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# cee191-fa04-mt-Madanat-exam - avoid ﬂuctuation of the...

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CE152: Civil and Environmental Engineering Systems Analysis Midterm Prof. Madanat and Sengupta Fall 04 Problem 1 (6 points) A standard problem in logistics is to determine the optimal size of shipments (i.e., the number of items) to ship from a warehouse to a retailer, assuming constant demand. The manager seeks the shipment size that provides the best tradeoff between the inventory (or holding) cost and the transport (or movement) cost. The inventory cost (in \$) is given by: C i = AV where A is a variable cost per item in inventory, and V is the shipment size. The transport cost (in \$) is given by: C t = B/V where B is a fixed cost. Solve for the optimal shipment size. Problem 2 (6 points) As production manager of a factory your task is to determine the monthly production quantity for the next T months. The inventory I t at the end of month t is: I t = I t - 1 + P t - 1 - d t - 1 , t = 1 , . . . , T where P t is the monthly production quantity and d t the monthly demand forecast. Your aim is to

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Unformatted text preview: avoid ﬂuctuation of the production quantity from month to month. This avoids labor shortages or under-utilization. Thus the production plan should minimize the cost function: c inv T X t =1 I t + c prod T-1 X t =0 ± ± P t +1-P t ± ± Formulate the production planning problem as a linear program. Include all reasonable constraints in your formulation. Do not include unnecessary constraints. Your factory is unable to hold more than K units of inventory at the end of a given month. Make sure you state the meaning of any additional variables you introduce. 1 CE152 Midterm 2 Problem 3 (8 points) Derive an optimal solution to the following linear program: min X 1 ,X 2 ,Y 1 ,Y 2 2( X 1 + X 2 ) subject to Y 1 = X 1-2 X 1 + Y 2 = X 2 + 3 X 1 ≥ X 2 ≥ Y 1 ≥ Y 2 ≥ Graphical or analytical derivations are acceptable....
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