A food truck vendor needs to schedule the delivery of water bottles for a 10-day period. Two options are on the table, a daily frequency, or one delivery every other day. Besides the purchasing cost, the vendor has to pay a flat fee of $10 per delivery, so he clearly prefers the second option. However, that would increase inventory which, given the limited space of the truck, is an inconvenience. Although water bottles do not lose value over time, the vendor has estimated an inconvenience cost of $.10 per bottle, per day. Based on this, the vendor would now prefer the first option, so that he can also save room for more profitable food products and kitchen utilities. As of now the vendor has 73 bottles in stock, and he as to communicate his frequency option choice to the supplier, along with a delivery order quantity, to be kept the entire period. Bottles come in cases of 50, so given that he estimates a daily demand uniform between 80 and 100 units and wishes a fill rate of at least 90%, he needs to figure out how many (up to four) cases to order per delivery and their frequency starting on day one.
a. What are the model's objective, decision variable(s) and tradeoffs?
b. How many parameters are there? Which are deterministic? Which are stochastic (random)?
c/d/e. What is/are the optimal decision(s)? Show as many tables as you want, including a description of all the results and the simulation runs that may be needed to prove the solution.