CleanU Inc. produces different models of vacuum cleaners. It wants to plan ahead
ID: 367221 • Letter: C
Question
CleanU Inc. produces different models of vacuum cleaners. It wants to plan ahead for the months starting from January to June 2012 in order to effectively address the seasonal variation appearing in the annual demand of its products. The (aggregate) demand forecast for the six months (Jan –June 2012) along with the number of working days are as follows:
Month
Jan
Feb
Mar
Apr
May
Jun
Demand
4500
5500
7000
10000
6000
5500
Days
22
19
21
21
22
20
VCleanU has estimated the following costs during the planning horizon.
Materials $20/unit
Holding costs $5/unit /month
Backorder cost $8/unit/month
Hiring cost $3000/worker
Layoff cost $5000/worker
Straight time labor cost $10/hour
Overtime labor cost $15/hour
Subcontract cost $17/hour
The past experience shows that a worker takes 30 minutes to produce one unit.
VCleanU works on 8 hour shift in each working days. VCleanU expects that there will be 15 workers working in December 2011. Its current planning shows that there will be 250 units available in the inventory at the end of December 2011 and it wants to have at least 400 units in inventory at the end of June 2012. VCleanU is restricted that the overtime production cannot exceed 20% of the regular production in each month.
A) For an LP Model what are the decision variables, objective function, and constraints? (Just write these out. No excel)
Month
Jan
Feb
Mar
Apr
May
Jun
Demand
4500
5500
7000
10000
6000
5500
Days
22
19
21
21
22
20
Explanation / Answer
A) LP model is as follows:
Decision variables:
Hi = Number of workers hired in month i
Li = Number of workers laid off in month i
Wi = Number of workers available in month i
Ri = Regular time production in month i
Oi = Overtime production in month i
Si = Subcontracting units in month i
Ei = Ending inventory of month i
Bi = Backorder units of month i
Objective: Minimize 3000*Hi + 5000*Li + 5*Ei + 8*Bi + 20*(Ri + Oi + Si) + (10/2)*Ri + (15/2)*Oi + (17/2)*Si for i = 1 to 6
(note that it takes 30 mintes to produce one unit. So labor cost per unit is half of hourly labor cost, hence straight time cost, overtime cost and subcontract cost are divided by 2 in objective function)
Constraints:
R1 + O1 + S1 + 250 - E1 + B1 = 4500
R2 + O2 + S2 + E1 - E2 - B1 + B2 = 5500
R3 + O3 + S3 + E2 - E3 - B2 + B3 = 7000
R4 + O4 + S4 + E3 - E4 - B3 + B4 = 10000
R5 + O5 + S5 + E4 - E5 - B4 + B5 = 6000
R6 + O6 + S6 + E5 - E6 - B5 + B6 = 5500
E6 >= 400
Oi <= 0.2Ri (for i=1 to 6)
R1 = 22*8*2*W1 (considering productivity per worker per month = days in month * working hours per day / standard time (0.5 hour)
R2 = 19*8*2*W2
R3 = 21*8*2*W3
R4 = 21*8*2*W4
R5 = 22*8*2*W5
R6 = 20*8*2*W6
15 + H1 - L1 = W1
W1 + H2 - L2 = W2
W2 + H3 - L3 = W3
W3 + H4 - L4 = W4
W4 + H5 - L5 = W5
W5 + H6 - L6 = W6
Hi, Li, Wi, Ri, Oi, Si, Ei, Bi >= 0
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