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Lecture 6 Notes

# Lecture 6 Notes - Space IOE 202 lecture 6 outline...

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Space IOE 202: lecture 6 outline Announcements Last time... Other examples of optimization models EOQ with shortages Cutting Stock problem Radiation treatment planning models IOE 202: Operations Modeling, Fall 2009 Page 1 Space Last time Using integer variables in models where variables represent non-divisible quantities Post o ce sta ng problem Using binary (0-or-1) variables to represent yes/no decisions Course selection: used constraints on the variables to represent logical restrictions Pollution reduction: combining binary and continuous variables; using “forcing” constraints to ensure feasibility and to correctly account for fixed costs Investment with brokerage fees Important observation: all models we constructed were Linear Integer Programs, that is, objective and constraints involved only linear functions of the variables. This is crucial to our ability to find optimal solutions to the models we formulate. IOE 202: Operations Modeling, Fall 2009 Page 2

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Space Cutting Stock problem The Better Food Company produces cream-filled sponge rolls with a standard width of 20 cm each. Each 20 cm roll costs the company \$2.00 to produce. Special customer orders with di ff erent widths are produced by cutting (slitting) the standard rolls of sponge into shorter lengths. Typical orders are summarized in the following table. These orders need to be met at least cost. Desired Desired Number Order Width (cm) of Rolls A 5 150 B 7 200 C 9 300 IOE 202: Operations Modeling, Fall 2009 Page 3 Space How to split the rolls An order is filled by cutting a standard 20 cm. roll into the desired widths; there are several ways in which a standard roll can be slit to fill a given order. We will consider below three possible ways to cut up a 20-cm roll. Note that the shaded area in each diagram represents lengths of sponge that are too short to be used in meeting orders, and so these pieces must be thrown away. Although there are other feasible settings, we limit the discussion for the moment to considering settings 1, 2 and 3 in the figure. IOE 202: Operations Modeling, Fall 2009 Page 4
Space Three possible knife-setting patterns Setting 1 Setting 3 Setting 2 20 20 20 7 9 4 5 5 7 3 5 5 9 1 5 cm rolls produced 7 cm rolls produced 9 cm rolls produced Pattern 1 Pattern 2 Pattern 3 IOE 202: Operations Modeling, Fall 2009 Page 5 Space Two possible solutions Number of times pattern is used No of 5 cm rolls (150 ordered) No of 7 cm rolls (200 ordered) No of 9 cm rolls (300 ordered) Pattern 1 300 Pattern 2 75 Pattern 3 0 Totals: Number of times pattern is used No of 5 cm rolls (150 ordered) No of 7 cm rolls (200 ordered) No of 9 cm rolls (300 ordered) Pattern 1 200 Pattern 2 0

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Lecture 6 Notes - Space IOE 202 lecture 6 outline...

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