Case study: Mr. Pretzel
Mr. Pretzel sells soft pretzels to movie theaters, skating rinks, and snack bars. The company bakes the pretzels in its factory and delivers them fresh daily to its various accounts. Mr. Pretzel has recently signed a contract to purchase 50 pretzel vending machines. Management feels that these machines will enable the company to sell its pretzels in new locations, thus expanding company revenue. Mr. Pretzel's marketing department is busy trying to determine suitable locations for the vending machines. It has decided that, at a minimum, pretzel demand at a vending machine location must average at least 25 units per day. Each vending machine is capable of holding 140 pretzels. The marketing department is interested in determining what compensation it should offer the owners of the sites at which the vending machines will be placed. According to the company's accounting department, the cost of producing a soft pretzel (fixed and variable) is approximately $.32. The pretzels to be sold in the vending machines are sealed in plastic, adding $.005 to their cost. They are delivered daily and sell for $.75. Any pretzels left in the vending machine from the previous day are removed and returned to the factory. There they are ground up and sold for use in cattle feed, for which the company receives approximately $.02 in net revenue from each returned pretzel. The cost of delivering new pretzels and removing old ones is estimated to be $4.20 per vending machine per day. An additional capital cost of $2.50 per day is associated with each vending machine.
If the vending machine runs out of pretzels, there is some likelihood that a dissatisfied customer may kick the machine, causing some damage. Since the company has not had any operating history regarding these machines, it is uncertain of the goodwill and potential damage cost of not having enough pretzels in the machine to satisfy all customers. The company has three different compensation schemes for site owners:
1. Pay the site owner a fixed revenue of $3 per day.
2. Pay the site owner a commission of $.08 per pretzel sold.
3. Lease the vending machine to the site owner with the stipulation that Mr. Pretzel will service the machine. Mr. Pretzel will charge the site owner $3.25 per day for leasing the machine and $.45 apiece for the pretzels. Mr. Pretzel will give no credit for unsold pretzels, and the pretzels have no salvage value to the site owner.
Prepare a management report indicating the expected daily profit to Mr. Pretzel for each compensation plan, assuming daily demand follows a Poisson distribution with means, A, of either 25, 50, 75, or 100 units. Use the normal distribution approximation to the Poisson distribution (μ = λ and σ = Vλ). Assume that if Mr. Pretzel leases the vending machine to the site owner, the site owner will order the optimal number of pretzels from the company. Do the analysis for at least three possible goodwill costs, including $.05, $.25, and $.75.