Problem:
Bushwood Supermarkets is a major food retailer in the Philadelphia area. The chain has over 60 stores that receive merchandise from their Scranton, Pennsylvania warehouse. The warehouse receives shipments of merchandise throughout the day from the various vendors and manufacturers with whom Bushwood does business.
The Scranton warehouse has eight loading docks available for delivery of goods. Trucks arrive at the warehouse approximately once every six minutes according to a Poisson process. If all the loading docks are occupied, an arriving truck waits in a queue until a dock becomes available.
Currently, each dock is staffed by a single worker, who unloads a truck in an average of 30 minutes. Bushwood management had been getting complaints from some of its suppliers that their truckers are spending too much time unloading merchandise at the Scranton warehouse. Hence Bushwood has come up with a number of possible strategies to address this problem: (1) hire a second worker for each loading dock, reducing the average time to unload a truck to 18 minutes (workers earn $16 per hour in salary and benefits); (2) equip each loading dock with an electric forklift that can be leased for $5 per hour and reduce the time required to unload a truck to an average of 24 minutes; or (3) build two more loading docks (accounting for capital costs, each additional dock will cost Bushwood $6 per hour).
While strategies 1 and 2 are mutually exclusive, the firm may decide to implement strategy 3 either alone or in combination with 1 or 2. Thus possible options include Strategy 1, Strategy 2, Strategy 3, Strategy 1 &3, Strategy 2&3. Bushwood estimates the goodwill cost of a delivery truck being in the system at $60 per hour.
Required:
Question 1) Prepare your recommendation for Bushwood if their objective is to minimize costs. Assume that service times for each option follow exponential distributions. Explain the solution in detail.