solv The demand for a product over the next 3 quarters is 350, 750 and 550 units

Question

solv

The demand for a product over the next 3 quarters is 350, 750 and 550 units, respectively. The manufacturer supplying the product has different productions capacities estimated at 400, 500 and 200 for the three quarters respectively. The production costs per unit for the three periods is fixed and is equal to $300 per unit. Back-ordering is not allowed, but the manufacturer may use overtime to fill the immediate demand, if necessary. The overtime capacity for each period is half the regular capacity. The overtime production cost per unit is 60% higher than the regular production cost. If a product is produced now for use in later periods, an additional storage cost of $100 per unit per quarter is incurred. Formulate the problem as a transportation model and draw the transportation tableua. Find the northwest starting solution of the model.

Explanation / Answer

Demands for 3 QTRS are : { 350,750 and 350} Production capacity is 400,500 and 200. There are 2 sources of Production in each quarter. Regular Time and Overtime. Overtime Capacity in all 3 quarters will be 200 , 250 and 100.

Production cost in each month: Regular Time = $300/unit. Overtime = $ 560/unit and Inventory holding cost = $100/unit/quarter.

For Nortwest Starting solution

$728000

QTR 1 QTR 2 QTR 3 SUPPLY REGULAR PRODUCTION 400 500 200 1100 OVERTIME 200 250 100 550 DEMAND 350 750 550 1650

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