Simulating a Production/Inventory Problem
Management of Ebony, a leading manufacturer of bath soap, is trying to control
inventory costs. The weekly cost of holding one unit of soap in inventory is $30 (one
unit is 1000 cases of soap). The marketing department estimates that weekly demand
averages 120 units, with a standard deviation of 15 units, and is reasonably modeled by a
normal distribution. If demand exceeds the amount of soap on hand, those sales are lost that is, there is no backlogging of demand. The production department can produce at
one of three levels: 110, 120, or 130 units per week. The cost of changing production
from one week to the next is $3000. Management would like to evaluate the following
production policy. If the current inventory is less than l = 30 units, then produce 130
units in the next week. If the current inventory is greater than u = 80 units, then produce
110 units in the next week. Otherwise, continue producing at the previous week’s
production level. Ebony currently has 60 units of inventory on hand. Last week’s
production level was 120 units.
A
Create a spreadsheet to simulate 52 weeks of operation at Ebony. Graph the
inventory of soap over time. What is the total cost (inventory cost + production
change cost) for the 52 week period?
B
Use a simulation of 200 trials to estimate the average 52 week cost with values of
u ranging from 30 to 80 in increments of 10. Keep l = 30 for each trial. Calculate
the mean and standard deviation of the 52 week cost under each policy. Using
those results, construct 90% confidence intervals for the average 52 week cost for
each value of u. What is the best policy?