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: 1800 5000 8000 6000 2500 Producing one unit costs $30 on regular time of labor hour and $40 on overtime. The current level of inventory is 400 units. Holding one unit in inventory per year costs $5 charged on the average inventory. Shortage cost is estimated as $50 per unit per quarter. Each quarter has 450 hours. The firm has 22 workers now. Each worker can produce 120 units in regular time per quarter. Hiring one worker costs $1500 and laying off costs $2500. Overtime is restricted to 15% of the regular workforce. (Clearly state any assumption you made) 1. Find the aggregate production and workforce planning using Chase, Level and mixed strategy. Which method will provide minimum cost? 2. Develop a Linear Programming (LP) formulation for the aggregate production plan and workforce plan. 3. Solve your formulation. 4. Write a report detailing your production and workforce schedules as obtained from the LP solution. 5. Discuss about any other alternative approaches for this aggregate planning and workforce planning.

Explanation / Answer

Demand is given for the five quarters (not six ) as 1800, 5000, 8000, 6000, and 2500 with total of 23,300.

Production can be using regular and or overtime (restricted to 15% of regular workforce). Each worker can produce 120 units per quarter therefore overtime production may be 18 units per quarter per worker.

There are 22 workers at present, who can produce 13,200 units ( 120*5*22) on regular basis and 1980 units (18*5*22) during overtime for the five quarters.

Holding one unit in inventory per year costs $5 charged on the average inventory. Shortage cost is estimated as $50 per unit per quarter.

Producing one unit costs $30 on regular time of labor hour and $40 on overtime.

Hiring one worker costs $1500 and laying off costs $2500.

Chase strategy implies matching demand and production period by period. Level strategy means constant production for each period and Mixed strategy can have combinations of two or more strategies.

Solution under the chase strategy is as follows:

Should we use OT hours or hire extra worker and work for regular hours only? As hiring cost is $1500 and per unit addition is $12.5 (1500/120) whereas in case of OT additional cost is $10 (40-30), therefore make use of Overtime production. Similarly in case of layoff the cost is more and therefore worker may be preferred for regular time production.

Quarter Q1 Q2 Q3 Q4 Q5 Demand 1800 5000 8000 6000 2500 Opening Inventory 400 40 0 0 0 Regular Production 1440 4320 6960 5280 2280 OT.Production 0 640 1040 720 220 Total Production 1440 4960 8000 6000 2500 Workers required 12 36 58 44 19 Closing inventory 40 0 0 0 0 Average Inventory 220 20 0 0 0 No. of workers Previous 22 12 24 58 44 No. Of workers hired 0 24 34 0 0 No. Of workers layoff 10 0 0 14 25 Cost of Reg.Prod 43200 129600 208800 158400 68400 Cost of OT.Prod 0 25600 41600 28800 8800 Hiring cost 0 36000 51000 0 0 Layoff cost 25000 0 0 35000 62500 Inventory cost 275 25 0 0 0 Total cost 68475 191225 301400 222200 139700

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