How do you find b)?

Problem 4: A Swedish owned company delivers tools and merchandise to industrial companies in all Nordic countries. In Norway, the company has shops in the following seven cities: Oslo, Kristiansand, Stavanger, Bergen, Trondheim, Bode and Tromso. The company has two main stocks for serving the shops, one is positioned outside Gothenburg and another outside Stockholm Deliveries are performed by trucks from the main stocks to the shops. Estimated number of deliveries to each are shown in the table below. The demand is registered as the number of deliveries per month, even if the exact delivery of different items can vary from time to time Oslo Kristiansand Stavanger Bergen Trondheim Bode Troms Demand 156 38 88 90 14 54 Each of the stocks can maximum perform 250 deliveries per month to serve the Norwegian market . The distance in km from the main stocks to the shops are shown in the table below Distance Oslo Kristiansand Stavanger Bergen Trondheim Bode Troms Stockholm 529 769 1002 990 779 1176 Gothenburg 293 488 722 754 781 1524 1904 42 1556 The company wants to compose a delivery plan to minimize the transportation costs, which is considered equivalent to the number of km. driven per month. a) Formulate an LP-model for solving this problem. Define objective function, variables and constraints, and explain the parameters used in the model. 1. Implement the model and solve it using Solver in Excel. The company considers establishing a separate stock in Norway, and has access to a suitable building in Lillestrm. This stock will also have a capacity of 250 deliveries per month to the shops in Norway, but it has to be served from the two main stocks in Sweden. The distance from the main stock in Stockholm to Lillestrm is 500 km, and from Gothenburg to Lillestrm the distance is 300 km. However, due to economies of scale by using larger trucks, the company considers the transportation costs between Sweden and Lillestrm to be only 80% compared to transportation directly to the shops. The distance from Lillestrm to the shops in Norway is as follows: Distance Oslo Kristiansand Stavanger Bergen Trondheim Bode Troms Lillestrm 22 339 573 482 478 1179 1784 b) Extend the LP-model from a to include an intermediate stock in Lillestrm. It should still be possible to deliver directly from the main stocks in Sweden to the Norwegian shops i. Implement the model and solve it using Solver in Excel. ii. Comment the solution from i. How does the solution change, and what is the savings in transportation costs by establishing the stock in Lillestrm