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Quantitative Techniques: Guide for decision making 65 Unit 2 - Assignment Problem Transportation and assignment problems have mathematical features which have allowed managers to develop very effective, unique approaches to mathematical solution. These methods are variants of the standard simplex solution technique. Like the simplex process, these models have put these comprehensive manual and mathematical solutions in place. Learning Outcomes At the end of this unit, you will be able to: Develop interpretation using different types of assignment models in making managerial decisions. Pretest Instructions: Write True if the statement is Correct and False if the statement is Wrong. 1. The transportation simplex method can be used to solve the assignment problem. 2. The transportation simplex method is limited to minimizetion problems. 3. For an assignment problem with 3 agents and 4 tasks, the assignment matrix will have 3 rows and 4 columns. 4. If a transportation problem has four origins and five destinations, one of the destinations will not be fully supplied. 5. When an assignment problem involves an unacceptable assignment, a dummy agent or task must be introduced. Content Definition and Characteristics of Transportation, and Assignment Models The Transportation Model There are many definitions of transportation model; different authors give different views as regards to its definitions. Taylor (2013) stated that transportation model is formulated for a special case of problems with the following characteristics: . A product is transported from a number of sources to a number of destinations at the minimum possible cost; each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product. Although the general transportation model can be applied to a wide variety of problems, it is this particular application to the transportation of goods that is most familiar and from which the problem draws its name.Quantitative Techniques: Guide for decision making 76 Learning Activities Application Instructions: Formulate and perform the steps in linear programming using Computer Software (Excel or Spreadsheet) for both transportation and assignment models. Please make a decision statement after each case problems. Then, submit your answer in the google classroom. 1. CBA Mills produces carpet at plants in Dipolog and Dapitan. The carpet is then shipped to two outlets, located in Manukan and Roxas. The cost per ton of shipping carpet from each of the two plants to the two warehouses is as follows Cost From Manukan Roxas Dipolog 40 65 Dapitan 70 30 The plant at Dipolog can supply 250 tons of carpet per week; the plant at Dapitan can supply 400 tons per week. The Manukan outlet has a demand of 300 tons per week, and the outlet at Roxas demands 350 tons per week. The company wants to know the number of tons of carpet to ship from each plant to each outlet in order to minimize the total shipping cost. Solve this transportation problem. 2. Given a transportation problem with the following costs, supply, and demand, find the optimal solution by using the computer: To (cost) From P6 2 Supply A P7 P4 100 180 C 200 Demand 135 175 170 3. Solve the following linear programming problem: minimize Z = 3x11 + 12x12 + 8x13 + 10x21 + 5x22 + 6x23 + 6x31 + 7x32 + 10x33 subject to X11 + X12 + X13 = 90 X21 + X22 + X23 = 30 X31 + X32 + X33 = 100 X11 + X21 + X31 $ 70 X12 + X22 + X32 $ 110 X13 + X23 + X33 $ 80 X 20