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Unformatted text preview: University of Toronto Department of Mechanical and Industrial Engineering MIE376: Mathematical Programming Winter 2011 Lab 5 – Stochastic Linear Programming 1. Formulate the SLP Problem and Program it into AMPL A retailer has 3 stores in which it needs to ship to. The demand 1 month from today is unknown, but the company has estimated the following: Demand (1000 units) Probability Store Low Mid High Low Mid High 1 125 160 170 0.3 0.35 0.35 2 250 270 300 0.25 0.55 0.2 3 600 700 800 0.32 0.33 0.31 In one month from today, the actual demand will be known. There are two ways to ship the products to the stores: Normal Shipping (takes one month to arrive) and costs $1.00 per unit; Super‐Express Shipping (arrives immediately) and costs $2.50 per unit. a) Formulate a 2‐stage SLP that ensures all demand is met one month from today assuming decisions on shipping have to be made today. b) What is the optimal solution to the SLP formulated above? c) What happens to the shipping schedule if the cost of the Super‐Express Shipping goes up to $3.00/unit, $5.00/unit, or down to $1.20/unit? d) Compare this with a model that ships according to the expected demand in 1 month. Assume that lost sales costs are $3.00 per unit and excess stock just sits at the store. ...
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- Spring '11