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Supply Chain Management Pathways for Research and Practice Part 8

Tham khảo tài liệu 'supply chain management pathways for research and practice part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Information Sharing a Quantitative Approach to a Class of Integrated Supply Chain 129 Fig. 5. Inventory position of the each supplier and the retailer in 0 ts mQ In the same way it can be seen that the jth unit in the batch Q0 2 which will be received from the path i will be used to fill the R j th retailer demand after the retailer order. Then the jth unit in the batch Q0 2 will have the same expected retailer and warehouse costs as a unit in a base stock system with S0 s mQ and S1 R j. Therefore the expected holding and shortage costs for the jth unit in the batch Q0 2 will be equal to ci s mQ R j j 1 . Q 2 A 12 . Similarly one can easily see that the jth unit in the batch Q0 2 which will be received from the path j will be used to fill the R Q 2 j th retailer demand after the retailer order. Then this unit will have the same expected retailer and warehouse costs as a unit in a base stock system with S0 s mQ and S1 R Q 2 j and the expected holding and shortage costs for this unit will be equal to Cj s mQ R Q 2 j j 1 . Q 2 A 12 . It should be noted that each customer demands only one unit of a batch. If we number the customers who use all Q units of these batches from 1 to Q then the demand of any customer will be filled randomly by one of these Q units. That is each unit of two batches of total size Q will be consumed by the jth j 1 2 . Q customer according to a discrete uniform distribution on 1 2 . Q. In other words the probability that the ith i 1 2 . Q unit of two batches of total size Q is used by the jth j 1 2 . Q customer is equal to 1 Q. Therefore we can now express the expected total cost for a unit demand as 130 Supply Chain Management - Pathways for Research and Practice 1 Q 2 Q k 0 P12- C1 S mQ R i C2 s mQ R i Q _ i 1 i Q 2 1 o P21- QlC2 s mQ R i TC1 S mQ R i Q _ i 1 i Q 2 1 _ 17 Since the average demand per unit of time is equal to Ằ the total cost of the system per unit time can then be written as Q 2 Q TC R m s Ả.k P12. C1 S mQ R i C2 s mQ R i Q _