For the General Appliance Corporation transportation model discussed in Chapter 14, suppose that the company wants to enforce a single sourcing constraint that each distribution center be served from only one plant. Assume that the capacity at the Marietta plant is 1,500. Set up and solve a model to find the minimum cost solution.

Chapter 14 GAC transportation model discussed iat the botton of page 476 below:

Applications of Linear Optimization 476 Chapter 14 Figure 14.19 Little Investment Advisors Solution after Scaling the Expected Return Risk Measure Model 3 Bond Fund 4.62 6.11% Ohio National Bond 7.22 7.61% 2 PIMCO Global Bond Unhedged 9.75 5.29% 3 Federated High Income Bond 3.95 4 Morgan Stanley UlF Core Plus Fixed Inco 2.79% 7.37% 6.04 5 PIMCO Real Return 5.17 5.65% 6 PIMCO Total Return Investment $350 (n thousands) 5.00 Targe sk 4 Mode Amount Invested (in thousands 6 Bond Fund $256.34 1 Ohio National Bond $0.00 2 PIMCO Global Bond Unhedged $0.00 3 Federated High Income Bond $0.00 4 Morgan Stanley UIF Core Plus Fixed Inco 20 $93.66 5 PIMCO Real Return $0.00 6 PIMCO Total Return 22 $350.00 Tota 23 24 5.00 Risk 25 6.45% Percent Return 26 variables and investment constraint (in hundreds of thousands of dollars). Figure shows the result after the data have been scaled by expressing the decision variables and nvestment amount to thousands of dollars. This is the correct answer. So check your mod els carefully for possible scaling issues Transportation Models Many practical models in supply chain optimization stem from a very simple model called the transportation problem. This involves determining how much to ship from a set sources of supply (factories, warehouses, etc.) to a set of demand locations (warehouses, customers, etc.) at minimum cos EXAMPLE 14.7 General Appliance Corporation General Appliance Corporation (GAC) produces refriger ship between each plant and distribution center to m mize the total transportation cost, not exceed available ators at two plants: Marietta, Georgia, and Minneapolis, Minnesota. They ship them to major distribution centers capacity, and meet customer demand To develop a linear optimization model, we first in Cleveland, Baltimore, Chicago, and Phoenix. The ac- fine the decision variables as the amount to ship between counting, production, and marketing departments have provided the information in Table 14.6, which shows the each plant and distribution center. In this model, we use unit cost of shipping between any plant and distribution double-subscripted variables to simplify the formula center, plant capacities over the next planning period Define X amount shipped from plant i to distribution 1 represents Marietta i 2 repre and distribution center demands. GAC's supply chain center j, where i manager faces the problem of determining how much to sents Minneapolis, j 1 represents Cleveland, and so on. 14. Table GAC Cost, Ca and Demand un Using the shipping is e shipped, sum tribution cen minimize tota minimiz Becaus from each p amount shi Similarly, t the constrain Next, we mu center is me any distribut mand. For Figure General Ap Corporation Spreadshee and Solutio