Problem 10 Question Help Sanchez Trucking has been experiencing delays at its wa

Question

Problem 10 Question Help Sanchez Trucking has been experiencing delays at its warehouse operations. Management hired a consultant to find out why service deliveries to local businesses have taken longer than they should. The consultant narrowed down the problem to the number of work crews loading and unloading trucks. Each crew consists of 7 employees who work as a team on a variety of tasks; each employee works a full 40 hours a week. However, costs are also a concern. The consultant advised management that they could supplement work crews with short-term employees, at a higher cost, to cover unexpected needs on a weekly basis. Each work crew permanently hired by Sanchez costs $3,100 per week in wages and benefits, while a crew of short-term employees costs $5,500 per week. Complicating the decision is the fact that the weekly hourly requirements for work crews is uncertain because of the volatility in the number of deliveries to be made. Deliberating with management, the consultant arrived at the following data Requirements (man-hours) Probability Number of crews 840 0.1 1,120 0.4 4 1,400 0.4 5 1,680 0.1 If the consultant wants to offer a solution that minimizes the expected weekly costs for Sanchez, how many work crews should Sanchez have on its permanent payroll? A payroll containing work crews he lowest cost alternative with expected weekly costs o Sanchez o $ nter your responses as integers.

Explanation / Answer

expected number of crews=0.1*3+0.4*4+0.4*5+0.1*6=4.5

Let x be the number of permannet employees

so, weekly cost=x*3100+(4.5-x)*5500=22750-2400x

We see that as x increases, cost would decrease

hence, x=6 (the maximum) expected weekly cost=22750-6*2400=$8350

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