Partial Exam 3 Bavarian Wood is a manufacturer of high-quality wooden furniture. The product port- folio includes all types of furniture, made from a wide variety of wood types. A typical

customer of Bavarian Wood is solvent and willing to pay a very high price for a high quality and durable product. The company faces the logistical challenge of organising the transport of wood as a production raw material from various import warehouses on the North Sea coast (Rotterdam i = 1, Wilhelmshaven i = 2, Bremerhaven i = 3, Hamburg i = 1) to the three production sites located in the distant hinterland (Munich j = 1, Salzburg j = 2, Prague j = 3). Since the Bavarian Wood does not use its own vehicles for the transport, it aims to or- ganise the allocation of import warehouses to production sites in such a way that the freight charges to be paid to contracted transport service providers are minimised in total. In the following table the stock of the import warehouses a, the demand of the pro- duction sites d; as well as the transportation costs ; between them are listed: from/to | 1 2 3|a₁ 1 THE 40 39 40 30 35 36 31 15 2 3 33 43 42 20 37 35 38 35 4 d; 40 25 35 | (a) Use the Matrix Minimum Method to calculate a feasible initial solution. Provide the complete solution. (b) With the help of the Column Minima Method the following initial solution with total costs of € 3635 was determined. zu = 30 211 = 15 1=20 241 = 5 241 = 25 241 = 5 Calculate an optimal solution applying the MODI method. Use the initial solution of the Column Minima Method. Provide the complete optimal solution./nBecause of increasing fuel costs Bavarian Wood seeks to reorganize its customer de- livery from the production site in Salzburg. A new employee, who studied Transporta- tion Economics in Dresden University of Technology, is instructed to do this job. He collected the following data: Ten customers (N = {1,...,10), indices: i, j) are to be supplied by the production facility in Salzburg (i = 0); for this purpose five identical vehicles (K) with a capacity (CAP) of 40 units (per vehicle) are available. The demands a; of the customers are given as follows: Node 0 1 2 3 4 5 6 7 8 9 10 Demanda 0 5 10 15 5 15 10 10 5 10 15 The symmetric transportation cost matrix cj is given as well: 2 Cij 0 1 2 3 4 5 6 7 8 9 10 002354263895 1 2075 X 8 346 3 4 3706493587 7 5560884359 4 4 4 X 480 56 57 5 2 28985 09 4 4 3 9 6 3 3 4 6 90 8 2 6 7 345 354802 6 8 7 8 8 685 742 20 3 3 9 9 3 79 5 3 6 6 3 0 8 10 5 4 7 4 297 8 3 8 0 اب اسلم لماما 3 5 6 IL/n(c) The transportation cost value cu (ca, respectively) is missing. Use the Dijkstra's algorithm to determine c. Consider the following digraph: 4 A B 1 w 5 6 2 3 4 D 1 1 4 (d) Determine the order in which the customers are served (rije), the vehicles used for supplying the customers (V) as well as the total costs F. Use the model from exercise E11 and assume, independently of your calculations in subtask (c), that c₁4 = cal = 7.