Spring 2010, Professor Eckstein

Assignment 10

For each problem, make an Excel model, simulate the situation using YASAI, and hand in the
standard printouts for a
simulation problem.

**Q1.** (30 points) You are operating the pumping
station at the municipal water utility of Westleybrook, NJ. For the coming hour, you
can configure your pumping station in one of three possible ways:

Pump Configuration |
Cost |

1 | $400, plus $1 for each gallon over 900 gallons |

2 | $450, plus $0.80 for each gallon over 1,000 gallons |

3 | $550, plus $0.65 for each gallon over 1,200 gallons |

Water customers in your town use an average of 2 gallons per hour, with a standard deviation of 0.5 gallons. There are 500 customers in your town. However, part of the neighboring town's water system is being repaired, and there is a 30% chance you will also have to supply an additional 200 customers in that town. These customers have the same water use average and standard deviation as customers in Westleybrook. You may assume that each water customer's consumption is independent of all other customers' consumption.

Which pump
configuration will yield the lowest expected operating cost? Use a
simulation sample size of 1000.

**Q2.** (35 points) You own a retail store that sells a
product for $129 per unit. Every time you order the product from your
supplier, it costs you a $79 flat fee, plus $87 per unit. Each day, there
is 12% chance of a traffic jam. On days with no traffic jam, demand has a
Poisson distribution with a mean of 20.8. On days with a traffic jam,
demand is lower, having a Poisson distribution with a mean of 12.1. On
days when you have less inventory than customers, you only sell as many units as
you have in stock, and the additional customers purchase the item from another
store. Otherwise, any inventory left at the end of the day is carried over
to the next day.

You make inventory replenishment decisions each morning when
you open the store: if the amount *S* you have in stock when you open
the store is at or below *R* units, you place an order for *L*
- *S* units (enough to bring the current stock level up
to *L*). If you place an order, it is delivered the following
morning, shortly before you open the store (and is counted as part of the
opening inventory for the next day). You calculate your holding costs to
be $3 per unit of ending inventory per day.

Evaluate all possible combinations
of *R* = 30, 40, 50, or 60 and *L* = 50, 60, 70, or 80. Simulate
a time period of 100 days, with a beginning inventory of 31 units. For all
inventory left in stock or on order at the end of day 100, apply a "salvage"
credit of $110 per unit. With and without this adjustment, which policy gives the
highest adjusted profit? For the policy maximizing expected profit *with*
the adjustment, estimate the probability that the adjusted profit for the 100
days will be at least $75,000. Use a sample size of at least 250 (or up to
1000 if you have a fast enough computer)

**Q3. **(35 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 (or up to 1000, if you have a sufficiently fast computer), 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 your choice of policies to those with an average of at most 0.5 customers giving up per day, which blaster configuration gives you the best profit?