For each problem, make an Excel model, simulate via YASAI, and hand in the
standard printouts for a
simulation problem.
Q1. (50 points) Your store sells a product for which the daily demand is Poisson with an average value of 10. The product sells for $50, and (because it requires special environmental conditions to store) the holding cost is $3.50 per unit per day. Every time you order the product, your costs are as follows:
There is a one day "lag" after an order is placed: for example, an order placed at the end of day 1 will arrive at the beginning of day 3. If you run out of stock, sales are lost.
Your ordering policy is as follows, described by two parameters R and L:
On day one, you have a starting inventory of 43, and you have not ordered in the previous two days. Using a period of 100 days and a sample size of at least 250, experiment with all combinations of
Which gives the highest profit? Give your answer both with and without
a $25/unit "salvage" correction, applied to all units in inventory
during the last day and ordered in the last two days.
Q2. (50 points) You have just taken over management of the local "Roto-Blaster" franchise, which performs emergency drain cleaning. Based on data from the previous management, the number of requests for service you receive each day appears to have Poisson distribution with an average value of 8.5. You receive $179 for each service call you answer.
You can arrange long-term contracts to lease two kinds of equipment, regular blasters and super blasters. A regular blaster costs $275/day to lease and can serve up to 3 calls per day. A super blaster cost $415/day to lease and can serve up to 5 calls per day. You are considering all 9 possible combinations of leasing either 0, 1, or 2 regular blasters and 0, 1, or 2 super blasters (the 0/0 option means essentially shutting down the business).
Depending on how many of each kind of blaster you lease, you may not have enough capacity to service all the customers who might call on a given day. Historical records suggest that each customer who wants service, but is not served by the end of the day, has an independent 43% chance of "giving up" and finding another firm to resolve their problem. The rest remain with you and try to obtain service the next day.
Using a sample size of at least 500, simulate a 100-day period.
Which blaster configuration should you lease to obtain the highest average profit? With this arrangement, what is the average number of customers giving up per day? If you limit the average number of customers giving up per day to 0.5, which blaster configuration gives you the best profit?