Program in GAMS the mathematical model that you developed in step 1, so that in the program you can modify the parameters for different situations. What is the optimal production plan for the company if we assume that preparation of the machines for production is not necessary? Based on the results obtained, will it be possible to satisfy the demand once preparation times have been considered? (if the answer is NO, discuss where the problem will be most evident) What is the optimal production plan for the company if a portion of the demand is allowed to remain unfulfilled? (with the aim of satisfying as much of the demand as possible) Where should FDC focus its efforts to improve its demand compliance? Using the GAMS program, obtain the optimal solution and record the obtained values of the objective function and the decision variables. Interpret these results to generate a final report that shows the results in graphs and/or tables. (GAMS screenshots are NOT allowed) EXTRA POINTS: Choose 1 of the following points to develop:

What is the optimal production plan for the company assuming that inventory is allowed to be carried at no cost? maintaining the goal of minimizing overtime What is the optimal production plan for the company if we assume that it is allowed to subcontract part of the production to another company? Considering that outsourced hours cost twice as much as overtime What is the optimal production plan for the company if we assume that FDC's productivity increases by 2% each week? Consider the scenario described in the case study in which demand is uncertain with a variation of 5%. Propose a production plan for the company.

Falcon Die Casting Company (FDC) is an automo- Similarly, Machine 4 can only produce Parts 2 and 3. tive parts manufacturer based in Ohio. FDC recently While FDC has the design capacity needed to meet patented an innovative method of high volume die the customer's long term demand for the five parts, casting using traditional die casting machines. This the effective capacity at present is just enough to satpatent was instrumental in FDC receiving a long term isfy the demand because a significant percentage of contract from a major automobile manufacturer for items produced are not at a quality level demanded the bulk of its requirements for five key die cast items by the customer. This situation is likely to remain the used in most of its automobiles. The customer provides FDC with an indication of are gradually brought under control through experithe possible demand for the next 12 weeks with the ence and continuous improvement. FDC's industrial understanding that demand beyond Week 2 is tenta- engineers developed yield factors, which are quite tive and subject to change depending on auto sales accurate in predicting the proportion of parts that during the preceding weeks. Table 1 shows the pro- jected demand for the next 12 weeks. jected demand for the next 12 weeks. FDC can produce the parts on five die casting the production rates for the five parts on the five machines along with the yield factors. For instance, machines, each of which is capable of producing a producing Part 1 on Machine 1 for 3 hours yields 72 subset of the parts as indicated in Table 2. For exam- (=3400.6) items of Part 1 that meet the specificaple, Part 1 can be produced only on Machines 1 and 2 . tions and, thus, can be used to fulfill demand. There is no wastage of metal because defective parts can be melted and reused. Production takes place Monday through Friday with three eight-hour shifts per day, yielding 120 hours 154 Rao and Belin: Case: Production Scheduling at Falcon Die Casting INFORMS Transactions on Education 15(1), Pp. 154-155, ( ) 2014 INFORMS 155 Falcon Die Casting Company (FDC) is an automo- Similarly, Machine 4 can only produce Parts 2 and 3. tive parts manufacturer based in Ohio. FDC recently While FDC has the design capacity needed to meet patented an innovative method of high volume die the customer's long term demand for the five parts, casting using traditional die casting machines. This the effective capacity at present is just enough to satpatent was instrumental in FDC receiving a long term isfy the demand because a significant percentage of contract from a major automobile manufacturer for items produced are not at a quality level demanded the bulk of its requirements for five key die cast items by the customer. This situation is likely to remain the used in most of its automobiles. The customer provides FDC with an indication of are gradually brought under control through experithe possible demand for the next 12 weeks with the ence and continuous improvement. FDC's industrial understanding that demand beyond Week 2 is tenta- engineers developed yield factors, which are quite tive and subject to change depending on auto sales accurate in predicting the proportion of parts that during the preceding weeks. Table 1 shows the pro- jected demand for the next 12 weeks. jected demand for the next 12 weeks. FDC can produce the parts on five die casting the production rates for the five parts on the five machines along with the yield factors. For instance, machines, each of which is capable of producing a producing Part 1 on Machine 1 for 3 hours yields 72 subset of the parts as indicated in Table 2. For exam- (=3400.6) items of Part 1 that meet the specificaple, Part 1 can be produced only on Machines 1 and 2 . tions and, thus, can be used to fulfill demand. There is no wastage of metal because defective parts can be melted and reused. Production takes place Monday through Friday with three eight-hour shifts per day, yielding 120 hours 154 Rao and Belin: Case: Production Scheduling at Falcon Die Casting INFORMS Transactions on Education 15(1), Pp. 154-155, ( ) 2014 INFORMS 155