Consider the dummy plant to obtain optimal schedule

In Example 5.1-2, suppose that for the case where the demand exceeds the supply (Table 5.4), a penalty is levied at the rate of $300 and $190 for each undelivered car at Denver and Miami, respectively. Additionally, no deliveries are made from the Los Angeles plant to the Miami distribution center. Set up the model, and determine the optimal shipping schedule for the problem. Example 5.1-2 In the MG model, suppose that the Detroit plant capacity is 1300 cars (instead of 1500). The total supply (= 3500 cars) is less than the total demand (= 3700 cars), meaning that part of the demand at Denver and Miami will not be satisfied. Because the demand exceeds the supply, a dummy plant (source) with a capacity of 200 cars (= 3700 3500) is added to balance the model. The unit transportation cost from the dummy plant to the two destinations is zero because the plant does not exist. TABLE 5.4 MG Model with Dummy Plant Denver Miami Supply 80 215 Los Angeles 1000 1000 100 108 Detroit 1300 1300 102 68 New Orleans 1200 1200 Dummy Plant 200 200 Demand 2300 1400