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Consider a transportation problem setting where suppliers must make deliveries to satisfy the customer demands. Let m be the number of supply points, n the number of demand points, si bet the supply available at point i for i{1,,m},dj be the demand at point j for j{1,,n}, and cij be the unit transportation cost from supply point i for i{1,,m} to demand point j for j{1,,n}. a-) Assume that the problem is balanced, i.e, i=1msi=j=1ndj, unmet demand is not allowed and total supply can satisfy the total demand. Model this problem as a linear integer program. b-) Now, assume that the total demand exceeds fie total supply, i. e,i=1mi<j=1ndj. As it is not possible to satisfy the demand of all customers, we would like to ship the products in such a way that the transportation cost does not exceed a given budiget and the total penalty cost for unmet demand is minimized. Let B the given budget, and pj for j{1,,n} be the penalty of unmet demand at demand point j c-) If we slowly increase the budget. B, what would be the trend in the the objective function value for part b-), i.e., does it increase or decrease with increasing budget? Is this change indefinite?.

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Consider a transportation problem setting where suppliers must make deliveries to satisfy the customer demands. Let m be the number of supply points, n the number of demand points, si bet the supply available at point i for i{1,,m},dj be the demand at point j for j{1,,n}, and cij be the unit transportation cost from supply point i for i{1,,m} to demand point j for j{1,,n}. a-) Assume that the problem is balanced, i.e, i=1msi=j=1ndj, unmet demand is not allowed and total supply can satisfy the total demand. Model this problem as a linear integer program. b-) Now, assume that the total demand exceeds fie total supply, i. e,i=1mi<j=1ndj. As it is not possible to satisfy the demand of all customers, we would like to ship the products in such a way that the transportation cost does not exceed a given budiget and the total penalty cost for unmet demand is minimized. Let B the given budget, and pj for j{1,,n} be the penalty of unmet demand at demand point j c-) If we slowly increase the budget. B, what would be the trend in the the objective function value for part b-), i.e., does it increase or decrease with increasing budget? Is this change indefinite?

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Consider a transportation problem setting where suppliers mu.pdf

  • 1. Consider a transportation problem setting where suppliers must make deliveries to satisfy the customer demands. Let m be the number of supply points, n the number of demand points, si bet the supply available at point i for i{1,,m},dj be the demand at point j for j{1,,n}, and cij be the unit transportation cost from supply point i for i{1,,m} to demand point j for j{1,,n}. a-) Assume that the problem is balanced, i.e, i=1msi=j=1ndj, unmet demand is not allowed and total supply can satisfy the total demand. Model this problem as a linear integer program. b-) Now, assume that the total demand exceeds fie total supply, i. e,i=1mi<j=1ndj. As it is not possible to satisfy the demand of all customers, we would like to ship the products in such a way that the transportation cost does not exceed a given budiget and the total penalty cost for unmet demand is minimized. Let B the given budget, and pj for j{1,,n} be the penalty of unmet demand at demand point j c-) If we slowly increase the budget. B, what would be the trend in the the objective function value for part b-), i.e., does it increase or decrease with increasing budget? Is this change indefinite?