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Über dieses Buch

This third edition, which has been fully updated and now includes improved and extended explanations, is suitable as a core textbook as well as a source book for industry practitioners. It covers traditional approaches for forecasting, lot sizing, determination of safety stocks and reorder points, KANBAN policies and Material Requirements Planning. It also includes recent advances in inventory theory, for example, new techniques for multi-echelon inventory systems and Roundy's 98 percent approximation. The book also considers methods for coordinated replenishments of different items, and various practical issues in connection with industrial implementation.

Other topics covered in Inventory Control include: alternative forecasting techniques, material on different stochastic demand processes and how they can be fitted to empirical data, generalized treatment of single-echelon periodic review systems, capacity constrained lot sizing, short sections on lateral transshipments and on remanufacturing, coordination and contracts. As noted, the explanations have been improved throughout the book and the text also includes problems, with solutions in an appendix.



1. Introduction

For more or less all organizations in any sector of the economy, Supply Chain Management, i.e., the control of the material flow from suppliers of raw material to final customers is a crucial problem. Today the strategic importance of this area is fully recognized by top management. The total investment in inventories is enormous, and the control of capital tied up in raw material, work-in-progress, and finished goods offers a very important potential for improvement. Scientific methods for inventory control can give a significant competitive advantage. This book deals with a wide range of different inventory models that can be used when developing inventory control systems.
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2. Forecasting

There are two main reasons why an inventory control system needs to order items some time before customers demand them. First, there is nearly always a lead-time between the ordering time and the delivery time. Second, due to certain ordering costs, it is often necessary to order in batches instead of unit for unit. These two reasons mean that we need to look ahead and forecast the future demand. A demand forecast is an estimated average of the demand size over some future period. But it is not enough to estimate the average demand. We also need to determine how uncertain the forecast is. If the forecast is more uncertain, a larger safety stock is required. Consequently, it is also necessary to estimate the forecast error, which may be represented by the standard deviation or the so-called Mean Absolute Deviation (MAD).
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3. Costs and Concepts

In Chaps. 3–6 we consider a large and very important class of inventory problems, for which, in general, we can offer satisfactory solutions that can be used in practice relatively easily. This class of systems is characterized by two qualities:
  • Different items can be controlled independently.
  • The items are stocked at a single location, i.e., not in a multi-stage inventory system.
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4. Single-Echelon Systems: Deterministic Lot Sizing

When using an (R, Q) policy we need to determine the two parameters R and Q. We shall first consider the determination of the batch quantity Q. (When using an (s, S) policy, Q essentially corresponds to S—s.) We shall in this chapter assume that the future demand is deterministic and given. If the lead-time is constant, it does then not affect the problem and we can therefore just as well assume that the lead-time L = 0. The only difference in case of a positive lead-time is that we need to order L time units earlier. See also the discussion in Sect. 4.1.3. (If the demand is stochastic, we cannot disregard the lead-time.)
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5. Single-Echelon Systems: Reorder Points

We shall now consider different techniques for determining reorder points, or equivalently safety stocks, when the demand is a stationary stochastic process. To do this we first of all need a suitable demand model. In practice the demand during a certain time is nearly always a nonnegative integer, i.e., it is a discrete stochastic variable. (Exceptions may occur when we deal with products like oil.) Provided that the demand is reasonably low, it is then natural to use a discrete demand model, which resembles the real demand. However, if the demand is relatively large, it may be more practical to use a continuous demand model as an approximation. See Sect. 5.2. As before it is assumed that individual items can be controlled separately.
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6. Single-Echelon Systems: Integration–Optimality

In practice it is most common to determine the batch quantity from a deterministic model. The stochastic demand is then replaced by its mean. In Chap. 4 we have considered different methods for determination of batch quantities under the assumption of deterministic demand. Stochastic variations in the demand, and possibly in the lead-time, are then only taken into account when determining the reorder point. As discussed in Chap. 4 this procedure is, in general, an adequate approximation. In Chap. 5 we have described various techniques for determining the reorder point for a given batch quantity.
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7. Coordinated Ordering

In Chaps. 3, 4, 5, and 6 it was assumed that different items in an inventory could be controlled independently. We shall now leave this assumption and consider situations where there is a need to coordinate orders for different items. In this chapter we shall still, as in Chaps. 3, 4, 5, and 6, assume that the items are stocked at a single location. (Multi-stage inventory systems are dealt with in Chaps. 8, 9, and 10.) We consider traditional inventory costs and constraints, i.e., holding costs, ordering or setup costs, and backorder costs or service constraints.
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8. Multi-Echelon Systems: Structures and Ordering Policies

So far we have considered a single installation. In practice, though, it is also common to see multi-stage, or multi-echelon, inventory systems, where a number of installations are coupled to each other. For example, when distributing products over large geographical areas, many companies use an inventory system with a central warehouse close to the production facility and a number of local stocking points close to the customers in different areas. Similarly, in production, stocks of raw materials, components, and finished products are coupled to each other. To obtain efficient control of such inventory systems it is necessary to use special methods that take the connection between different stocks into account. In Chaps. 8–10 we will show when and how such methods can be used.
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9. Multi-Echelon Systems: Lot Sizing

In Chap. 8 we have discussed why and how multi-echelon inventory systems appear in practice, and how the most common ordering systems work. We shall now turn to the problem of choosing batch quantities for a multi-echelon inventory system. Note that this important problem must be solved independently of which type of ordering system we use.
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10. Multi-Echelon Systems: Reorder Points

This chapter deals with various techniques for determining safety stocks and reorder points in multi-echelon inventory systems. Throughout the chapter we assume that the batch quantities are given.
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11. Implementation

In Chaps. 2–10 we have described different methods for forecasting and inventory control. An inventory control system is usually based on a suitable selection of these methods. However, efficient algorithms cannot guarantee successful control. It is also necessary to create a good environment for practical application of the methods. This means, for example, correct inventory records and sound objectives for the control. Section 11.1 deals with various prerequisites for implementation of inventory control. In order to succeed, it is also necessary to understand how different control parameters like holding costs and service levels can be used for adjusting the control system. The implementation process, as well as adjustments of the control system, should be planned carefully and it is very important to monitor the results closely. We discuss issues concerning implementation and adjustments in Sect. 11.2.
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