The J. Mehta Company\'s production manager is planning a series of one-month pro

Question

The J. Mehta Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows: Demand for Stainless Steel Sinks 120 160 260 180 Month 2 4 The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $95 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices (1) he can produce up to 35 more sinks per month in overtime but at a cost of $125 per sink (2) he can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period is 450 sinks, at a cost of $150 each); (3) Or, he can fill the demand from his on-hand inventory (i.e. beginning inventory). The inventory carrying cost is $10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is $10 per sink). There are 10 Sinks in Inventory at the beginning of Month 1 Setup the Production Smoothing problem with the goal of minimizing cost

Explanation / Answer

Reg time Prod month 1 = 100

min cost:

Month 1 2 3 4 Demand 120 160 260 180 B Inv 10 25 0 0 Reg Time 100 100 100 100 OT 35 35 35 35 <= 35 Prod constraint Outside 0 0 125 45 170 <= 450 Sourcing constraint Closing Inv 25 0 0 0 >= 0 Available 170 160 260 180 >= >= >= >= 120 160 260 180 Limit Rate Demand fulfilment 100 95 Reg Cost 9500 9500 9500 9500 35/month 125 OT Cost 4375 4375 4375 4375 450/quarter 150 Outside Cost 0 0 18750 6750 10 Inv cost 250 0 0 0 Total cost 81250 Obj Func Min

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