Advanced Operations Management (33:623:400), Professor Eckstein, Fall 2006
Homework Assignment 8, Due December 7

Q1.  Suppose that for each of the next seven days the probability distribution of demand for a product is as follows:

Demand   Probability
0   0.1
1   0.3
2   0.3
3   0.2
4   0.1

You can store up to 12 units of inventory, and you can produce up to 6 units of inventory per day.  Your production costs consists a $10 setup charge for each day you have non-zero production, plus a unit cost of $3.  Holding cost is $0.50 per unit per day, assessed on the amount of inventory left over at the end of the day.  Any inventory left over at the end of the seventh day are sold for salvage, yielding $2 per unit.  Assuming that you have 3 units of inventory at the start of day 1, find the cheapest way to meet all possible customer demands through day 7.  Hint: make relatively minor modifications to the JavaScript programs prob-inventory.html or prob-inventory-big.html on the class website.
 

Q2.  For the next 12 months, you have forecast the following expected demand for a product:

Month   Expected Demand
1   4.5
2   4.9
3   5.1
4   4.8
5   4.2
6   3.4
7   3.1
8   3.0
9   3.2
10   4.0
11   4.2
12   4.3

In each month, you model demand as having a Poisson distribution; for example, in month 3, you model demand as a Poisson random variable with mean 5.1.  Assume that your inventory and production capacity are both 10 units.  Costs and revenues are as follows:

Production setup cost:   $1000 for each period with production
Variable production cost:   $400 per unit
Holding cost:   $75 per unit per month, assessed on month-end inventory
Salvage value:   $200 per unit
Revenue:   $900 per unit sold.

You have the option of producing amounts that might not meet demand, or might overflow your inventory capacity.  Each month you can satisfy any amount of demand up to your starting inventory plus your production.  If demand is higher than that, you simply do not get the revenue for the unsatisfied part of demand.  If your month end inventory exceeds your capacity of 10, any surplus is immediately sold for its salvage value. 

Assuming that you have no starting inventory, find the production policy that yields the highest expected profit for the next 12 months.  Assume any inventory left over after 12 months is sold at the salvage value.  Hint: make much more extensive modifications to the JavaScript programs prob-inventory.html or prob-inventory-big.html on the class website.  To calculate Poisson probabilities, use the function at the beginning of the planebook.html program on the class website (use the most recent version).
 

Q3.  Download the spreadsheet hwk8q3data.xls from the class website.  It shows the number of calls to a customer service center over the span of 6 weeks.  Predict the number of calls for the seventh week using each of the following methodologies:

  1. Additive Holt-Winter
  2. Multiplicative Holt-Winter (with an additive trend and multiplicative daily/seasonal factors)
  3. Linear regression, using a linear trend and day-of-week additive adjustments
  4. Linear regression to logarithms (with a trend and day-of-week adjustments)
  5. Regression with a linear trend and multiplicative day-of-week adjustments

For each, hand in a spreadsheet showing (along with anything else you need):

Formula printouts are not required, but might be helpful for me to diagnose mistakes.