ABC Company uses overtime, inventory and subcontracting to absorb the fluctuations in demand for its playgrounds for children. An aggregate production plan is devised annually and updated quarterly. Cost data, expected demand, and available capacities in units for the next four quarters are given here. Demand must be satisfied in the periods it occurs; that is, no backordering is allowed. Design a production plan that will satisfy demand at minimum cost.
Expected Regular Overtime Subcontract
Quarter Demand Capacity Capacity Capacity
1 650 750 100 500
2 1250 950 150 500
3 1350 1050 200 500
4 2750 1050 200 500
Regular production cost per unit $200
Overtime production cost per unit $250
Subcontracting production cost per unit $300
Inventory holding cost per unit per period $30
Beginning Inventory 300 units