EOQ_homeworkE10

# EOQ_homeworkE10 - E10 IEOR Module Srping 2010 Prof....

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Unformatted text preview: E10 IEOR Module Srping 2010 Prof. Leachman Module Homework Assignment #1 Due at start of class Friday Feb. 5 1. Consider a simple inventory system with the following characteristics: Constant demand rate D, finite replenishment rate P > D, ordering (setup) cost A, inventory holding cost h per unit per unit time. The setup time (duration from when replenishment is requested until replenishment begins) is L. Sketch a graph of inventory versus time for this case. Develop the total cost rate function and determine the optimal order size. 2. Consider an EOQ inventory system with multiple items i = 1, 2, … , n whose replenishments must be coordinated. All items must be jointly replenished and the replenishments must be sized to cover T days of demand. (That is, the frequency of replenishments is once every T days for all items.) Develop an expression for the total cost rate as a function of T. Then find the best value for T. Use the following notation: Di is the demand rate for item i, Ai is the ordering cost for item i, and hi is the inventory holding cost rate for item i, i = 1, 2, … , n. 3. Consider an inventory system with multiple items i = 1, 2, … , n whose inventories must be replenished using a single machine. The machine can only replenish one item at a time. When switching the machine from producing one item to produce another item, say, item i, there is a changeover time ci required to re‐tool the machine. Suppose the items are produced according to a simple rotation cycle of length T days, whereby a supply of each item i is produced that is adequate to last T days before changing over the machine to produce item i+1. We have the following data: Di is the demand rate per day, Pi is the production rate per day, ci is the a changeover time (days), Ai is the changeover cost, and hi is the inventory holding cost rate (\$ per unit per day) for item i, i = 1, 2, … , n. Develop an expression for the total cost rate as a function of T. (You don’t have to solve for the best value of T.) Also, as a function of T, develop an expression for how long it will take the machine to finish one rotation cycle. (Obviously, this must be less than or equal to T for the cycle to be feasible.) 4. Consider the basic EOQ inventory problem but with backorders allowed. That is, we may allow an inventory shortage to develop before the replenishment arrives. In addition to the usual parameters D, A, and h, there is a penalty cost b per unit short per unit time. Let Q denote the decision variable for the order size, and let s denote the decision variable for the amount of shortage at the end of the replenishment cycle, i.e., just before a new replenishment arrives. As a function of Q, s and D, what is the length of the replenishment cycle? Develop an expression for the total cost rate T(Q, s). ...
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## This note was uploaded on 02/19/2010 for the course ENGINEERIN 72826 taught by Professor Sengupta/leachman/johnson during the Spring '10 term at Berkeley.

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