1 The Problem The Guinness Brewery Company has two breweries (Dublin-B and Kilarny) and three markets Dublin-M, Galway, and Cork). They have three warehouse locations (Kilgore, Sligo, and Galway) but don't necessarily have to use all of them. They have transportation costs (dollars/case) for moving cases of beer from brewery to warehouse, and from warehouse to market (see the table below). Note that it is possible to transport cases directly from the brewery to the market in Dublin (Dublin-B to Dublin-M). Otherwise, the cases must visit a warehouse before being transported to a market. If they use a warehouse, each one has a monthly operating cost, as well as a maximum capacity. Each brewery has a monthly supply, and each market has a monthly demand shown below Transportation Costs DublinB (B) Kilarny (B) Dublin-M (M) Galway (M) Cork (M) Kilgore (W) 15 10 16 11 Sligo (W) 20 25 21 28 Galway (W) 15 20 16 12 Dublin-B (B) 18 Brewery Supply Market Demand Warehouse Cost Capacity Dublin-B 600 700 Dublin-M Kilgore 240 400 Kilarny 800 Galway 500 Sligo 450 800 Cork 300 Galway 820 600 They want to meet all demand at minimum cost. Part 1: Concrete and Abstract Models a. Draw a model of the network. b. Write a concrete model to solve the Guiness fixed-charge transportation problem. Hint: Begin with a standard minimum-cost network flow model with three warehouses, then modify the model as needed to accomodate the warehouse cost, capacities, and logical constraints. c. Convert the concrete model to abstract form