Practice Problems - Sensitivity Analysis (Solutions) .pdf - BU275 Solutions to Practice Problems Linear Programming What-if Analysis Question 1 Optimal

Practice Problems - Sensitivity Analysis (Solutions) .pdf -...

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BU275: Solutions to Practice Problems Linear Programming What-if Analysis Question 1: Optimal solution: 0 pants, 250 Dresses, 40 Skirts, 60 Blouses Objective Function Value= 0*15+250*16+40*12+60*16=5440 a) $10 increase, less than the allowable increase (13). P is a non-basic variable, hence, optimal solution and OFV are unchanged b) $2 decrease, inside the allowable decrease range, optimal solution is unchanged. New OFV=0*15+250*14+40*12+60*16=4940 c) Simultaneous changes in objective function coefficients: $3 decrease in profit B (allowable decrease: $12) $2 increase in profit S (allowable increase: $4) 100% rule: (-3)/(- 12)+2/4≤1 Since 100% rule satisfies optimal solution is unchanged. New OFV=0*15+250*16+40*14+60*13=5340 New OFV can also be calculated as below: New OFV=old OFV + (2)(40)+(-3)(60)=5440+80-180=5340 d) Simultaneous changes in objective function coefficients: $3 decrease in profit S (allowable decrease: $4) $2 increase in profit B (allowable increase: $4) 100% rule: (-3)/(-4)+2/4>1 Since 100% rule does not satisfy, we need to resolve the problem. e) 200 hours decrease in RHS of cutting constraint. Less than the allowable decrease for a non- binding constraint (330), hence, the optimal solution and OFV are unchanged. f) 90 hours increase in the RHS of packing constraint. It is more than the allowable limit (80), we need to resolve the problem. g) 30 unit increase in RHS of the “Blouses & Skirts” constraint. The increase is inside the allowable range (40). It is a binding constraint, hence, we need to resolve to find the new optimal solution. However, New OFV=old OFV + (30)(-4)=5440-120=5320 h) Simultaneous changes in the RHS of constraints: 300 hours decrease in cutting (allowable decrease: 330) 50 units increase in minimum production (allowable increase: 50) It is a special case of 100% rule. Although we are changing RHS of 2 constraints, because both of them are non-binding, we do not need to check the ratio of changes. If both RHS change in their allowable range (which is the case here), optimal solution and OFV are unchanged. (Note that if at least one of the constraints is binding, then we had to calculate the ratio and apply 100% rule, see part m)
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i) 300 units decrease in RHS of minimum number constraints. It is less than the allowable decrease for a non-binding constraint. Optimal solution and OFV are unchanged. (Note that you can also look at this question as removing a non-binding constraint, which yields to a same result.) j) Unlimited increase in RHS of packing constraints. It is more than the allowable increase (80), hence we need to resolve (Note that you can also look at this question as removing a binding constraint, which yields to a same result.)
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  • Winter '13
  • HosseinZolfagharinia

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