s02rec11 - and purchasing prices for the next 5 months...

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Recitation 11 15.053 Introduction to Optimization Friday May 3, 2002. 1. Shortest path on an acyclic network: Given an acyclic network with topological ordering, write the stages, recursion, initial condition and the final goal for solving the shortest path problem. 2. Resource Allocation Problem : Finco has $6000 to invest, and three investments are available. If d j dollars (in thousands) are invested in investment j , then the net present value (in thousands) of r j (d j ) is obtained, where the r j (d j )’s are as follows: r 1 (d 1 ) = 7 d 1 + 2 (d 1 > 0) r 2 (d 2 ) = 7 d 2 + 2 (d 2 > 0) r 3 (d 3 ) = 7 d 3 + 2 (d 3 > 0) r 1 (0) = r 1 (0) = r 1 (0) = 0. The amount placed in each investment must be an exact multiple of $1000. To maximize the net present value obtained from the investments, how should Finco allocate the $6000 ? First write a recursion for the general case and then solve for the above problem. 3. Inventory Problem : A manufacturing company has the following requirement schedule
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Unformatted text preview: and purchasing prices for the next 5 months. Month Requirement (thousands) Price ($/thousand pieces) 1 5 10 2 10 11 3 6 13 4 9 10 5 4 12 The storage capacity for this item is limited to 12,000 units; there is no initial stock, and after the five-month period the item will no longer be needed. a. Derive a monthly purchasing schedule if total purchasing cost is to be minimized b. Assuming that a storage charge of $250 is incurred for each 1000 units found in inventory at the end of a month. What purchasing schedule would minimize the purchasing and the storing cost ? c. Generalize the above problem for the case when there are n months with requirement of r 1 , r 2 , …,r n and the cost of c 1 , c 2 , …,c n for each month. With storage capacity of S and storage cost of SC per 1000 units, formulate a recursion that would solve the generalized problem....
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