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Unformatted text preview: 0 680 1 1 1 0.8 4.5 4.5 -1 1 -1 1 -1 4 300 1 5.7 1 The strawberry example with length of activity determined in model. le 700 le 1200 le 0 le 0 le 0 Equilibrium Model Extended Equilibrium An equilibrium model can include a sequence of activities. Sequencing problems are discussed in section 7.5 of the text. We did not explicitly cover them in class before. Sequencing (7.4) Sequencing Some activities must be completed before others are begun Sequencing may be controlled within a variable or between variables using constraints The technique used depends on the situation Example from Chapter 7 Example A firm produces one output using two tasks (events). There is a 3­week production horizon, and the two events can take place any time during that period, but the second event must take place after the first event – although the two events can take place in the same week First Case: Returns Independent of Timing Returns X1, X2, X3: amount of activity 1 done in weeks 1, 2, 3, respectively Y1, Y2, Y3: amount of activity 2 done in weeks 1, 2, 3, respectively. For week 1: Y1 LE X1 For week 2: Y2 LE X1 + X2 – Y1 For week 3: Y3 LE X1+X2+X3­(Y1+Y2) Sequencing handled by constraints Tableau: Case 1 Tableau: X1 OBJ week1 trans week2 trans week3 trans week1 res week2 res week3 res -1 -1 -1 a X2 -1 -1 X3 -1 b Y1 P 1 1 1 d Y2 P 1 1 Y3 P 1 e c f le le le le le le 0 0 0 T1 T2 T3 Second Case: Second Returns Depend on Timing If the returns depend on timing, we must define a variable for each combination of timing possible. Example: A1B2 is the variable meaning that activity A (first activity) is done in week 1and activity B (second activity) is done in week 2. Tableau Case 2 Tableau OBJ wk1 wk2 wk3 A1B1 A1B2 A1B3 A2B2 A2B3 A3B3 P11 P12 P13 P22 P23 P33 a b d c f g e h i le le le T1 T2 T3 Chapter 8 : Chapter Crop Ro...
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