What are the minimum capacity changes at Glasgow that will alter the optimum set of routes and what will those alterations be? Explain how you arrive at each one of your answers.

Linear Programming

Paint Transhipment Problem
A company has two factories, one each at Bristol and Leeds. The factories produce paints which are sold to five wholesalers.
A. Formulate a linear programming model to determine the minimum cost transportation schedule.
Explain clearly the variables you use and the constraints you construct. What is the minimum cost transportation schedule and what are the corresponding costs?
B. Discuss the effect on the minimum transportation cost when capacity at each factory or warehouse is altered by adding or subtracting one ton. What are the minimum capacity changes at Glasgow that will alter the optimum set of routes and what will those alterations be? Explain how you arrive at each one of your answers.
C. The management of the company is considering the possibility of closing down one of the warehouses as this is expected to result in substantial labour and maintenance savings. Further, the manager of the Birmingham warehouse is considering sub-letting some of the capacity of this warehouse. Such sub-lets would have to be in exact multiples of 1000 tons. It is estimated that each 1000 tons of capacity could be let for £21,000 per week. Formulate a mixed integer linear programming model – or, if necessary, different model variants – to examine and evaluate the alternative courses of action. What would you recommend the company to do, and why?
Discuss the alternatives, also taking into account the solution from part (a) and explain which additional information you might need to give the company more specific advice.