Question

A manufacturer wants to develop a production plan for the month of February through June. The forecasted demand for those months are 2500, 3700, 3900, 5000, and 2000 units, respectively. The regular-time production capacity in February and March are 3000 units and 2500 units, respectively. The overtime production capacity in February and March are 600 units and 500 units, respectively. The regular production cost is $30 per unit and the overtime production cost is $45 per unit. The cost of holding a unit in inventory is $0.55 per month. The monthly cost of holding inventory is calculated based on the inventory level at the end of the month. The inventory level at the beginning of February is estimated to be 140 units. The manufacture wants to fully satisfy monthly demands. Furthermore, the manufacturer also wants to have at least 50 units in inventory at the end of each month. To simplify, we will only look at the production decision in February and March. We must help the manufacturer to find the most economical production decision without SOLVER. What is the best production decision for the manufacturer? Explain briefly. What is the total production and inventory cost for February and March?

Answer 1

Production required in February = Forecasted demand - beginning inventory + desired ending inventory

= 2500-140+50

= 2410 units

Regular production capacity in February is 3000 units. Therefore, overtime production is not required in Feb

However, demand exceeds the capacity in March, And it is much cheaper to produce more in regular time and hold in inventory, than producing using overtime. Therefore, fully capacity of regular-time production is utilised in Feb to produce 3000 units

Projected ending inventory of Feb = 140+3000-2500 = 640 units

Total production required in March = 3700-640+50 = 3110

However, regular time production capacity in March is only 2500 units.

Shortfall in March = 3110-2500 = 610

To make up for this shortfall of 610 units, 110 units are produced in overtime in Feb and 500 units are produced in overtime in March

Revised ending inventory of Feb = 140+3000+110-2500 = 750

Best production decision for the manufacturer:

3000 and 2500 units to be produced in regulartime in Feb and March respectively

110 and 500 units to be produced using overtime in Feb and March respectively

Total production and inventory cost Feb and March = cost of regular production + cost of overtime production+ cost of inventory

= (3000+2500)*30+(110+500)*45+(750+50)*0.55

= $ 192,890