A Simulation Environment for Supply Chains


Introduction

Defining a supply chain

A supply chain is a goal-oriented network of processes and stockpoints used to deliver goods and services to customers. Processes represent the individual activities involved in producing and distributing goods and services. Stockpoints represent locations in the supply chain where inventories are held. Processes and stockpoints are connected by a network, which describes the various paths by which goods and services can flow through a supply chain. Finally, note that our definition of a supply chain specifies that it is goal oriented.

Strategy

From an operations perspective, a business unit is evaluated in terms of:

  1. Cost
  2. Quality
  3. Speed
  4. Service
  5. Flexibility

Quality vs. Cost:

Speed vs. Cost:

Service vs. Cost:

Flexibility vs. Cost:

Having observed that different business conditions call for different operational capabilities, we can look upon supply chain design as consisting of two parts:

  1. Ensuring operational fit with strategic objectives.
  2. Achieving maximal efficiency within the constraints established by strategy.

Copying best practices, generally called benchmarking, can only partially ensure that an operations system fits its strategic goals (i.e., because the benchmarked system can only approximate the system under consideration). And benchmarking cannot provide a way to move efficiency beyond historical levels, since it is by nature imitative. Thus, effective operations and supply chain management requires something beyond benchmarking.

Setting goals

By describing how a system works, a supply chain science offers the potential to:

  • Identify the areas of greatest leverage;
  • Determine which policies are likely to be effective in a given system;
  • Enable practices and insights developed for one type of environment to be generalized to another environment;
  • Make quantitative tradeoffs between the costs and benefits of a particular action;
  • Synthesize the various perspectives of a manufacturing or service system, including those of logistics, product design, human resources, accounting, and management strategy.

Structuring the study

With this as our objective, the remainder of this book is organized into three parts:

  • Station Science: considers the operational behavior of an individual process and the stockpoint from which it receives material. Our emphasis is on the factors that serve to delay the flow of entities (i.e., goods, services, information or money) and hence causes a buildup of inventory in the inbound stockpoint.
  • Line Science: considers the operational behavior of process flows consisting of logically connected processes separated by stockpoints. We focus in particular on the issues that arise due to the coupling effects between processes in a flow.
  • Supply Chain Science: considers operational issues that cut across supply chains consisting of multiple products, lines and levels. A topic of particular interest that arises in this context is the coordination of supply chains that are controlled by multiple parties.

Capacity

The fundamental activity of any operations system centers around the flow of entities through processes. The flows typically follow routings that define the sequences of pro- cesses visited by the entities. In almost all operations systems, the following performance measures are key:

  • Throughput: the rate at which entities are processed by the system,
  • Work in Process (WIP): the number of entities in the system, which can be mea- sured in physical units (e.g., parts, people, jobs) or financial units (e.g., dollar value of entities in system),
  • Cycle Time: the time it takes an entity to traverse the system, including any rework, restarts due to yield loss, or other disruptions.

Typically, the objective is to have throughput high but WIP and cycle time low. The extent to which a given system achieves this is a function of the system?s overall efficiency. A useful measure of this efficiency is inventory turns, defined as

$$InventoryTurns=Troughput/WIP $$

where throughput is measured as the cost of goods sold in a year and WIP is the dollar value of the average amount of inventory held in the system. This measure of how efficiently an operation converts inventory into output is the operational analogy of the return-on-investment (ROI) measure of how efficiently an investment converts capital into revenue. As with ROI, higher turns are better.

![alt text](figure/f-1-1.png "Figure 1.1: A System with Yield Loss.")

Measuring capacity

A major determinant of throughput, WIP, and cycle time, as well as inventory turns, is the system?s capacity. Capacity is defined as the maximum average rate at which entities can flow through the system, and is therefore a function of the capacities of each process in the system. We can think of the capacity of an individual process as:

$$\text{process capacity} = \text{base capacity} − \text{detractors}$$

The process that constrains the capacity of the overall system is called the **bottleneck**. Often, this is the slowest process. We measure this through the utilization level, which is the fraction of time a station is not idle, and is computed as:

$$\text{utilization} = \text{rate into station} / \text{capacity of station}$$

      1. Limits on Capacity

Principle (Capacity): The output of a system cannot equal or exceed its capacity.

The short term fluctuations are due to variability, but the trend is unmistakably toward station overload.

Over the long run, WIP will go up. When release rate is the same as the production rate, the WIP level will stay high for a long time because there is no slack capacity to use to catch up. Theoretically, if we run for an infinite amount of time, WIP will go to infinity even though we are running exactly at capacity.

![alt text](figure/f-1-2.png "Figure 1.2: WIP versus Time in a System with Insufficient Capacity.")

![alt text](figure/f-1-3.png "Figure 1.3: Two Outcomes of WIP versus Time at with Releases at 100% Capacity.")

      1. Impact of Utilization

The behavior illustrated in the above examples underlies the second key principle of capacity:

Principle (Utilization): Cycle time increases in utilization and does so sharply as utilization approaches 100%.

As we have seen, when utilization is low, the system can easily keep up with the arrival of work (e.g., Figure 1.4) but when utilization becomes high the system will get behind any time there is any kind of temporary slowdown in production (e.g., Figure 1.3).

One might think that the “law of averages” might make things work out. But because the machine cannot “save up” production when it is ready but there is no WIP, the times the machine is starved do not make up for the times it is swamped.

![alt text](figure/f-1-4.png "Figure 1.4: Two Outcomes from Releasing at 82% of Capacity.")

The only way the machine can be always busy is to have a large enough pile of WIP in front of it so that it never starves. If we set the WIP level to anything less than infinity there is always a sequence of variations in process times, outages, setups, etc. that will exhaust the supply of WIP. Hence, achieving higher and higher utilization levels requires more and more WIP. Since entities must wait behind longer and longer queues, the cycle times also increase disproportionately with utilization. The result is depicted in Figure 1.5, which shows that as a station is pushed closer to capacity (i.e., 100 percent utilization), cycle times increase nonlinearly and explode to infinity before actually reaching full capacity.

![alt text](figure/f-1-5.png "Figure 1.5: Nonlinear Relationship of Cycle Time to Utilization.")

![alt text](figure/f-1-6.png "Figure 1.6: Mechanics Underlying Overtime Vicious Cycle.")

    1. Variability

$$\text{WIP} = \text{throughput} × \text{cycle time}$$

      1. Measuring Variability

Coefficient of variation (CV) which is defined as: $$\text{CV} = \text{standard deviation} / \text{mean}$$

Interestingly, if we have a large collection of independent customers arriving to a server (e.g., toll booths, calls to 9-1-1) the CV will always be close to one. Such arrival processes are called Poisson and fall right between the high variability (CV > 1) and low variability (CV < 1) cases.

![alt text](figure/f-2-1.png "Figure 2.1: High and low variability arrivals.")

      1. Influence of Variability

$$\text{Cycle Time} = \text{Delay} + \text{Process Time}$$

![alt text](figure/t-2-1.png "Table 2.1: Effective Process Times from Various Processes.")



    1. Literature Review
    2. Method
      1. Definitions
        1. Default production facility

1. INPUT: Inventory unitRaw material 2. PROCESS: Production unit 3. OUTPUT: Inventory unitFinished product  Input = 100 Process = Input x 0.7 (%30 is waste) Output = Process AB

    1. Analysis
    2. Conclusion