Berlin Becker, personnel No. 1002, is a Sales representative in Office 1100, Gro

Question

Berlin Becker, personnel No. 1002, is a Sales representative in Office 1100, Group 300 of Sales Organization No. 1200. He receives orders for the Pump UDP-500, the main product of the Hamburg Plant (No. 1000) of the IDES. After compiling all the orders, he came up with the following aggregate requirements for the next six quarters. Quarter: 1 2 3 4 5 Demand: 1500 5000 8000 6000 3000 Producing one unit costs $25 on regular time of labor hour and $35 on overtime. The current level of inventory is 500 units. Holding one unit in inventory per year costs $3 charged on the average inventory. Shortage cost is estimated as $35 per unit per quarter. Each quarter has 480 hours. The firm has 20 workers now. Each worker can produce 125 units in regular time per quarter. Hiring one worker costs $1000 and laying off costs $2000. Overtime is restricted to 10% of the regular workforce. (Clearly state any assumption you made) Find the aggregate production and workforce planning using Chase, Level and mixed strategy. Which method will provide minimum cost? Develop an Linear Programming (LP) formulation for the aggregate production plan and workforce plan. Solve your formulation. Write a report detailing your production and workforce schedules as obtained from the LP solution.

Explanation / Answer

Please note hiring an extra worker costs = hiring + lay off cost = 1000 + 2000 = 3000 $

each labour produces 125 unit. so each hired labour produces 125 units . But if 125 units are not prodiced in quarter and carried forward to next quarter , then the cost = 125 * 35 ( shortage cost) = 4375 $ which is higher than cost of extra hired labour. So it is not recomended to have shortages in any quarter.

Now opening balance of quarter 1 is 500 units. Demand in quarter 1 is 1500 units. So the balance requirement is only 1000 units. But currently we have 20 workers . Total production by 20 workers = 20*125 = 2500 units. Cost for each unit = 2500 * 25 = 62500 $ . We will ask 10% extra overtime in quarter1 to reduce the burden in next month .

So Say 10% of 2500 units = 250 units . its cost is 250* 35$ = 8750. Total units produced = 3250. Cost of production is 62500 + 8750= 71250$. Total units over produced or closing balance after demand = 1750 units.

Quater 2 : Opening balance = 1750 units ( closing balance of quarter 1 ) . Demand is 5000 units. balance requirement = 5000- 1750 = 3250 Regualr workers produce 2500 +250 ( overtime ) = 2750 units. So the net balance requirement is 3250-2750= 500 units. If we hire extra workers, then the balance demand can be fulfilled.

each extra worker produce 125 units. So for 500 units , we need 500/125 = 4 extra workers. So cost of regular worker with 10% overtime = 71250. Cost of each extra workers = 3000 $ * 4 = 12000 . So total cost to meet the demand = 71250+12000= 83250 $.

In this way we can calculate the cost and demand of workers for rest of the quarters . Following table gives the results.

as none of units held for an year , so there is no holding cost

Quarter Demand Opening Balance workers Units per worker total units 20 workers Overtime work force 10% of 20 extra Qty produced Total QTY produced by regular workers with extra time QTY Requirement as per demand Extra Worker required Total QTY Shortage closing balance Q1 Cost of 20 workers overtime 10% of total work force Hiring and lay off costs per extra worker Total cost of production 1 1500 500 20 125 2500 2 250 3250 0 1750 62500 8750 71250 2 5000 1750 20 125 2500 2 250 4500 500 4 5000 0 0 62500 8750 12000 83250 3 8000 0 20 125 2500 2 250 2750 5250 42 8000 0 0 62500 8750 126000 197250 4 6000 0 20 125 2500 2 250 2750 3250 26 6000 0 0 62500 8750 78000 149250 5 3000 0 20 125 2500 2 250 2750 250 2 3000 0 0 62500 8750 6000 77250

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