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Course: CE100 13972, Spring 2011
School: Berkeley
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Civil CE152: 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 tradeo between the inventory (or holding) cost and the...

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Civil CE152: 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 tradeo between the inventory (or holding) cost and the transport (or movement) cost. The inventory cost (in \$) is given by: Ci = AV where A is a variable cost per item in inventory, and V is the shipment size. The transport cost (in \$) is given by: Ct = B/V where B is a xed 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 It at the end of month t is: It = It1 + Pt1 dt1 , t = 1, . . . , Pt T where is the monthly production quantity and dt the monthly demand forecast. Your aim is to avoid uctuation of the production quantity from month to month. This avoids labor shortages or under-utilization. Thus the production plan should minimize the cost function: T 1 T cinv Pt+1 Pt It + cprod t=1 t=0 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 Problem 3 (8 points) Derive an optimal solution to the following linear program: min X1 ,X2 ,Y1 ,Y2 2(X1 + X2 ) subject to Y1 = X1 2 X1 + Y2 = X2 + 3 X1 0 X2 0 Y1 0 Y2 0 Graphical or analytical derivations are acceptable. 2
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