Eric Johnson started the Johnson grocery Company after years ofnot being able to get fresh baked goods in Grand Rapids. JohnsonGrocery originally specialized in cakes, tarts, breads, anddoughnuts sold from Eric’s home. His success with the affluent,gourmet foodies allowed him to expand to a second store within sixmonths and a half-dozen outlets within the first year. He hasexpanded into bagels, salads, and gourmet foods such as ice creamand pet food.
Once Eric got beyond a dozen stores, he moved to a centralkitchen/supply location that restocked his stores. The distributioncenter is causing problems in the form of underutilized employeesand long lines for truck loading.
The loading dock at the distribution center will accommodate onlyone truck for loading or unloading at a time. Company owned trucksarrive according to a Poisson distribution with a rate of fourtrucks per day. Presently, the company employs a crew of three toload and unload the trucks, and the unloading/loading rate isPoisson distributed with a mean rate of five trucks per day. Thecompany can employ additional or fewer persons in the loading crewand increase the loading rate by one truck per day for eachadditional employee up to a maximum of six persons who can beutilized effectively in the process, e.g. a crew of four couldunload six trucks per day or a crew of two could unload four trucksper day. The company estimates that the cost of an idle truck anddriver is $50 per hour and the company pays $15 per hour (fullyfringed) for each employee in the loading crew.
Eric addressed the problem with Linda Froeb, supervisor of theloading crew. Linda hates to see idle workers and she thinksthey’re overstaffed. Barry Bruce supervisors the truck fleet andreported his drivers did not like to wait to be loaded orunloaded
Identify the optimal level of loading/unloading crew .
Is Eric’s business plan the right one to serve hiscustomers?
