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412 CHAPTER 10 INVENTORY MODELS

cost for several possible order quantities. As a starting point, let us consider
Q ¼ 8000. The total annual cost is:
3 328 000
TC ¼ Q þ
Q
3 328 000
¼ 8 000 þ ¼ E8 416
8 000
A trial order quantity of 5000 gives:
3 328 000
TC ¼ 5 000 þ ¼ E5 666
5 000
The results of several other trial order quantities are shown in Table 10.1. It shows
the lowest cost solution to be about 2000 cases. Graphs of the annual holding and
ordering costs and total annual costs are shown in Figure 10.3.

Table 10.1 Annual Holding, Ordering, and Total Costs for Various Order Quantities
of Cape Cola
Annual Cost
Order Quantity Holding, E Ordering, E Total E

5 000 5 000 666 5 666
4 000 4 000 832 4 832
3 000 3 000 1 109 4 109
2 000 2 000 1 664 3 664
1 000 1 000 3 328 4 328

Figure 10.3 Annual Holding, Ordering and Total Costs for Cape Cola

Annual
6000 Total Cost

4000
Cost (€) Annual Inventory
Holding Cost

2000 Annual Ordering
Cost

1000 2000 3000 4000 5000 6000
Q* Order Quantity (Q)

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