A dishwasher manufacturer is in the process of aggregate production planning for the next six months. The company manufactures different models of dishwashers, and aggregates these models as an aggregated unit: "dishwasher". Currently, it is March 31. The company wants to develop an aggregate production plan from April to September. The forecasted aggregate demand for these months is DApril, DMay, DJune, DJuly, Daugust and DSeptember, respectively. Suppose that there are 20 working days in each of the 6 months ahead. Suppose that 2 hours of labor is required to produce one dishwasher. As of March 31, there are W regular workers on the payroll. Suppose that it is not allowed to hire or lay-off workers as a company policy. Therefore, the company will continue to have w regular workers in each of the months over the planning horizon. Regardless of the forecasted demand, each regular worker works 10 hours per day and produces 5 dishwashers every day. It costs $RPC to produce one dishwasher using regular production. Backordering is not allowed and all demand must be met in each month. If regular production capacity is not enough to cover forecasted demand in a month, firstly, they use overtime but to do so costs them $50 per dishwasher above the regular production cost. Total overtime hours used in a month is limited by 1000 hours; equivalently, total overtime capacity is 500 units in each month. If through regular and overtime capacity, the demand is still not satisfied, they can subcontract, but to do so costs them $100 per dishwasher above the regular production cost. There is no upper bound on the number of units to be subcontracted in any month. They can use inventory, but inventory holding costs are $IC per month per dishwasher, based on the number of dishwashers in inventory at the end of the month. Inventory holding cost is charged based on ending inventory level for each month. They currently have (as of the end of March 31) I, dishwashers in facility warehouse inventory. (Before solving the question, select an integer value from the given interval, fill in the following table and copy only the 1& 3 columns it into your answer sheet) Parameter Interval Selected value DApril Dylay [5.000; 10,000] [5,000: 10,000] [5,000: 10,000] Djuns Djuly [5,000: 10,000] DAugust [5.000; 10,000] Dseptember [5,000; 10,000) [50; 60) W SRPC [100: 2001 SIC [5:20] I. [1,000; 1,500) a) Formulate the problem as a linear program (LP) to minimize total cost over the planning horizon. Clearly define your index/indices and decision variables. Write the model in open form (That is, do not use any "summation" or "for all" symbol & substitute the values of all parameters in the model.) b) Find the optimal solution of the LP model in part a). Write the optimal values of all decision variables f and the optimal objective function value. (You can use any tool such as Excel Solver, GAMS, IBM ILOG OPL. Only, it is enough to write the optimal values. Do not copy or submit any code/screenshot related to the software you used). A dishwasher manufacturer is in the process of aggregate production planning for the next six months. The company manufactures different models of dishwashers, and aggregates these models as an aggregated unit: "dishwasher". Currently, it is March 31. The company wants to develop an aggregate production plan from April to September. The forecasted aggregate demand for these months is DApril, DMay, DJune, DJuly, Daugust and DSeptember, respectively. Suppose that there are 20 working days in each of the 6 months ahead. Suppose that 2 hours of labor is required to produce one dishwasher. As of March 31, there are W regular workers on the payroll. Suppose that it is not allowed to hire or lay-off workers as a company policy. Therefore, the company will continue to have w regular workers in each of the months over the planning horizon. Regardless of the forecasted demand, each regular worker works 10 hours per day and produces 5 dishwashers every day. It costs $RPC to produce one dishwasher using regular production. Backordering is not allowed and all demand must be met in each month. If regular production capacity is not enough to cover forecasted demand in a month, firstly, they use overtime but to do so costs them $50 per dishwasher above the regular production cost. Total overtime hours used in a month is limited by 1000 hours; equivalently, total overtime capacity is 500 units in each month. If through regular and overtime capacity, the demand is still not satisfied, they can subcontract, but to do so costs them $100 per dishwasher above the regular production cost. There is no upper bound on the number of units to be subcontracted in any month. They can use inventory, but inventory holding costs are $IC per month per dishwasher, based on the number of dishwashers in inventory at the end of the month. Inventory holding cost is charged based on ending inventory level for each month. They currently have (as of the end of March 31) I, dishwashers in facility warehouse inventory. (Before solving the question, select an integer value from the given interval, fill in the following table and copy only the 1& 3 columns it into your answer sheet) Parameter Interval Selected value DApril Dylay [5.000; 10,000] [5,000: 10,000] [5,000: 10,000] Djuns Djuly [5,000: 10,000] DAugust [5.000; 10,000] Dseptember [5,000; 10,000) [50; 60) W SRPC [100: 2001 SIC [5:20] I. [1,000; 1,500) a) Formulate the problem as a linear program (LP) to minimize total cost over the planning horizon. Clearly define your index/indices and decision variables. Write the model in open form (That is, do not use any "summation" or "for all" symbol & substitute the values of all parameters in the model.) b) Find the optimal solution of the LP model in part a). Write the optimal values of all decision variables f and the optimal objective function value. (You can use any tool such as Excel Solver, GAMS, IBM ILOG OPL. Only, it is enough to write the optimal values. Do not copy or submit any code/screenshot related to the software you used)
