Major Medical, producer of portable EKG units, is developing a 4 month aggregate plan. Month 1 Month 2 Month 3 Month 4 Regular Time Capacity 235 255 290 300 OT Capacity 20 24 26 24 Subcontract Capacity 12 15 17 17 DEMAND 255 294 321 301 The cost of producing each unit is $985 on regular time, $1,310 on overtime, and $1,500 on a subcontract. Inventory carrying cost is $100 per month. There is no beginning inventory, and no ending inventory requirement. Backorders are permitted, but cost $400 per month per unit. Find the optimal solution.

                                          Month 1   Month 2   Month 3   Month 4

DEMAND                             255         294           321           301

Regular Time Capacity       235         255          290          300

OT Capacity                          20           24             26            24

Subcontract Capacity           12            15              17             17

Month 1:

regular 235 units

OT 20 units

total production cost = (235 x $985) + (20 x $1,310) = $257,675

Month 2:

regular 255 units

OT 24 units

subcontract 15 units

total production cost = (255 x $985) + (24 x $1,310) + (15 x $1,500) = $305,115

Month 3:

regular 290 units

OT 21 units

subcontract 5 units

total production cost = (290 x $985) + (21 x $1,310) + (5 x $1,500) = $320,660

Month 4:

regular 300 units

OT 1 units

total production cost = (300 x $985) + $1,310 = $296,810

Explanation:

You have to minimize subcontract capacity and backorders since they are too expensive, e.g. OT cost $1,310 + $400 = $1,710 which is even higher than subcontract orders. There is no excess capacity sine regular capacity is always lower than demand. The only month where you could consider producing extra units during overtime is month 4 but it depends on month 5' demand.  

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