# Determining Periodic-Review Inventory Control Policy Values

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## CHAPTER II BACKGROUND ON INVENTORY CONTROL

In order to set the framework and establish the terminology used in this research, this section describes the history of inventory control, the periodic-review inventory control technique, and the just-in-time technique. This section also explains how kanbans support the JIT technique.

HISTORY OF INVENTORY CONTROL

The advent of Scientific Management by Frederick W. Taylor led to the formation of the Operations Management (OM) discipline. His work formulas were the precursors to a variety of mathematical models that assist management at all levels of plant design and control. From the operations management field, a number of sub-disciplines were created for different OM problem areas. “Of the operations management subdisciplines that spawned mathematical models, none was more central to factory management nor more typical of the American approach to OM than that of inventory control,” (Hopp and Spearman, 1996).
One of the earliest and simplest forms of inventory control was the economic order quantity (EOQ) model, in which a mathematical equation was used to determine the most economic number of parts to order each time the inventory levels at the plant reached zero (Hopp and Spearman, 1996).     The equation for the EOQ model is Q* =  2 AD , where Q* is the optimal ordering quantity, A is the ordering or set-up cost, D is the demand per unit time, and h is the annual inventory holding cost per unit (Sipper and Bulfin, 1997). The reorder point, T, is defined as QD* .The limitation to the EOQ model is that it assumes a known and constant demand level and that stockouts do not occur (Nahmias, 1997).
Other early models, which are more sophisticated but mostly based on the EOQ formulation, are the economic production lot model, and the probabilistic reorder point approaches (which include the Newsvendor model, the base stock model, and the (Q, r) model) (Hopp and Spearman, 1996). For example, the (Q, r) model is a variation of the EOQ model that allows for a probabilistic demand and the possibility of stockouts. In this model, Q is the order quantity, and r is the reorder point. The heuristic used to calculate the values in the (Q, r) model, as shown in Hopp and Spearman (1996), are as follows
Another variation to the EOQ formulation is the periodic-review, or (s, S) inventory model. Often, the periodic-review model is a more realistic and maintainable policy for a manufacturing firm (Nahmias, 1997).
In contrast to the simple EOQ model is the more sophisticated MRP system. In the 1960’s, employees at IBM developed the MRP system, as computers were becoming more frequently used in accounting, as well as for other repetitive functions (Hopp and Spearman, 1996). The basic function of the MRP system is to plan the materials that are required to meet the customer’s demand. In order to meet this demand, MRP utilizes a formal plan that dictates what will be produced and when, based on the Master Production Schedule (MPS), and the Bill of Materials (BOM), to create a schedule.
Around the same time that the MRP revolution began in the United States, a completely different form of inventory control was being developed on the other side of the globe (Hopp and Spearman, 1996). This Japanese paradigm, called just-in-time, focuses on reducing waste, with one of the wastes being inventory (Hopp and Spearman, 1996). The inventory control function in JIT is accomplished through the use of kanbans.
The three inventory policies of importance for this research are a periodic-review, (s, S) model, and two versions of JIT policies using kanbans. These policies will be described in more detail in the following three sections.

### PERIODIC-REVIEW INVENTORY CONTROL POLICY

A periodic-review inventory policy is a policy where the inventory is reviewed periodically to see if more inventory is needed. This policy is in contrast to a continuous review policy, where the inventory is monitored continuously, and replenishment inventory is ordered exactly when the inventory level reaches the reorder point. Sipper and Bulfin (1997) describe two different models for periodic-review inventory control policies, the (S, T) model and the (s, S) model, both of which are extensions of the EOQ and (Q, R) models.
The (S, T) model is similar to the EOQ model, except that the (S, T) model is based on the value of the reorder period. In this model, S is the inventory target level and T is the review period, and the difference between S and the current inventory will be ordered every review period. The equation for S is S = D(T + τ ) + s , where D is the average demand, T is the reorder period, τ is the leadtime, and s is the amount of safety stock. The reorder period can be convenience based (once per week, month, etc.) or based on the EOQ model (Sipper and Bulfin, 1997). If the optimal value for the reorder period (T*) is used, the only difference between the EOQ model and the (S, T) model is that the (S, T) model includes safety stock.
The (s, S) model, also called the optional replenishment system, is based on two inventory levels, defined as (s, S) (Nahmias, 1997; Sipper and Bulfin, 1997). If the inventory at any review point is less than s, then the decision is to order the difference between S and the current inventory level. However, if the inventory at the review point is greater than s, then no inventory is ordered at that time. The advantage of the (s, S) model over the (S, T) model is that inventory is only ordered if the inventory level is at or below a certain point. Therefore, inventory is only ordered if it has dropped below the reorder point, reducing the average inventory level. According to Sipper and Bulfin (1997), this model is particularly useful when both review and ordering costs are significant.

JUSTIN-TIME

The focus of JIT is to provide each process with the exact number of the exact part, at the exact point in time it is needed (Shingo, 1989; Karlsson and Åhlström, 1996; Kasul and Motwani, 1997). The ultimate goal of JIT is to have one part arrive at a process precisely when the operator has completed the previous part, with reference to the individual products on the line (Karlsson and Åhlström, 1996). For example, if a minivan were following a sports car in the manufacturing cell, the seat that is placed in the minivan follows the seat that is placed in the sports car, and arrives at the workstation the same time as the minivan. To accomplish JIT flow, Lean Production Systems often use kanbans.

#### HOW JUST–IN-TIME PRODUCTION IS SUPPORTED BY A KANBAN SYSTEM

The kanban, which is Japanese for card, controls the production quantities in every process from the supplier to the customer. According to Monden (1998), in a kanban system, the type and quantity of units needed are displayed on a card which is sent between processes. This card indicates which parts an upstream process needs to produce for one of its downstream processes. The functions of a kanban, as described by Ohno (1988), are as follows:

1. Provides pick-up or transport information;
2. Provides production information;
3. Prevents overproduction and excessive transport;
4. Serves as a work order attached to goods;
5. Prevents defective products by identifying the process making the defects; and
6. Reveals existing problems and maintains inventory control.

Although many types of kanban systems exist, the most common type is the two-card system. As the name implies, the systems contains two types of cards, the withdrawal kanban, and the production-ordering kanban (Monden, 1998). The withdrawal kanban tells a worker how many parts they should take from the upstream process; while the production-ordering kanban tells the upstream process how many parts they need to produce. An example of this system, shown in Figure 2-1, is explained below.

Abstract.
Acknowledgements
Chapter I Introduction
1.1. TPM, Kaizen, 5S, and Supplier Reliability
1.2. Stable Manufacturing Processes, Standard Work, and JIT Production
1.3. Jidoka and Heijunka
1.4. Focus of this Research
Chapter II Background on Inventory Control
2.1. History of Inventory Control
2.2. Periodic-Review Inventory Control Policy
2.3. Just-in-Time
2.4. How Just-in-Time Production is Supported by a Kanban System.
Chapter III Literature Review.
3.1. General Ordering Policy
3.2. Supplier Performance
3.3. Variable Demand
3.4. Summary of Literature Review
Chapter IV Research Description
4.1. Research Method
4.2. Analysis of Factors
Chapter V Description of Ordering Policies
5.1. Determining Periodic-Review Inventory Control Policy Values
5.2. Various Models for Determining the Number of Kanban Cards in a System.
5.3. Kanban Models Chosen for this Analysis
Chapter VI Case Application Company and the Manufacturing Cell
6.1. Products Created in the Manufacturing Cell
6.2. Description of the Processes
6.3. Supplier Information
Chapter VII Description of Simulation Model
7.1. Simulation Logic Description
7.2. Verification and Validation of the Simulation Model
7.3. Simulation Specific
Chapter VIII Case Application Results and Analysis
8.1. Flowtime.
8.2. On-Time Delivery
8.3. Number of Motors Shipped
8.4. Work-In-Process Inventory
8.5. Stockout Factor
8.6. Supplied Part Inventory Factor
8.7. Results Summary.
Chapter IX Summary and Conclusions
References
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ANALYSIS OF THE EFFECT OF ORDERING POLICIES FOR A MANUFACTURING CELL TRANSITIONING TO LEAN PRODUCTION