The Build-Em-Fast Company has agreed to supply its best customer with three widgits during each of the next 3 weeks,even though producing them will require some overtime work.The relevant production data are as follows: The Build-Em-Fast Company has agreed to supply its best customer with three widgits during each of the next 3 weeks,even though producing them will require some overtime work.The relevant production data are as follows: The cost per unit produced with overtime for each week is $100 more than for regular time.The cost of storage is $50 per unit for each week it is stored.There is already an inventory of two widgets on hand currently,but the company does not want to retain any widgets in inventory after the 3 weeks.Management wants to know how many units should be produced in each week to minimize the total cost of meeting the delivery schedule.A special restriction for this problem is that overtime should not be used in any particular period unless regular time in that period is completely used up.Explain why the logic of separable programming implies that this restriction will be satisfied automatically by any optimal solution for the transportation problem formulation of the problem.(You only need to explain this logic without formulating the transportation problem.)

Question

The Build-Em-Fast Company has agreed to supply its best customer with three widgits during each of the next 3 weeks,even though producing them will require some overtime work.The relevant production data are as follows: The Build-Em-Fast Company has agreed to supply its best customer with three widgits during each of the next 3 weeks,even though producing them will require some overtime work.The relevant production data are as follows:  The cost per unit produced with overtime for each week is $100 more than for regular time.The cost of storage is $50 per unit for each week it is stored.There is already an inventory of two widgets on hand currently,but the company does not want to retain any widgets in inventory after the 3 weeks.Management wants to know how many units should be produced in each week to minimize the total cost of meeting the delivery schedule.A special restriction for this problem is that overtime should not be used in any particular period unless regular time in that period is completely used up.Explain why the logic of separable programming implies that this restriction will be satisfied automatically by any optimal solution for the transportation problem formulation of the problem.(You only need to explain this logic without formulating the transportation problem.)

Quizplus · Accepted Answer

The Answer is Since regular time production is cheaper than overtime,the objective of minimizing cost will force regular time to be used first in an optimal solution.To see why,consider any feasible solution (one that satisfies all the constraints of the problem)that violates the special restriction because overtime is used in a particular period even though regular time is not completely used up in that period.Therefore,because regular time is cheaper,increasing regular time in that period by a small amount and decreasing overtime by the same amount will yield a feasible solution with a better value of the objective function,so the original feasible solution cannot be optimal.

The Build-Em-Fast Company Has Agreed to Supply Its Best Customer