical scenario of limited access to information regarding other firms in a multi-stage supply chain.

It is often conjectured by both practitioners and researchers that performance of the pull policy is generally superior to the push policy (Spearman and Zazanis 1990). Although the hybrid policy combines the push and pull policies, the conjecture regarding superior performance of the pull policy does not hold as strongly when compared with the hybrid policy. Previous studies have shown that the performance of the pull and hybrid policies is affected by demand uncertainty, forecast error and buffer stock levels (e.g. Masuchun et al. 2004). However, these studies have not systematically examined how lead-time uncertainty and buffer stocks affect performance across the two policies. In the extant studies, the inventory policies, specifically the buffer stocks, have been chosen somewhat arbitrarily. Consequently, the relative efficacy of the two policies remains unclear.

We address these issues by examining the performance dynamics under varied levels of demand uncertainty and production/distribution lead-time variability when the buffer stocks are chosen for a specified service level. Specifically, our study intends to answer the following research questions:

(1) How do demand and lead-time uncertainties affect the performance of a three-stage supply chain? (2) How do the performances of the pull and hybrid policies differ in a three-stage supply chain?

We utilise simulation models in our analysis because the simultaneous impact of multiple types of uncertainties such as demand uncertainty, lead-time uncertainty and forecast error is very difficult to examine analytically in a multi-stage supply chain.

The remainder of the paper is organised as following. The relevant literature is reviewed in the next section. This is followed by a description of the supply chain structures considered, simulation models and assumptions, as well as the experimental design. Then, the simulation results for a single retailer supply chain are discussed. This is followed by a sensitivity analysis for a multiple retailer supply chain. Finally, the conclusions and managerial implications of the study are presented.

2. Literature review

Several studies have examined the effectiveness of the push, pull and hybrid policies under a variety of operating conditions; however, they differ significantly in the implementation of the three policies. Since the push and pull policies are fundamental to characterise the alternate policies, it is useful to understand their distinctions. Pyke and Cohen (1990) characterised the differences between the push and pull policies in terms of production and order quantity, timing of the production and shipment request, order prioritisation rules and degree of managerial interference. On the other hand, Bonney et al. (1999) characterised the push and pull policies in terms of the flow of control information. In a pull system the control information flow typically is in the opposite direction of the material flow. In contrast, the control information flow in a push system is in the same direction as the material flow. Furthermore, while in the pull system a downstream facility with primarily local information exercises a greater decision authority regarding the volume of supplies to receive from the upstream facility, in the push system the upstream facility with information that may be local or global has a greater decision authority regarding the volume of dispatch to the downstream facility (Pyke and Cohen 1990). Spearman and Zazanis (1990) noted that the operating principles of the push and pull policies are radically different. They observed that the push policy controls operations in terms of production or distribution plan and measures performance through work-in-progress (WIP) inventory. In contrast, the pull policy controls operations in terms of the level of WIP inventory and measures performance in terms of the unmet demand.

Extant researchers have utilised analytical and simulation based approaches to evaluate the performance of the three alternate operating policies. While the analytical studies (e.g. Spearman and Zazanis 1992, Pandey and Khokhajaikiat 1996, Vidyarthi et al. 2009) utilised inventory and queuing models to establish a functional relationship between the various control variables in relatively simple operating contexts, simulation studies (e.g. Bonney et al. 1999, Maschun 1999, Li 2003, Maschun et al. 2004) explored the interactions among a large number of variables in relatively more complex operating contexts. Most of the analytical studies have dealt with either deterministic scenarios (e.g. Wang and Sarker 2006) or stochastic analysis in relatively simple settings (e.g. Spearman and Zazanis 1992, Pandey and Khokhajaikiat 1996).

Vidyarthi et al. (2009) utilised queuing theory to develop analytical models to minimise response time while optimally allocating workloads and creating capacity in make-to-order and assemble-to-order supply chains.

4700 S. Mahapatra et al.

Their study did not analyse the performance of the push policy for firm orders. Consequently, it provided limited insights into the relative performance of the three policies. Wang and Sarker (2006) proposed non-linear mixed integer programming models for optimal Kanban-based control of a manufacturer, warehouse and retailer supply chain with deterministic demand and lead-time. The study illustrated the usefulness of Kanban-based pull policy but did not offer insights into its relative advantages over alternative operating policies.

Pandey and Khokhajaikiat (1996) examined the performance of the three alternate policies in a production system that was modelled as a discrete time Markov process. The system accounted for supply and production lead- time uncertainty, demand uncertainty and raw material constraints. They noted that no policy is distinctly superior at all levels of demand uncertainty. While the performance of the hybrid policy was generally superior, the push policy (i.e. MRP based lot sizing) outperformed the hybrid policy in the presence of raw material constraints. The performance of the pull policy (i.e. Kanban based) was superior only when the demand was very stable. Spearman and Zazanis (1992) compared the performance of the push and pull systems when processing time follows a Poisson distribution, while demand is exponentially distributed. They observed that the pull policy is easier to control and performs better than the push policy because in the pull policy the WIP inventory is bounded; however, the hybrid policy (i.e. pull policy only at the final stage) can outperform pure push and pull policies.

A few studies attempted to combine analytical approaches with simulation approaches (e.g. Gonçalves et al. 2005, Su et al. 2010). In general, these studies formulated models to describe the operations. The effectiveness of these models was subsequently assessed using simulation. For example, Gonçalves et al. (2005) formulated a model for analysing the effect of demand uncertainty in a hybrid system. Su et al. (2010) developed an M/M/1 base-stock model to evaluate the effectiveness of delayed differentiation when there are arrival and production variability in a single-stage push system. Both studies utilised simulation to obtain the performance results. It is apparent that it is difficult to develop analytical models to compare the performance of the three policies while capturing the underlying details. Consequently, past studies (e.g. Spearman and Zazanis 1992) have recommended simulation studies to determine the effectiveness of alternate policies. In a recent study, Almeder et al. (2009) observed that analytical and simulation based researches should serve as complements in studying supply chains.

In a typical supply chain, activities such as manufacturing, warehousing and distribution have dissimilar task complexities and lead-times, and are spatially and temporally dispersed. These elements in combination affect the supply chain performance; the combined impact of these factors in a multi-stage supply chain has not been examined adequately. In particular, most of the previous studies (e.g. Closs et al. 1998, Grosfeld-Nir et al. 2000, Kim et al. 2002, Li 2003, Masuchun et al. 2004, Teeravaraprug and Stapholdecha 2004) do not examine how the supply chain performance is affected by different levels of demand uncertainty and lead-time variability.

The implementation and performance of the push, pull and hybrid policies vary significantly from study to study. In general, the studies differ in terms of the assumptions regarding the inventory control policy, demand uncertainty, lead-time variability, location of the order decoupling point and knowledge of demand information which affect the performance. Furthermore, most of the studies do not explicitly account for forecast error, a key determinant of the efficacy of push-based operations. Forecast errors, usually include two components (i.e. variability and bias), which have a significant impact on the firm’s operational performance (Lee and Everett 1986, Ritzman and King 1993). Forecast error is influenced by the operational planning horizon, which is dependent upon the operational lead-times and the frequency of plan updates. The longer the planning horizon, the higher is the forecast error (Chen et al., 2000). Based on a study of population forecast errors, Smith and Sincich (1991) concluded that there exists a linear or nearly linear relationship between forecast inaccuracy and the length of the forecast horizon. Therefore, it is useful to include these considerations while accounting for the forecast errors.

As noted earlier, the existing studies are somewhat arbitrary in their choice of the inventory policy. For example, while some papers keep the same level of safety stocks for the various policies to maintain comparability (e.g. Pandey and Khokhajaikiat 1996, Closs et al. 1998), others adjust the safety stocks arbitrarily with the change in demand (e.g. Bonney et al. 1999, Masuchun et al. 2004). Most of the studies have reported the snapshot performance of the various operating policies (e.g. Closs et al. 1998), ignoring to reveal how the performance changes over time. Prior studies have used a variety of performance measures such as fill rate, throughput rate, system inventory, retailer inventory, production lead-time, inventory costs and the variability of fill rate. These measures can be broadly classified into three categories: order fulfilment rate, cycle time and inventory level. Reporting of results in multiple forms presents difficulty in comparing the performance.

To address some of the above shortcomings this study considers the impact of forecast error, demand uncertainty and lead-time variability on the inventory and fill rate performance of the pull and hybrid policies. We examine both longitudinal and snapshot results for the two performance metrics. The experimental environment

International Journal of Production Research 4701

including the supply chain structures, simulation models, assumptions as well as the experimental design are discussed next.

3. Experimental environment

Our study considers a single-product supply chain with geographically dispersed facilities. The supply chain consists of a manufacturing plant, a warehouse and a retailer (or three retailers in the multiple retailer system), and is affected by varied levels of demand uncertainty and lead-time variability. It is assumed that there is no capacity constraint at any of the facilities. Labeling, packaging and shipping operations are conducted in the warehouse. The warehouse acts as a stocking point and supplies the retailer(s) according to orders received from them. In the hybrid policy, the warehouse receives supplies from the plant according to demand forecasts at the plant; however, in the pull policy, the warehouse receives supplies according to the orders placed to the plant. Thus, the warehouse acts as the order decoupling point in the hybrid policy. By assigning the warehouse as the order decoupling point, we are able to implement the pull operating policy to all or a part of the supply chain. Two types of inventories (i.e. inputs and outputs) are held at the plant and the warehouse. However, only one type of inventory (finished goods) is held at the retailer. The supply chain structures considered in the study are depicted in Figure 1(a) and 1(b).

There are multiple lead-times in the supply chain: LT1 is associated with the outside supplier (i.e. it takes LT1 days for the plant to receive a raw material order from the supplier); LT2 is the production lead-time; LT3 is the transportation lead-time between the plant and the warehouse; LT4 is the warehouse assembling lead-time; and LT5 is the distribution lead-time between the warehouse and the retailer(s).

Implementation of the push and pull policies can be carried out in multiple ways (Pyke and Cohen 1990, Hopp and Spearman 2004). In our model, the operations in the pull policy at all upstream facilities are carried out based on the replenishment orders from the immediate downstream facility. The facilities review the inventory level (local stock plus pipeline inventory) at the beginning of each week and place an order to bring the inventory to the order- up-to-level which is determined by the average demand during the protection interval (the sum of the time period between two successive reviews and the supply lead-time), plus safety stocks to avoid shortage during the protection interval. However, in the hybrid policy, while the operations at the plant and dispatch to warehouse are governed by the forecast requirements as in the push policy, the operations and order fulfilments at the warehouse and the retailer(s) are governed by actual orders as in the pull policy. Thus, the plant develops the production plan based on the customer demand forecasts and safety stock requirements, without the knowledge of downstream inventory levels. In the hybrid policy, the safety stocks for the push based operations are maintained to avoid shortage during the supply lead-times.

Pure forecast-based fulfilment from the plant to the warehouse represents poor information flow between the warehouse and the plant (Pyke and Cohen 1990). Note that such unco-ordinated supply chains characterised by the lack of cross-company integration and poor information flow are observed in a variety of industries (Davis and Spekman 2004). Figures 2 and 3 illustrate the operational details of the pull and hybrid policies, respectively.

Plant

(b)

(a) Warehouse

Supplier

Purchasing Production Assembly Distribution

LT1 LT4

LT3 LT2 LT5

Customer

Retailer

Plant Warehouse

Supplier

Purchasing Production Assembly Distribution

LT4 LT3

LT2 LT1

LT5

Customer

Retailer 1

Retailer 2

Retailer 3

Figure 1. (a) Supply chain structure: single retailer system; (b) Supply chain structure: multiple retailer system.

4702 S. Mahapatra et al.

We assume that the supplier has enough capacity to fulfil all orders from the plant. Nevertheless, raw material safety

stocks are held at the plant to cover for the demand and supplier-to-plant transportation lead-time uncertainties. The supplies from the plant and warehouse are constrained by the available inventory. The unmet demands at the plant and the warehouse are backlogged and manufactured with a lag in the pull policy. However, in the

hybrid policy only the shortages of inputs that lead to production shortfalls at the plant are backlogged (refer to Figure 2). The input shortages at the warehouse and output shortages at the plant are not backlogged because the respective supplies occur based on push principles. Accordingly, replenishment order for the input at the plant is based on the forecast demand for week (t), the input safety stock and the input shortage. At the retailer, if

there is insufficient inventory to satisfy the customer demand, the unmet demand is lost without backordering in both policies.

The supply chain structure allows postponement strategy in packaging and shipping (i.e. operations that move labelling processes such as language required, product stickers and user manuals to the final phase of packaging).

Postponement processes produce generic products, which are later customised upon receipt of an order. For example, Hewlett-Packard has applied this strategy to packaging and labelling of printers before shipping to customers (www.kongandallan.com, 10 June 2007). Other examples of the postponement strategy in packaging and

shipping include fast moving consumer goods companies that sell a product under various brand names or in various packaging sizes.

The principles for the push and pull policies in our study are illustrated below in terms of production at the plant and dispatch quantities to the warehouse.

Customer’s/retailer’s/warehouse’s order arrives

Retailer/warehouse/plant checks if available inventory can

satisfy the order?

Satisfy customer’s /retailer’s / warehouse’s order and update retailer’s/warehouse’s /plant’s

inventory status

Backlog any shortage at warehouse /plant and

send available inventory to retailer/warehouse

Yes

Calculating order -up-to level at retailer/warehouse /plant according to anticipated customer demand

during the protection interval

Retailer /warehouse /plant checks if available inventory is less than the order-up-to level?

Retailer/warehouse /plant orders the difference between

inventory and order -up-to level

No action is needed No

Yes

Figure 2. Illustration of the pull policy.

International Journal of Production Research 4703

Push policy: Production at the plant and dispatch quantities to the warehouse:

Forecast requirement for week (t) from plant¼forecast demand for week (t)þsafety stock at the warehouse

where,

safty stock ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½vaciance of weekly demand in week ðtÞ �avg: manuf: and warehouse delivery

lead-time in weeks�þ ½squared avg: weekly demand in week ðtÞ �variance of manuf: and

warehouse delivery lead-time in week�

vuuuuut

and

z standardised normal distribution statistic for the specified service level

Production is carried out if and only if:

Output inventory at the plant in week (t)5 forecast requirement for week (t) Production at the plant for week (t)¼min [forecast requirement for week (t), potential output

by the available input inventory in week (t)] Shortages of inputs at plant in week (t)¼max [required inputs for producing the forecast requirement

for week (t) – available input inventory in week (t), 0] Dispatch to the warehouse for week (t)¼min [forecast requirement for week (t), output inventory

at the plant in week (t)]

Pull policy: order to the plant and dispatch to the warehouse

Warehouse’s (input) order-up-to-level while reviewing for week (t)

¼average demand during the protection intervalþsafety stock at the warehouse

where,

safety stock ¼

avg. manuf. and warehouse delivery

lead-time in weeksþ review period in weeks

� ��

þ½squared avg. weekly demand in week ðtÞ �variance of manuf. and warehouse delivery

lead-time in weeks]

vuuuuuut

Customer demand forecasts at plant for week t

Enough output inventory at plant?

Calculation of required output at plant

Calculation of required input at plant accounting

for shortage

Yes

Dispatch available output to warehouse and produce

required output at plant and update inventory status

Sourcing raw material if necessary

Dispatch required output to warehouse and update

inventory status

Customer’s/retailer’s order arrives

Retailer/warehouse checks if available inventory

can satisfy the order?

Satisfy customer’s/retailer’s order and update retailer’s/

warehouse’s inventory status

Backlog any shortage at warehouse and send available inventory to

retailer

Yes

Calculating order-up-to level at retailer/warehouse according to anticipated customer demand during the protection interval

Retailer/warehouse checks if available inventory is less than

the order-up-to level?

Retailer orders/warehouse assembles the difference between

inventory and order-up-to level

No action is needed No

Yes

Figure 3. Illustration of the hybrid policy.

4704 S. Mahapatra et al.

Replenishment order is placed to the plant if and only if:

(input) inventory at the warehouse in week (t) 5 order-up-to-level for week (t) Order quantity to the plant for week (t)¼max [order-up-to-level for week (t) – (input) inventory at

the warehouse in week (t)þshortages of inputs in week (t), 0] Where, shortages of inputs in week (t)¼min [0, (input) inventory at the warehouse

in week (t) – warehouse output’s order quantity for week (t)]

Input inventory at the warehouse includes the inventory in transit between the plant and the warehouse.

Dispatch to the warehouse for week (t)¼min [warehouse’s order to the plant for week (t),

available inventory at the plant in week (t)]

Next, we describe the functional forms for demand and forecast that are used to generate safety stocks, and

production and dispatch requirements. We adopt the following demand function from Zhao et al. (2002) to generate

the customer demand at the retailer. The weekly demand function is given by the following equation:

Demandt ¼ baseþ slope� tþ season� sin 2�

SeasonCycle � t

� � þnoise� snormal ðÞ ð1Þ

where, Demandt is defined as the demand in week t, snormal() represents the standard normal distributed random

number generator, and SeasonCycle represents the weekly demand effects (set to four in this study). The parameters

base, slope, season and noise characterise the level, growth, seasonality and variability of the demand process,

respectively. The noise is expressed as a percentage of the base demand. During the simulation, the average demand

for a specific week t is given by the first three terms of the demand function. The standard deviation of demand for

computing safety stocks is calculated by the product of the average demand and the coefficient of variation which is

generated according to the demand samples of Equation (1). We utilise the above demand function because it is

comprehensive and includes the key elements that typically characterise the demand in practice. In the push policy, the demand forecast for week t, Forecast , made in week t0 for (t�t0) is generated by the

following equation (Zhao et al. 2002):

Forecastt ¼ Demandt �f1þEBþED�½1þðt� t0Þ=4:85�� snormal ð Þg ð2Þ

Forecasti has two components: customer demand during week (t) and a forecast error coefficient which consists

of three components. The three components of forecast error term are: the bias (EB), the variability (ED) which is

normally distributed, and a parameter (i.e. 1/4.85) representing the rate of linear increase in ED with time to account

for higher forecast error for higher forecast horizon (e.g. t � t0). The forecast accuracy, forecast horizon, expected lead-times and targeted service level are maintained as control

variables. The forecast horizons for procurement and production at the plant are 7 and 6 weeks, respectively. Note

that the forecast horizon at the plant is longer than the average supplier procurement and production lead-time.

This is consistent with the practice at many firms that utilise a longer forecast horizon than the actual transportation

and manufacturing lead-time to account for developing the forecast, communicating with the supplier or internal

divisions, arranging for resources, etc. that are extraneous to the operations considered in our analysis. We examine the performance implications through a series of experiments. In our experiments, we consider three

levels of lead-time variability (i.e. LT standard deviation), as well as three levels of demand uncertainty (i.e. noise).

The lead-time variability is assumed to be normally distributed (Bowersox et al. 2002). We vary the manufacturing

lead-time variability at the plant, the transit lead-time variability between the plant and the warehouse and the

transit lead-time variability between the warehouse and the retailer. However, we do not vary the variability of

supplier lead-time because in a typical supply chain, contracts are often executed to ensure timely supplier delivery

and the manufacturer can hold the supplier responsible for poor delivery performance. We also do not vary the

variability of warehouse processing lead-time as the activities in a warehouse are comparatively simpler and unlikely

to vary significantly. In summary, we consider different levels of lead-time variability that are more relevant to the

manufacturer as well as those that involve comparatively complex processes and more likely to vary. Across all

experiments, the safety stocks are maintained for a specified customer service level in both policies and the forecast

error in the hybrid policy is considered fixed. Thus, the experimental variables used in the study are:

. Two operating policies: pull and hybrid

International Journal of Production Research 4705

. Production, transportation and distribution lead-time variability levels (LT Std dev): for LT2, LT3 and LT5, with an average of 3 days and standard deviation of 0.5, 1 and 1.5 days, respectively

. Three demand uncertainty levels (noise): (10%, 20%, 30%)�base.

Accordingly, a 2�3�3 full factorial experiment with 30 replications is conducted, resulting in 540 models. The

main assumptions considered in our models can be summarised as:

(1) The entities operate in a decentralised manner. Each facility takes decisions based on locally available

inventory and shortage information. (2) The operations at the plant, the warehouse and the retailer(s) are not affected by capacity constraints. (3) Lead-time uncertainty, demand uncertainty and forecast error are normally distributed. (4) Noise and lead-time parameters remain constant over time and are independent of each other.

The parameters used in the simulation models are summarised in Table 1. The numerical values for the

parameters are hypothetical. However, the values are comparable to those in fast moving consumer goods industry

and were set based on discussions with the executives who participated in the Global Supply Chain Management

Executive Seminar held at Clarkson University, USA, in August 2009. In a given context appropriate data may be

chosen to derive useful insights. ARENA V12.0 was utilised to develop the simulation models (Kelton and Sadowski 2004). This software is widely

used in simulation studies (e.g. Closs et al. 1998, Masuchun et al. 2004, Teeravaraprug and Stapholdecha 2004). The

models were started in an empty and idle state and the first 26 weeks of data were truncated to account for the warm-

up period. Note that input inventory accumulates at the warehouse due to the mismatch between the forecast based

supply from the plant and the downstream demand in the hybrid policy. Consequently, the steady-state condition will

not be reached for the input warehouse inventory in the corresponding simulation models. Therefore, we utilise a

terminating simulation in our analysis. In practice, firms utilising the push or hybrid policies engage in flushing

inventory in a variety of ways (e.g. halting production) from time to time (Spearman and Zazanis 1992, Hopp and

Spearman 2004). We do not allow flushing out accumulated inventory in our models to avoid the inclusion of

confounding variables while trying to compare the performance of the two policies. In our analysis, we use the overall system inventory, the inventory level at the retailer(s), and fill rates at

the retailer(s) as performance metrics. Fill rate and inventory levels are common performance indicators used in

the previous studies (e.g. Closs et al. 1998). Statistics were collected for 78 weeks after the warm-up

period. It was determined via pilot runs that 20 replications would achieve the sufficient precision needed to

estimate the mean differences in performance (Kelton et al. 2004). Yet, 30 replications were completed to

allow the assumption of the law of large number to apply so that normality conditions can be invoked in the data

analysis.

Table 1. Summary of simulation model parameters.

Features Parameters

Demand model Base¼100 units (300 for multiple retailer system) Slope¼5/52 Season¼1 SeasonCycle¼4 Noise¼10%, 20%, 30% (experimental variable) Snormal(): standard normal distribution

Forecasting model Mean of forecast errors: EB¼0 Initial variability: ED¼5% Increase rate: 1/4.85 Snormal(): standard normal distribution

Lead-time (days) LT1: mean¼5, standard deviation¼1 LT2: mean¼3, standard deviation¼0.5, 1, 1.5 (experimental variable) LT3: mean¼3, standard deviation¼0.5, 1, 1.5 (experimental variable) LT4: mean¼1, standard deviation¼0.5 LT5: mean¼3, standard deviation¼0.5, 1, 1.5 (experimental variable)

Service level Desired service level: 98%

4706 S. Mahapatra et al.

4. Discussion of simulation results

The performance of the two operating policies is measured on a weekly basis in terms of item fill rate at the retailer, inventory level at the retailer, the inventory upstream of the warehouse (i.e. the inventory at the plant, plus the input inventory at the warehouse), and the system inventory (i.e. the total inventory at the plant, the warehouse and the retailer). In a three-stage supply chain, inventory level and fill rate at any stage are influenced by both the inventory policy and the supply-demand dynamics. Prior studies have primarily reported snapshot results that do not reflect the performance dynamics adequately (e.g. Closs et al. 1998, Kim et al. 2002). We report both longitudinal and snapshot results to address the issue.

Longitudinal analysis involves weekly average performance across the 30 replications over time to capture the supply-demand dynamics. Snapshot analysis involves comparisons of performance of the 30 replications at three distinct times: week 52, week 78 and week 104. To make a statistical assessment of the extent of association between the experimental and performance variables we pooled the data across the two operating policies and conducted regression analysis while using the experimental variables, the demand, the time period as the independent variables, and each of the performance variables as the dependent variables. In the longitudinal analyses, time series data were adjusted for auto-correlation when auto-correlation was noted (i.e. Durbin-Watson statistic was outside the 1.5–2.5 range suggested by Hansen and Fisher (1980)).

In the regression analysis, the operating policies and snapshot time points are represented as dummy variables. Note that the base case represents the pull policy. In addition, in snapshot analysis, week 52 represents the base case. The results are presented in Tables 2–5 and Figures 4–14. In the figures we limit our presentations to the highest and lowest levels of demand uncertainty and lead-time variability. We compare and contrast our analysis of the performance impact of the pull and hybrid operating policies with those of the past studies. We first present the results for the single retailer supply chain, and subsequently discuss how the results differ for the multiple retailer case.

4.1 Average retailer inventory (longitudinal analysis)

It is apparent from the regression results (see Table 2) that the average retailer inventory level is marginally lower in the hybrid policy. The results further indicate that the inventory levels increase with demand uncertainty (Noise), the lead-time variability (LT standard deviation) and the demand; however, there is no significant increase in inventory over time (Week). Among the three significant influencing variables, demand is noted to be the most influencing variable. Interestingly, we find that the effects of lead-time variability and demand uncertainty are practically small. Given that the inventory increase reflects the combined effects of demand, degree of uncertainty (i.e. safety stock) and supply-demand mismatch, our results indicate that the change in the level of inventory over time is mostly driven by the change in the level of demand. These results are fairly similar to the finding of Closs et al. (1998) that the retailer inventory level is somewhat insensitive to demand uncertainty. Note that our experimental environment

Table 2. Regression results for the single retailer case. The regression coefficients refer to standardised coefficients. Longitudinal data analysis.

Average retailer inventory*

Average inventory upstream of

the warehouse* Average

system inventory* Average

retailer fill rate

Adjusted R 2

0.928 0.258 0.730 0.775 F statistic (df¼1367) 3530.920 96.120 741.820 787.673 Intercept (un-standardised) �12.212 �14.247 13.256 0.739 Hybrid �0.025 0.302 �0.141 0.042 Week 0.005

ns 0.102 0.035 �0.148

Noise 0.067 0.127 0.083 �0.552 LT standard deviation 0.064 0.239 0.028 �0.203 Demand 0.955 0.224 0.783 �0.017

Retailer inventory NA NA NA 1.315

Notes: *Adjusted for auto-correlation; ns, non-significant; significance level, p5 0.05.

International Journal of Production Research 4707

Table 4. Regression results for the multiple retailer case. The regression coefficients refer to standardised coefficients. Longitudinal data analysis.

Average retailer

inventory*

Average inventory

upstream of the warehouse*

Average system

inventory*

Average retailer fill rate

Adjusted R 2

0.516 0.935 0.904 0.770 F statistic (df¼1367) 292.118 3924.645 2582.171 761.650 Intercept (un-standardised) 3.857 �37.124 �6.482 0.725 Hybrid 0.021 �0.075 �0.107 0.037 Week 0.024 0.022 0.023 �0.157 Noise �0.099 0.064 0.052 �0.541 LT standard deviation 0.126 0.049 0.055 �0.196 Demand 0.645 0.912 0.880 �0.003

Retailer inventory NA NA NA 1.299

Notes: *Adjusted for auto-correlation; ns, non-significant; significance level, p 5 0.05.

Table 5. Regression results for the multiple retailer case. The regression coefficients refer to standardised coefficients. Snapshot data analysis.

Retailer inventory

Upstream inventory at the warehouse System inventory Service level

Adjusted R 2

0.583 0.391 0.488 0.114 F statistic (df¼1619) 315227.277 174.532 258.304 30.854 Intercept (un-standardised) 112.882 �24.794

ns 617.379 0.883

Hybrid �0.292 �0.053 �0.120 �0.152 Week_78 0.055 0.107 0.101 �0.029

Week_104 0.150 0.207 0.207 �0.023 ns

Noise 0.597 0.423 0.502 0.062 ns

LT standard deviation 0.349 0.423 0.437 0.128 Demand �0.028 �0.003

ns �0.01

ns �0.034

Retailer inventory NA NA NA 0.170

Notes: Significance level, p 5 0.05; ns, non-significant.

Table 3. Regression results for the single retailer case. The regression coefficients refer to standardised coefficients. Snapshot data analysis.

Retailer inventory

Upstream inventory at the warehouse System inventory Retailer fill rate

Adjusted R 2

0.583 0.391 0.484 0.094 F statistic (df¼1619) 378.129 174.378 254.564 25.112 Intercept (un-standardised) 110.652 �68.816 134.641 0.904 Hybrid �0.298 0.006

ns �0.067 �0.151

Week_78 0.035 0.116 0.107 �0.006 ns

Week_104 0.103 0.211 0.211 0.019 ns

Noise 0.593 0.440 0.516 0.062 ns

LT standard deviation 0.365 0.408 0.426 0.106 Demand �0.027

ns �0.003

ns �0.011

ns �0.029

Retailer inventory NA NA NA 0.149

Notes: Significance level, p5 0.05; ns, non-significant.

4708 S. Mahapatra et al.

is a bit different from that of Closs et al. (1998), as they do not consider lead-time variability in their analysis and do not systematically link their safety stock to demand uncertainty for a target service level.

As time progresses, although inventory accumulates, the increases are negligible across both policies, demonstrating relative robust performance over time (refer to Table 2 and Figure 4). It is observed in Figures 5 and 6 that the change in retailer inventory is much more variable in the hybrid policy than the pull policy. Figure 5 indicates that as the lead-time variability increases, the retailer inventory increases the most in the hybrid policy when the demand uncertainty is low. However, Figure 6 indicates that the accumulation of retailer decreases when the demand uncertainty increases.

This non-intuitive finding can be explained as follows. Both the hybrid and pull policies result in higher levels of retailer inventory when demand uncertainty and lead-time variability increase due to higher base stock. Base stock refers to the inventory that is carried to meet the likely demand during two successive reviews, which equals to the expected demand during the protection interval plus safety stocks over the protection interval (i.e. the sum of the time between two successive reviews and the supply lead-time). Higher base stock leads to higher fill rate (i.e. better matching of supply and demand) resulting in lower rate of accumulation of retailer inventory in both policies. In the

Weeks

120

C h a n g e in

in ve

n to

ry le

ve l

Change in retailer inv by increasing LT std. dev (noise = 30%, single)

15 30 45 60 75

Figure 6. Change in retailer inventory as a result of increasing lead-time variability (noise¼30%).

Weeks 15 30 45 60 75

300

600

900

1200

1500

1800

2100

2400 In

ve n to

ry le

ve l

Inventory upstream of warehouse (single)

Figure 7. Inventory upstream of the warehouse with low and high levels of uncertainties.

Weeks

150

200

250

300

350 In

ve n to

ry le

ve l

Retailer inventory (noise = 30%, single)

15 30 45 60 75

Figure 4. Retailer inventory (noise¼30%).

15 30 45 60 75 Weeks

120

C h a n g e in

in ve

n to

ry le

ve l

Change in retailer inv by increasing LT std. dev (noise = 10%, single)

Figure 5. Change in retailer inventory as a result of increasing lead-time variability (noise¼10%).

International Journal of Production Research 4709

hybrid policy, the scope for improvement (due to higher base stock) in supply-demand matching is relatively higher for higher demand uncertainty because the pull policy has a higher fill rate to start with (i.e. when demand uncertainty is lower). We discuss this issue further in Section 4.4.

The inventory impact of lead-time variability is marginally lower than that of the demand uncertainty for both the hybrid and pull policies (refer to Table 2). The small magnitudes of the regression coefficients corresponding to the two uncertainties suggest that on the average, the performance of the pull and hybrid policies is robust with respect to demand uncertainty and lead-time variability. This results in better matching of supply and demand, enabling them to avoid excessive accumulation of inventory over time.

4.2 Average inventory upstream of the decoupling point at the warehouse (longitudinal analysis)

The upstream of the order decoupling point at the warehouse in the hybrid policy operates as a push system whereas the downstream side of the warehouse operates as a pull system. We compare the performance due to this difference

Weeks

200

400

600

800

In ve

n to

ry le

ve l

Inventory at plant input (single)

15 30 45 60 75

Figure 8. Inventory at plant input with low and high levels of uncertainties.

Weeks 15 30 45 60 75

200

400

600

800

In ve

n to

ry le

ve l

Inventory at plant output (single)

Figure 9. Inventory at plant output with low and high levels of uncertainties.

Weeks

600

900

1200

1500

1800

2100

2400

2700

In ve

n to

ry le

ve l

System inventory (noise = 30%, single)

15 30 45 60 75

Figure 10. System inventory (noise¼30%).

Weeks

15 30 45 60 75 0

200

400

600

800 C

h a n g e in

in ve

n to

ry le

ve l

Change in system inv by increasing LT std. dev (noise = 10%, single)

Figure 11. Change in system inventory as a result of increasing lead-time variability (noise¼10%).

4710 S. Mahapatra et al.

in terms of the inventory upstream of the warehouse (i.e. inventory at the plant, plus the input inventory at the warehouse) for the hybrid and pull systems. The inventory level is influenced by the inventory control policy and the

supply-demand mismatch. The inventory control policy in the pull system is the base stock policy that carries higher safety stocks than that of the push policy. Safety stock in the pull policy is higher because it is carried for the protection interval whereas in the push policy it is carried only for the supply lead-time. However, Table 2 indicates that the inventory upstream of the warehouse is relatively higher for the hybrid policy than for the pull policy.

Figure 7 clarifies that inventory upstream of the warehouse in the hybrid policy remains stable at lower levels of lead-time variability and demand uncertainty but accumulates at a high rate when lead-time variability and demand uncertainty increase. The higher accumulation of inventory upstream of the warehouse with higher lead-time variability and demand uncertainty can be attributed to higher potential for supply-demand mismatch due to push-

based dispatch from the plant to the warehouse. This is further confirmed by comparing Figure 7 with Figures 8 and 9 that describe the relatively stable input and output inventories at the plant.

15 30 45 60 75 Weeks

0.05

0.1

C h

a n g

e in

f ill

r a te

Change in fill rate by increasing LT std. dev (noise = 30%, single)

Figure 14. Change in retailer fill rate as a result of increasing lead-time variability (noise¼30%).

Weeks

200

400

600

800

1000

1200

1400

C h a n g e in

in ve

n to

ry le

ve l

Change in system inv by increasing LT std. dev (noise = 30%, single)

15 30 45 60 75

Figure 12. Change in system inventory as a result of increasing lead-time (noise¼30%).

15 30 45 60 75 Weeks

0.1

0.2

0.3

0.4

C h a n g

e in

f ill

r a te

Change in fill rate by increasing LT std. dev (noise = 10%, single)

Figure 13. Change in retailer fill rate as a result of increasing lead-time variability (noise¼10%).

International Journal of Production Research 4711

Note that compared with the retailer inventory, the inventory upstream of the warehouse increases at a relatively

higher rate with lead-time variability and demand uncertainty, but associates less strongly with demand (refer to

Table 2). This further illustrates the potential for greater supply-demand mismatch upstream of the retailer with

increase in demand uncertainty and lead-time variability.

4.3 Average system inventory (longitudinal analysis)

Table 2 indicates that on average, the hybrid policy results in relatively lower system inventory than the pull policy.

As noted, in the hybrid policy, the upstream side of the warehouse operates as a push system whereas the

downstream side of the warehouse operates as a pull system. The regression analysis indicates that, in general,

the hybrid system results in relatively higher inventory upstream of the warehouse. Thus, lower system inventory in

the hybrid system can be attributed to relatively lower downstream inventory. In the downstream side, inventory

level is influenced by the base stock levels and supply-demand mismatch. Since base stock levels are equal for both

systems, downstream of the warehouse, lower inventory in the hybrid system can be attributed to greater utilisation

of the safety stocks. For similar levels of demand, greater safety stock utilisation can be attributed to unavailability

of supplies from upstream stages. Thus, lower system inventory in the hybrid system can be attributed to

unavailability of supplies from the upstream side of the warehouse. This finding is somewhat comparable to that of

Kim et al. (2002) which indicated that the system inventory in the push policy can be lower than that of the pull

policy when demand is relatively stable. Compared with the retailer inventory, the system inventory increases at a relatively lower rate with respect to

lead-time variability and demand but at a higher rate with respect to demand uncertainty and time (refer to Table 2).

Our results with regards to the relationship between lead-time variability and system inventory are consistent with

the finding of Kim et al. (2002) and Maschun et al. (2004). In addition, our results regarding the relationship

between demand uncertainty and system inventory are consistent with the finding of Closs et al. (1998) who pointed

out that the system inventory increases at higher level of demand uncertainty. The increases in system inventory due

to demand uncertainty and the leadtime variability are nevertheless modest indicating that similar to the retailer

inventory, on average, the system inventory metric is reasonably robust with respect to these factors. However, the

extent of robustness is somewhat moderated because of increased supply-demand mismatch upstream to the

warehouse. It is apparent from Figure 10 that the system inventory levels in the pull policy though robust are higher than

that of the hybrid policy in the earlier periods due to higher base stock levels at the plant. Over time, the system

inventory in the hybrid policy increases and in fact crosses over the inventory levels in the pull policy when lead-time

variability is high. The crossover occurs at a somewhat later time than that of the retailer inventory (refer to

Figures 4 and 10). This is because the system inventory in the pull policy is proportionately higher than that of the

hybrid policy due to the higher base stock levels (refer to Table 2). This effect can also be observed when the

pattern of system inventory accumulation is compared with that of the retailer inventory accumulation (refer to

Figures 6 and 12). Figures 11 and 12 indicate that as demand uncertainty increases, the rate of accumulation of

system inventory in the hybrid policy increases. While this pattern is similar to that for the inventory upstream of warehouse (refer to Figure 7), it is opposite to

that of the retailer’s inventory (refer to Figures 5 and 6). Since the retailer is supplied based on specific orders in both

policies, greater increase in system inventory indicates that with the increase in demand uncertainty and lead-time

variability the net impact of supply-demand mismatch upstream of the warehouse is stronger than the impact of

higher base stock levels and supply-demand mismatch at the retailer in the hybrid policy. Overall, we observe that for a target service level, the system inventory in the pull policy is more stable between

the two policies in the presence of demand uncertainty and lead-time variability (refer to Figures 11 and 12).

This stability is due to greater amount of base stock inventory which ultimately contributes to lower accumulation

of system inventory. Closs et al. (1998) found that the system inventory in the responsive (pull) policy is lower

than that of the anticipatory (push) policy. As mentioned earlier, their analysis did not consider lead-time

uncertainty, the pull operation was triggered by customer orders at any instant and both policies maintained

the same level of safety stocks. Our findings provide an alternative explanation for lower accumulation of inventory

in the pull system.

4712 S. Mahapatra et al.

4.4 Average retailer fill rate (longitudinal analysis)

We analyse the order fulfilment performance in terms of item fill rate at the retailer in the two operating policies. Figures 13 and 14 illustrate the change in the fill rate performance in the two operating policies at varied levels of demand uncertainty as lead-time variability increases.

It is evident that the fill rates improve in the hybrid policy as the lead-time variability increases (refer to Figure 13). The improvement is somewhat subdued with higher demand uncertainty (refer to Figure 14) reflecting that the fill rate is generally higher at higher level of demand uncertainty. It is counterintuitive that the fill rate improves with the increased demand uncertainty and lead-time variability. Kim et al. (2002) and Closs et al. (1998) observed that the fill rates in the anticipatory (push) policy decrease with the increase in emergency orders and demand uncertainty, respectively. For a specified level of demand uncertainty, these studies assume the same level of inventory buffers for both operating policies so our results are not exactly comparable. Our counterintuitive result however, may be explained as more than proportionate (i.e. as defined by the service level) increase in item fill rates due to higher safety stocks that are maintained to account for increased level of uncertainty for a specific target service level (Bowersox et al. 2002). The regression results in Table 2 clarify that the fill rates in fact increase with higher level of inventory rather than with higher demand uncertainty and lead-time variability.

It is apparent from Figures 13 and 14 that the improvement in fill rate is not so noticeable in the pull policy because the fill rate is almost perfect to start with. Closs et al. (1998) and Kim et al. (2002) also showed that fill rates in the responsive (pull) policy outperform those of the anticipatory (push) policy. These findings are fairly contradictory to those of Bonney et al. (1999) and Masuchun et al. (2004) which reported higher fill rates in the push policy than the pull policy when demand uncertainty and forecast errors were higher. Both of these studies, however, maintained the same buffer inventory levels in the two policies.

4.5 Snapshot analysis

The snapshot analysis reflects the performance at specific points in time across 30 replications (i.e. weeks 52, 78 and 104) for varied levels of demand uncertainty and lead-time variability. The influences of time, levels of lead-time variability, demand uncertainty and actual demand are similar for all three types of inventory (refer to Table 3).

The influences are statistically significant for all independent variables except for demand. Comparing the regression coefficients in Tables 2 and 3 indicates that the influences of the two types of uncertainties on the performance are relatively stronger for the individual replications than for the averages. The inventory levels except for upstream inventory decline for the hybrid policy. All three types of inventory increase over time. The relative effects of lead-time variability become stronger from retailer inventory to system inventory. In contrast, the effects of demand uncertainty first decrease from the level of retailer inventory for the inventory upstream of warehouse and then increase for the system inventory. Thus, the effect of demand uncertainty is most significant for retailer inventory where as the effects of lead-time variability is most significant for the system inventory. Surprisingly, the effect of demand per se is not statistically significant. Overall, the regression coefficients indicate that at any time instant, changes in inventory are mainly driven by the demand uncertainty and lead-time variability.

In contrast to longitudinal analysis results, the fill rate declines for the hybrid policy and increases with lead-time variability. However, consistent with the longitudinal analysis, the fill rate increases with the level of retailer inventory. The effects of time, actual demand and the level of demand uncertainty are not significant. The non- significance of three of the regression coefficients indicate that the variability in the fill rate cannot be explained effectively by the independent variables because in general the fill rate is very close to 100% (due to the more than proportionate increase in fill rate with increase in safety stock). This is reflected in the low adjusted R

2 statistic in the

regression results. The combined assessment of inventory and fill rate reveals that for the chosen parameter values the performance is more affected by demand and demand uncertainty than by lead-time variability.

4.6 Sensitivity analysis: single versus multiple retailer case

We examine the performances of the two policies in a multiple retailer system to determine if they are different from that of the single retailer system. The structure of the multiple retailer supply chain is depicted in Figure 1B. The regression results for longitudinal and snapshot analyses are presented in Tables 4 and 5, respectively. Since many of the performance trends are similar to a single retailer system, we focus our discussion on the differences in the

International Journal of Production Research 4713

performance patterns. In addition, for retailers, we focus on one retailer’s inventory and fill rate performance as all the retailers are identical.

Comparing the standardised regression coefficients in Tables 2 and 4 indicates that the regression coefficients for multiple retailer system are characteristically different from those of the single retailer system. In the multiple retailer system, the retailer inventory is higher in the hybrid policy compared with the pull policy. The inventory level decreases with demand uncertainty but increases with time, lead-time variability and demand. However, compared with a single retailer system, the rate of increase is smaller for demand. Since the demands and lead-times are unaffected by the number of retailers, for a target service level, a lower rate of increase with demand and the decrease with demand uncertainty can be attributed to lower supplies from the warehouse. Note that the base stock inventory at the warehouse is maintained for the anticipated aggregated demand during the protection interval. Lower supplies at the warehouse can therefore be attributed to the risk pooling effect, which results in lower amount of inventory for a specified service level.

Comparison of the regression coefficients for the average inventory upstream of warehouse for the multiple and single retailer systems indicates that in the multiple retailer system, the inventory level decreases in the hybrid policy and increases at a lower rate with time, demand uncertainty and lead-time variability. The effect of demand, however, becomes stronger. This reflects relatively lower impact of demand and lead-time uncertainties and greater alignment with average demand in the multiple retailer system, which can be attributed to the risk pooling effect.

The nature of association between the independent variables and average system inventory level is similar to that of the single retailer system. However, the magnitudes of the regression coefficients are smaller for all independent variables except demand indicating greater responsiveness to demand in both the pull and hybrid operating policies. The performance difference between the hybrid policy and the pull policy is also reduced in the multiple retailer system. It is apparent from Table 4 that the effects of various independent variables on the fill rate across the multiple and single retailer systems are very similar. In summary, compared with the single retailer system, the retailer inventory is less responsive to demand as compared to the inventory upstream of warehouse and system inventory levels. The adjusted R

2 statistics improve for the inventory upstream of warehouse and system inventory,

deteriorate for retailer inventory and remain practically unaffected for retailer fill rate. The snapshot analysis results closely resemble those of the single retailer system.

5. Conclusions and managerial implications

We limited our analysis to the pull and hybrid policies, since in typical three-stage supply chains pure push policy throughout the supply chain is rarely practised. This study is distinct from the past studies on the performance impact of the pull and hybrid operating policies in several ways. First, this study examines the performance of the pull and hybrid operating policies in a three-stage supply chain where the impact of demand uncertainty and lead-time variability over time are simultaneously evaluated. The previous studies do not specifically discuss how performance is affected by both the demand uncertainty and lead-time variability. Second, the existing studies (e.g. Closs et al. 1998) evaluate the fill rate assuming a pre-specified level of safety stocks that remains constant across the policies. We compare the performance of the policies when the safety stocks are determined based on a target service level. Also, existing studies do not explore how the inventory and fill rate performances change over time. This study clarifies these issues and enhances the understanding of the performance over time.

In general, our results indicate that the hybrid policy performs better than the pull policy. Our analysis, however, indicates that the fill rate performance of the pull policy can be better than the hybrid policy partly due to relatively higher base stock levels carried in the pull system. Consistent with Pandey and Khokhajaikiat (1996) we find that the best control policy changes with demand and lead-time variability. However, we note that the implementation of the hybrid policy of Pandey and Khokhajaikiat (1996) is somewhat different from ours. While the downstream pull operations in both implementations are similar (i.e. aim to match the target inventory, while meeting the demand), in their model the upstream push operations utilised downstream inventory information so as to produce enough units such that they arrived in downstream stages to meet the expected demand in subsequent periods. In our model, the upstream push operations do not utilise the downstream inventory information. Utilisation of downstream information in push operations reduces the push characteristics thereby enhancing the potential for better performance (Spearman and Zazanis 1992). Consequently, although their result on the superior performance of the

4714 S. Mahapatra et al.

hybrid policy is somewhat similar to ours, our finding regarding the superior performance of the hybrid policy is relatively more distinct. Geraghty and Heavey (2004) compared the hybrid system described in Pandey and Khokhajaikiat (1996) with a CONWIP/pull system and noted that the performance of the two policies are equivalent when the target inventory and safety stocks are chosen optimally. They utilised a combination of simulated annealing and simulation based analysis to determine the optimal safety stock levels.

Spearman and Zazanis (1992) and Hopp and Spearman (2004) suggested that WIP inventory in the push system can be higher than that of the pull system due to inadequate feedback in the system. Hopp and Spearman (2004) in fact hinted that one may put a limit on this inventory (e.g. an amount equivalent to several years of demand). Consistent with their findings, our analysis shows that in the hybrid policy the accumulation of inventory (e.g. refer to Figure 7) upstream of the warehouse can lead to build-up of inventory resulting in higher system inventory than that of the pull system. Also, consistent with their observations we find that:

(1) The performance of the pull policy is more robust with respect to system inventory in an un-capacitated system, because the pull system limits the amount of inventory (e.g. the level of base stock, CONWIP, etc.), whereas inventory can grow without bound in the push policy.

(2) The WIP inventory in the pull system could err on the higher side resulting in more inventory than necessary when WIP inventory is set conservatively (e.g. higher base stock levels).

Our findings on inventory performance are somewhat counterintuitive and may be explained in terms of the following two effects:

(1) Relatively greater base inventory in the pull policy due to the periodic review inventory control policy that requires higher safety stocks for a specified review period.

(2) Relatively greater accumulation of inventory due to the frequent mismatch between supply and demand in the push policy (i.e. manifested in the hybrid policy) over time.

As mentioned before, in the hybrid policy, the upstream facilities release materials to the downstream facilities based on forecasts instead of actual orders. Thus, the deteriorating inventory performance at the upstream side of the warehouse in the hybrid policy could be improved by periodical flushing or halting of production upstream. However, since the theoretical and the working principles of engaging in these practices are unknown, such analysis is beyond the scope of this study.

Integrating these findings with those of Geraghty and Heavey (2004) we note that the relative superiority of the two operating policies is difficult to predict and is driven both by the nature of uncertainties and the inventory policies. One may expect that the pull policy with a strict limit on WIP inventory will have superior inventory performance compared with the hybrid policy that operates as a push policy upstream of the order decoupling point. Our study reveals that such possibility is less likely; therefore the conventional inventory policies such as base stock policies may not always yield the optimal performance in the pull policy. Thus, the managerial implications are that the relative advantage of the pull or hybrid policies is dependent on the level of uncertainty, the type of uncertainty, the inventory control policy and the performance measures of interest. Regarding the inventory performance, we note that the warehouse is more negatively affected by demand and lead-time uncertainties than the retailers in the hybrid policy. Moreover, the impact of lead-time uncertainties is relatively stronger on the performance of the upstream inventory. At lower levels of demand and lead-time uncertainties, the inventory performance is relatively worse in the pull policy. Interestingly, across both policies, the retailer inventory performance is more sensitive to the level of demand than the two types of uncertainties. Furthermore, the performance difference between the two policies is moderated in multiple retailer system due to the beneficial effects of risk pooling. These inferences are in contrast to the plausible notion that the pull policy being generally superior to the push policy would also perform better than the push-pull (i.e. hybrid) policy because of the poor performance impact of push control in the upstream of the order decoupling point. Consequently, firms should carefully consider these issues when determining the operating policy.

This investigation helps us identify several directions for future research. First, examining the performance of different operating policies under capacity constraint for varied levels of forecast error would be a useful contribution. Demand uncertainty and lead-time variability in a capacitated environment at varied levels of forecast errors would present different trade-offs in the performance of the operating policies which are difficult to discern and hence justify further research. Second, the hybrid policy can be implemented differently with regards to production and order quantities, timing of production and shipments, order prioritisation and the degree of managerial interference (Pyke and Cohen 1990). Exploring the relative effectiveness of alternate approaches to

International Journal of Production Research 4715

implement the hybrid policy for products with different potentials for postponement (i.e. performing different levels

of processing at the warehouse) can provide useful insights to manage make-to-stock supply chains in uncertain

environments.

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