6. The demand for a product over the next five periods may be filled from regula

Question

6. The demand for a product over the next five periods may be filled from regular production, overtime production, or subcontracting. Subcontracting may be used only if the overtime capacity has been used. The following table gives the supply, demand and cost data of the situation. Production Capacity (units) Period Regular Demand Overtime Subcontracting Time 100 40 90 60 70 50 60 80 50 50 30 80 70 20 100 153 2 3 4 200 200 203 The unit production costs for the three levels in each period are $4, $6 and $7, respectively. The unit holding cost per period is $0.50. Determine the optimal solution.

Explanation / Answer

So we need to minimize 4R+6O+7S+0.5H, where R stands for the total production in regular time, O stands for Overtime production, S stands for subcontracted production and H stands for the total holding units. In some of the periods, we don't have enough capacity to meet the demand, so we will use the extra capacity of the preceding period to meet this demand. Since we need to use all the regular and overtimes before we use the subcontracting, we therefore had to use the regular and overtime first, then if we have an expected backlog we use the available hours in the preceding period to meet the demand

The table below,show the schedule of production . The numberswithout brackets represent the capacity, numbers in the bracket shows the production for this period and the numbers in the underlined bracket are produced for the next period.

Therefore, R = 360, O=290, S=256 and H=90. Therefore the production cost for the 5 periods = 360*4+290*6+256*7+0.5*90 = 1440+1740+1792+45 = $5,017

Production capacity(units) Period Regular time Overtime Subcontracting Demand Stored units 1 100(100) 50 (50) 30 (3)(20) 153 20 2 40(40) 60(60) 80(80) 200 0 3 90(90) 80(60)(20) 70(50) 150 70 4 60(60) 50(40) 20 (20) 200 0 5 70 (70) 50(50) 100 (83) 203 360 290 256 906 90

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