Business & Finance Productions and Operations Assignment

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Process Analysis and Resource Utilization

Part Two

Prof. Fiyinfoluwa Abioye

Bowie State University

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Content

• Little’s Law

• Managing Waiting Lines

• The Theory of Constraints

Little’s Law

Flow time (cycle time) is the average time it takes to complete one cycle of a process. It makes sense that the flow time will depend not only on the actual time to perform the tasks required but also on how many other entities are in the work-in- process stage. Little’s Law is a simple equation that explains the relationship among flow time (T), throughput (R), and work-in-process (WIP):

𝑊𝑜𝑟𝑘 − 𝑖𝑛 − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 = 𝑡ℎ𝑜𝑢𝑔ℎ𝑝𝑢𝑡 × 𝑓𝑙𝑜𝑤 𝑡𝑖𝑚𝑒 𝑜𝑟

𝑊𝐼𝑃 = 𝑅 × 𝑇

Little’s Law provides a simple way of evaluating average process performance. If we know any two of the three variables, we can compute the third using Little’s Law. Little’s Law can be applied to many different types of manufacturing and service operations.

Little’s Law explains the relationship among work- in-process, throughput, and flowtime on an aggregate basis using long-term averages. While this provides useful insight for designing and managing processes, it does not capture the randomness in arrival and service rates and dynamic behavior that often exists in manufacturing and service systems. Queueing models, however, address these issues.

Managing Waiting Lines

A queue is a waiting line. Queues are common in both manufacturing and service processes when uncertainty exists in demand and service rates. Understanding queues allows us to analyze current and alternative process designs to understand their behavior, predict process performance, and better allocate resources. Queueing models help managers understand key performance measures such as waiting times, queue lengths, and machine or server idle times so that they can manage resources more effectively and provide better customer satisfaction.

Queueing System Characteristics

A queueing system consists of customers that arrive for a service, one or more servers that provide the service, and a queue (waiting line) of entities that wait for service if the server is busy. Customers need not be people but can be machines awaiting repair or airplanes waiting to take off. Servers might be people and might also be airport runways, machine tools, ATMs, or computers.

Customers, servers, and queues in a queueing system can be arranged in various ways. Three common queueing configurations are:

• One or more parallel servers fed by a single queue. This is the typical configuration used by banks and airline ticket counters.

• Several parallel servers fed by their own queues. This system is used by most supermarkets and discount retailers

• A combination of several queues in series. This structure is common in manufacturing facilities

Fig 1. Parallel Servers with (a) A Single Queue and (b) Multiple Queues

Fig 2. Queues in Series in a Typical Voting Facility

Queueing theory is the analytical study of waiting lines. Typical performance measures that are computed using queueing theory include:

• The probability that the system is empty (the probability that there are no units in both the queue and service)

• The average number of units waiting for service in the queue.

• The average number of units in the system

• The average time a unit spends waiting for service (time in queue)

• The average time a unit spends in the system (waiting time plus service time)

• The probability that an arriving unit has to wait for service.

• The probability of n units in the system

These performance measures can help to improve process designs. Managers weigh the benefits of shorter waiting times against costs in process design decisions. Understanding and managing these trade offs are vital to providing superior customer service and achieving long-run profitability.

The Theory of Constraints

The Theory of Constraints (TOC) is a set of principles that focuses on increasing total process throughput by maximizing the utilization of all bottleneck work activities and workstations. In the TOC, a constraint is anything in an organization that limits it from moving toward or achieving its goal. Constraints determine the throughput of a facility because they limit production output to their own capacity.

A physical constraint is associated with the capacity of a resource. Physical constraints result in process bottlenecks. At a bottleneck, the input exceeds the capacity, restricting the total output that is capable of being produced. A non- bottleneck work activity is one in which idle capacity exists. A nonphysical constraint is environmental or organizational, such as low product demand or an inefficient management policy or procedure.

Because the number of constraints is typically small, the TOC focuses on identifying them, managing bottleneck and non-bottleneck work activities carefully, linking them to the markets and financial performance metrics to ensure an appropriate product mix, and scheduling the non- bottleneck resources to enhance throughput.

For most business organizations, the goal is to maximize throughput and thereby maximize revenue, cash flow, contribution to profit and overhead, or total gross profit for a single product or a product mix. Inherent in this definition is that excess inventory is wasteful and it makes little sense to make a good or service until it can be sold.

The TOC helps mangers understand the relationship between demand, capacity, and resource utilization. Using TOC logic, it is acceptable for the non-bottleneck workstations to be idle as long as everything possible is being done to maximize throughput and utilization at the bottleneck workstations.

Operations managers have traditionally thought that everyone had to be busy all the time. TOC argues that by maximizing resource utilization for all non-bottleneck workstations, the system creates excess inventory that may not be sold. In addition, maximizing non-bottleneck utilization increases operating expenses and purchasing costs.

Example:

Tucson Electric manufactures electric motor armatures using several production cells. Two of the production cells are shown in Fig. 3. Machinist A and polisher A work on larger armatures. Machinist B and polisher B work on smaller armatures. Fig. 4. documents the selling price and net contribution and overhead for the two finished armatures.

Fig 3. Tucson Electric Production Cell

Fig 4. Net Contribution to Profits and Overhead

• Where are the bottlenecks in this process?

• What workstation(s) would you expect to have the most idle time (lowest workstation utilization)?

• Compute the total revenue and contribution to profit and overhead per hour for each armature by applying TOC logic.

Slide 1: Process Analysis and Resource Utilization Part Two
Slide 2: Content
Slide 3: Little’s Law
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Slide 7: Managing Waiting Lines
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Slide 15: The Theory of Constraints
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