Question 3: Multiperiod Scheduling (50 Points) A company wants to schedule a production plan for the next 6 months. Projected orders for the company's product are listed in the table. Over the 6-month period, units may be produced in one month and stored in inventory to meet some later month's demand. The company have a production capacity of 1,000 units a month. They could also produce overtime at the additional cost of $10/unit or purchase from a third party at the cost of $120/unit. The overtime capacity is 500 units and there is no limit for the third party order. The cost of holding an item in inventory for 1 month is $4/unit/mo. Items produced and sold in the same month are not put in inventory. The maximum number of units that can be held in inventory is 250. The initial inventory level at the beginning of the planning horizon is 200 units; the final inventory level at the end of the planning horizon is to be 100. The problem is to determine the optimal amount to produce in each month so that demand is met while minimizing the total cost of production and inventory. Shortages are not permitted. Month Demand Production cost 1 1300 100 2 1400 105 3 1000 110 4 800 115 5 1700 110 6 1900 110 Hint: Your network includes nodes from January to June. b. Define Decision Variables (and helper variables if you decide to use them). (9 points) c. Develop the Objective Function. Show all the steps of your calculations. (5 points) d. Write the constraints (10 points) e. Solve the problem using Excel Solver. (20 points) Question 3: Multiperiod Scheduling (50 Points) A company wants to schedule a production plan for the next 6 months. Projected orders for the company's product are listed in the table. Over the 6-month period, units may be produced in one month and stored in inventory to meet some later month's demand. The company have a production capacity of 1,000 units a month. They could also produce overtime at the additional cost of $10/unit or purchase from a third party at the cost of $120/unit. The overtime capacity is 500 units and there is no limit for the third party order. The cost of holding an item in inventory for 1 month is $4/unit/mo. Items produced and sold in the same month are not put in inventory. The maximum number of units that can be held in inventory is 250. The initial inventory level at the beginning of the planning horizon is 200 units; the final inventory level at the end of the planning horizon is to be 100. The problem is to determine the optimal amount to produce in each month so that demand is met while minimizing the total cost of production and inventory. Shortages are not permitted. Month Demand Production cost 1 1300 100 2 1400 105 3 1000 110 4 800 115 5 1700 110 6 1900 110 Hint: Your network includes nodes from January to June. b. Define Decision Variables (and helper variables if you decide to use them). (9 points) c. Develop the Objective Function. Show all the steps of your calculations. (5 points) d. Write the constraints (10 points) e. Solve the problem using Excel Solver. (20 points)
