Problem Statement The local appliance superstore offers free delivery and instal

Question

Problem Statement The local appliance superstore offers free delivery and installation within a 30-mile radius of the store. Managers have asked you to set up a process for planning the capacity of the store's delivery and installation resources over the next few months. Currently, two truck crews work out of the store. Considering the cost of labor and fuel and lease payments on the trucks, managers estimate the cost of each two-person crew to be $1,600 per week. The crews typically work a 40-hour week but when needed can work extra 20 hours a week at an hourly overtime rate of S60 per hour. Assume for planning purposes that there are four weeks in every month. Managers can lease a new truck and hire an additional crew for an upfront cost of $1500; the cost of ending the lease early and laying off the crew is estimated at $2,000 Alternatively, managers can hire a trucking company to do the overflow deliveries and installations. In this case, capacity is unlimited, but the cost is a flat $100 per hour, including all labor and equipment costs. Because all deliveries and installations must be completed on demand, back orders are not an option. Deliveries usually average an hour; the time for installation varies, depending on the item to be installed. Stoves and refrigerators take an additional half-hour beyond the hour to deliver them, while satellite dishes require an additional hour and dishwashers three additional hours. Expected demand over the next few months is as follows: Oct Nov |Dec Refrigerators 15 404090808010 170 220 500100 70 Stoves | 30 | 30 | 30 | 20 | 20 | 30 | 40 | 40 120 | 20 | 20 30 Satellite dish 12 10 10 30 30 4040 50 5060 60 100 Dishwasher | 45 45 40 | 40 | 40 | 40 | 40 | 40 | 40 | 30 | 30 30 Appliance/Month Jan Feb Mar Apr May JunJul Aug

Explanation / Answer

Time needed for delivery and installation

Jan = 125x1.5+30x1.5+12x2+45x4 = 436.5

Similarly, the demand for 12 months can be calculated as given in the table. ( In hours)

Cost of the plan =

Regular hours = 4800@ 40 /hr = 192000

Overtime hours = 1406.5@60 /hr = 84390

Hiring cost = 4x1500=6000

Firing cost 3x2000 =6000

Total cost = 288390

Cost of plan 2

no of hours = 6206.5

Cost@100 per hour = 620650

Plan I is better.

Month Jan Feb Mar Apr May June Jul Aug Sept Oct Nov Dec Requirement 436.5 455 435 385 370 405 465 575 770 1020 420 470 No of crew required 2 2 2 2 2 2 2 3 4 5 2 2 regular time 320 320 320 320 320 320 320 480 640 800 320 320 Overtime 116.5 135 115 65 50 85 145 95 130 220 100 150 To be hired 1 0 0 0 0 0 0 1 1 1 0 0 To be fired 0 0 0 0 0 0 0 0 0 0 3 0

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