Question

A manufacturer of the famous swimwear line needs help planning production for next year. Demand for swimwear follows a seasonal pattern, as shown below. Given the following costs and demand forecasts

 

Beginning workforce: 12 workers

Beginning inventory: 0

Subcontracting capacity: unlimited

Overtime capacity: 2000 units/month

Production rate per worker: 200 units/month

Regular wage rate : $10 per unit

Overtime wage rate: $20 per unit

Subcontracting cost: $25 per unit

Hiring cost: $150 per worker Firing cost: $250 per worker

Holding cost: $0.75 per unit/month

Backordering cost: $5 per unit/month

a. Level production with overtime and subcontracting, as needed.

b. Level production with backorders as needed.

c. 4000 units regular production from May through September and as much regular, over- time, and subcontracting production in the other months as needed to meet annual demand.

d. Which strategy would you recommend?

Answer 1

MONTH	JAN	FEB	MARCH	APRIL	MAY	JUNE	JULY	AUGUST	SEP	OCT	NOV	DEC
DEMAND	2000	1000	1000	1500	6000	8000	10000	6000	2000	1000	1000	4000

 

Opening workforce: 12 people
Production rate per worker: 200 units/month
No. of workers required each month = Demand each month/200 units (example for January= 2000/200=10 workers)

 

MONTH	JAN	FEB	MARCH	APRIL	MAY	JUNE	JULY	AUGUST	SEP	OCT	NOV	DEC
No. of workers	10	5	5	7.5 or 8	30	40	50	30	10	5	5	20

 

Note that extra number of workers are required only for months May, June, July, August and December. I will be addressing the following questions only for these months as for the rest of the months normal workers with normal wage rates will determine production.

 

a. Level production with overtime and subcontracting
Overtime capacity is 2000 units/ month
existing number of workforce* No. of units each can produce = 12*200= only 2400 units can be produced by existing workers in normal hours. If 4400 units > demand > 2400 units, overtime hours can be utilized.

 

For December, to produce 4000 units, labour cost for 12 workers would be = (2400*10)+(1600*20)= $56,000

Now, for the remaining months, i.e.. May to August, up to 4000 units, the labour cost would be the same ($56,000)

 

Calculations for excess production is as follows (subcontracting cost):
May: 6000-4000 units= 2000 units *25 per unit = $ 50,000
Total cost for May= $ 56,000+ $50,000 = $106,000

June: 8000- 4000 units = 4000*25 = $ 100,000
Total cost for June = $56,000 + $100,000= $ 156,000

July: 10,000-4000 units = 6000* 25 = $ 150,000
Total cost for July = $56,000+$150,000 = $206,000

August: 6000-4000 units = 2000*25 = $50,000
Total cost for August = $56,000 + $50,000 = $106,000

Total cost for these given months by using overtime/subcontracting = $106,000+$156,000+$206,000+$106,000+$56,000 = $630,000

 

b. level production with backorders

Now back orders are excess of demand over production. Pls note that this case arises again only when demand goes above 2400 units in any given month which is the case in months May to August and December. Backorder cost is $5 per unit /month. Let us calculate the backorder cost for these months:

May: Backlog cost = (6000-2400 units)*5 = $18,000
June: Backlog cost = (8000-2400units) *5= $28,000
July: Backlog cost = (10,000 - 2400 units)*5 = $38,000
August: Backlog cost = (6000-2400 units)*5 = $18,000
December: Backlog cost = (4000-2400 units)*5 = $8,000
Total excess cost = $110,000

 

c. If 4000 units produced from May to September

MONTH	JAN	FEB	MARCH	APRIL	MAY	JUNE	JULY	AUGUST	SEP	OCT	NOV	DEC
DEMAND	2000	1000	1000	1500	4000	4000	4000	4000	4000	1000	1000	4000

Annual demand according to original table is 43,500 units. In the table above only 31,500 units are being accounted for. Excess units that have to be adjusted in other months are 43,500 units - 31,500 units = 12,000. These 12,000 units can be adjusted in other months as follows: (note holding inventory per months is $0.75 per unit/month)
May to September demand = 32000 units, production = 20,000 units. Remaining 12000 units have to be produced in months Jan to April by producing extra that what is actually produced. extra 3000 units have to be produced in these months

Jan: demand = 2000, production= 2000+3000
Feb: demand = 1000, production = 1000+3000
March: demand = 1000, production = 1000+3000
April: demand = 1500, production = 1500+3000

Cost
Jan: (2400 units*10)+(2000*20)+(600*25) = $65,500 + holding excess inventory cost (2000*0.75*4)+(1000*0.75*5)= 9750
Total Jan cost = 75250
Feb: (2400 units*10)+(1600*20)+holding excess inventory cost (3000*0.75*4) = $65,000
March: (2400 units*10)+(1600*20)+holding excess inventory cost (3000*0.75*4) = $65,000
April: (2400 units*10)+(1600*20)+(500*25)+holding excess inventory cost (3000*0.75*3) = $75,250

Month	Jan	Feb	March	April	May	June	July	August	Sep	Oct	Nov	Dec	Total
Strategy A	20,000	10,000	10,000	15,000	106,000	156,000	206,000	106,000	20,000	10,000	10,000	56,000	725,000
Strategy B	20,000	10,000	10,000	15,000	42,000	52,000	62,000	42,000	20,000	10,000	10,000	32,000	325,000
Strategy C	75250	65,000	65,000	75,250	40,000*	40,000	40,000	40,000	20,000	10,000	10,000	40,000	480,500

40,000* it is given in the question that 4000 units would be regular production from months May to September. So I have assumed regular wage rate of $10 per unit per month

 

d. which strategy to choose
As you can see, cost is lowest in Strategy B, $325,000. This is because backorder cost is only $5 per unit/month while overtime and subcontracting is more.