Question

1. ABC Company needs to plan workforces and production levels for the six-month period of January to June to produce the famous ABCzappers. The following table shows forecasted demand for zappers. At the end of December there are 200 workers employed. Ending inventory in December is expected to be 500 zappers, and management would like to have 750 zappers on hand at the end of June. The cost of hiring one worker is expected to be $500, the cost of firing one worker is expected to be $1,000, and the cost of holding one zapper in inventory for one month is estimated to be S10. In the past, in a 46 working-day period of time, 174 workers produced 8,000 zappers Feb 2,750 Mar 2,400 Ma 3,750 June 3,500 an Demand forecast Number of working days 3,500 4,600 24 25 26 20 a) If ABC plans production using a chase strategy (zero inventory plan), what workforce and production plan should we use? b) What are the total hiring/firing and inventory holding costs for this plan? c) If ABC plans production using a constant workforce plan (equal workforce levels for January through June), what workforce and production plan should we use? d) What are the total hiring/firing and inventory holding costs for this plan? e) Develop a mathematical programming model of the problem

Answer 1

Worker productivity = 8000 zappers produced / (46 working days * 174 workers) = 8000/(46*174) = 8000/8004 ~ 1 zapper per worker per day

a) Chase Strategy - In this strategy workers are hired and fired to match the exact demand as much as possible.

Worker productivity = 8000 zappers produced/(46 working days * 174 workers) = 8000/(46*174) = 8000/8004 assymp 1 zapper per worker per day Chase Strategy - In this strategy workers are hired and fired to match the exact demand as much as possible. Formula: C6 = B6+ C5-C2�copy to C6: H6 C10 = B10+ C8-C9 copy to C10: H10 J12 = SUMPRODUCT(I6: I9, J6: J9) b) Total hiring/firing and inventory holding cost for this plan = $�178,940 c) Constant workforce plan - In this plan, workers are hired or fired at the beginning of the planning period and thereafter, workforce is held constant throughout the planning period. Total demand over 6 months period = (3500+ 2700+ 2400+ 4600+ 3750+ 3500) = 20450 Net requirement = Total demand - Initial inventory + Inventory required at the end of planning period = 20450-500+ 750 = 20700 Total working days in the planning period = 22+ 24+ 25+ 26+ 22+ 20 = 139

Formula:

C6 =B6+C5-C2 copy to C6:H6

C10 =B10+C8-C9 copy to C10:H10

J12 =SUMPRODUCT(I6:I9,J6:J9)

b) Total hiring/firing and inventory holding cost for this plan = $ 178,940

c) Constant workforce plan - In this plan, workers are hired or fired at the beginning of the planning period and thereafter, workforce is held constant throughout the planning period.

Total demand over 6 months period = (3500+2700+2400+4600+3750+3500) = 20450

Net requirement = Total demand - Initial inventory + Inventory required at the end of planning period = 20450-500+750 = 20700

Total working days in the planning period = 22+24+25+26+22+20 = 139

Therefore, level workforce required = 20700/139 = 149

Hence, number of workers to be fired in Jan = 200-149 = 51

Resulting plan is as follows:

d) Total cost of level workforce plan = $ 128,060

e) Mathematical model

Let Hi, Fi, Wi be the number of workers hired, fired and working in month i

Pi and Vi be the production and inventory in month i

Min ?Vi*10 + ?Hi*500 + ?Fi*1000

s.t.

P_i + V_i-1 - V_i = D_i , where Di is the demand in month i

V0 = 500

V6 >= 750

Vi >= 0

W_i = W_i-1 + H_i - F_i

P_i = n_i*W_i, where ni is the number of working days in month i

All variables >= 0