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?
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. The wholesalers are either supplied directly from the factories or through one of the company warehouses, the transportation costs being paid by the company. The company has three warehouses, one each in London, Birmingham and Glasgow. Table 1 shows the transportation costs per ton for deliveries from the suppliers to the warehouses or wholesalers and also from the warehouses to the wholesalers, omitting entries when delivery from a certain supplier or warehouse is impossible for some destination.
Warehouse Wholesaler Supplier London Birmingham Glasgow 1 2 3 4 5
Bristol 25 23 – 80 – 90 100 86
Leeds 30 27 30 – 70 54 – 100
London – – – 37 31 – 40 44
Birmingham – – – 36 40 43 40 46
Glasgow – – – 45 42 30 – 36
TABLE 1: TRANSPORTATION COSTS IN £’S/TON DELIVERED
The two factories at Bristol and Leeds can produce up to 40,000 and 50,000 tons per week respectively. No more than 20,000 15,000 and 12,000 tons can be moved each week through the
warehouse in London, Birmingham and Glasgow, respectively. Wholesalers 1, 2, 3, 4 and 5 require at
least 15,000, 20,000, 13,000, 14,000 and 16,000 tons per week respectively.
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.
Warehouse Wholesaler Supplier London Birmingham Glasgow 1 2 3 4 5
Bristol 25 23 – 80 – 90 100 86
Leeds 30 27 30 – 70 54 – 100
London – – – 37 31 – 40 44
Birmingham – – – 36 40 43 40 46
Glasgow – – – 45 42 30 – 36
TABLE 1: TRANSPORTATION COSTS IN £’S/TON DELIVERED
The two factories at Bristol and Leeds can produce up to 40,000 and 50,000 tons per week respectively. No more than 20,000 15,000 and 12,000 tons can be moved each week through the
warehouse in London, Birmingham and Glasgow, respectively. Wholesalers 1, 2, 3, 4 and 5 require at
least 15,000, 20,000, 13,000, 14,000 and 16,000 tons per week respectively.
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.