Unformatted text preview: Assignment 1 SC&IS 510
[email protected] Question 1 EOQ with partial backlogging Suppose we seek to extend the standard EOQ model with backlogging to the case with partial backlogging. Specically, let b be the number of customers that arrive while inventory is depleted. (This is the same denition as in the full backlogging case.) Now however, only α of those b customers choose to wait meaning we lose (1 − α)b sales per cycle. Use all the same notation and denitions from class (holding cost per unit time h, backlog cost per unit time p, demand rate µ, order quantity q , ordering cost K , b customers arriving when inventory is depleted) and one new parameter: let l be the cost per lost sale (not per unit time). Your decisions are still q, b. Write an expression for the cost function. Explain how you would try to nd a solution and guarantee uniqueness of that solution. (Hints: be careful about the length of the order cycle; check your work at various points noting that if α = 1 you should get the same answers as the full backlogging case.) Question 2 Cyclic Scheduling Suppose we are building a cyclic schedule for three products which have the same holding cost h, setup cost k, setup time a, production rate γ . The demand rate for all the three products is µ. Write the cost function for the cyclic schedule for these three products as concisely as possible, assuming that all three products are produced exactly once in the cyclic production schedule. Write a concise expression for: 1. the optimal total cost for the case where the cost minimizing cycle length is feasible; 2. the optimal total cost when the cost-minimizing cycle length is not feasible. For case 1 show how changes in the production and demand rates (µ and γ , respectively) aect the optimal cycle length and the total cost. For 2 show how changes in the production and demand rates (µ and γ , respectively) aect the optimal cycle length. 1 ...
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Dubey during the Spring '11 term at Amity University.
- Spring '11