The Actions and Decisions Given the three-year forecast as shown in Table 2, Julie and her group have to come up with an aggregate production plan that minimizes the total costs of all involved components; e.g. purchasing, production and inventory management, using operations research/optimization formulation and solution. Demand Forecast for Next Three Years The collaborative forecasting team used the historical demand data provided in Table 1 supplemented with stockout data to develop a forecast for quarterly demand for both clear and black plastic containers. The demand forecast between 2010 and 2012 is shown in Table 2. Tahle ? Demand Forecast for Clear and Rlack Plactic Containers Extruders The extrusion process is capital intensive, as is the investment in the facilities required to support it. The plant currently has 14 extruders. Each extruder has a rated processing capacity of 3,000 pounds per hour. A changeover is required whenever the extruder switches between clear and black sheets. SPC estimates that there is a 5 percent capacity loss due to changeovers. The effective processing capacity of an extruder is thus 2,850 pounds per hour. (Note: as long as you consider this effective capacity, for simplification, you can add up the demand of clear and black plastic containers and have the requirement of meeting that total demand.) Each extruder requires six workers. SPC pays each worker $15 per hour including benefits. Overtime is paid at 150 percent of regular-time salary. Workers are limited to 60 overtime hours per quarter. Extruders are fairly expensive, and the addition of an extruder requires the hiring of six additional people. Each new extruder incurs a fixed cost of $80,000 per quarter. Any new personnel hired need to be trained. Training cost per person is $3,000. As a result, SPC has decided not to purchase any new extruders over the current planning horizon. During any quarter, available extruders may be idled if they are not to be used. The only savings here is the salary of associated workers. Laying off each worker, however, costs $2,500. If idled extruders are brought online, SPC incurs a training cost of $3,000 per worker. Thermoforming Presses The plant currently has 25 thermoforming presses. Each thermoforming press requires one operator and can produce containers at the rate of 2,000 pounds per hour. SPC pays each operator $15 per hour including benefits. Overtime is paid at 150 percent of regular-time salary. Workers are limited to 60 hours of overtime per quarter. Presses may be idled for the quarter if they are not to be used. Laying off a thermoforming operator costs $2,500, and training a newly hired operator costs $3,000. Public Warehousing Public warehousing charges customers for both material handling and storage. The SPC plant contracts with local warehouses to store material on a per-thousand-pound basis. Material handling charges are from $4 to $6 per 1,000 pounds unloaded at the warehouse. Storage charges are from $10 to $12 per 1,000 pounds in storage at the end of each quarter. The SPC plant negotiates annually with local warehouses to establish rates for each cost element. SPC must consider several variables in determining the amount of warehouse space it requires. Usable warehousing space is the fraction of a warehouse that can actually be used to store inventory. Considerations are made for aisle space, shipping and receiving dock space, administrative office space, and ceiling height. Storage density is another consideration. SPC must also take into account velocity and times of materials movement because the staffing level required and storage configurations are dependent on both. For example, if materials must be retrieved readily, the warehouse layout must include a greater ratio of aisle and staging space to actual storage space