Regal Department Store runs a large warehouse to receive the merchandise that it then distributes to all its retail stores. Trucks arrive at this warehouse following a Poisson distribution with a rate of one every 5 minutes. Seven loading docks are available at the warehouse. A single worker runs each dock and is able to unload a truck in about 30 minutes on average, exponentially distributed. When all docks are occupied, arriving trucks wait in a queue until one becomes available

Regal has received several complaints from the trucking companies about how long the unloading process takes. In response, Regal is considering a number of options. One option is to hire an extra worker for each unloading dock. This is expected to reduce the average time it takes to unload a truck to 18 minutes, exponentially distributed. It costs approximately $25 in salary and benefits to employ each additional worker.

Alternatively, Regal can continue to use a single worker in each dock, but upgrade the forklift equipment used to unload the trucks. The company can do this at an extra cost of about $30/hour and is expected to reduce the unloading time to about 23 minutes on average, again exponentially distributed.

Finally, the company can build two new loading docks for a capitalized cost each of $22 per hour and hire two additional workers at a rate of $25 per hour each to run these two new locations. Regal estimates that making a truck wait (in line and unloading) costs it $100 per hour in lost goodwill. Which, if any, of these alternatives should it implement?

Answer rating: 100% (QA)

This is MMs queue model with Arrival rate 605 12 per hour Alternative 1 Hire extra worker for each u... View the full answer