Spring 2010, Professor Eckstein

Assignment 3

For each problem below, hand in an algebra formulation, and also solve using Excel and Solver, handing in the standard printouts.

The first two problems may be treated as "process models" along the lines of the
problem covered in class on February 2, although minor modifications to the
analysis might be needed.

**Q1.** (35 points) Problem 23 on page 34 of the course pack
(products A, B, and C). Note that there is no direct cost for any of the
processes in this model (for example, you may treat the costs as 0).

**Q2.** (35 points) Problem 20 on pages 33-34 of the course
pack (SunCo Oil). Note that the cost calculation in this model needs to be
expanded a bit since the costs of the inputs "crude 1" and "crude 2" are stated
separately from the direct costs of processes 1, 2, and 3. You need to
include both kinds of costs.

**Q3. **(30 points) Your
factory makes a single product. You anticipate the following customer
demand and unit production costs costs over the next 6 months:

Month |
Demand |
Unit
Production Cost |

1 | 1050 | $ 23.85 |

2 | 1200 | $ 24.25 |

3 | 1400 | $ 24.90 |

4 | 1175 | $ 25.15 |

5 | 850 | $ 24.35 |

6 | 1100 | $ 23.75 |

You can produce up to 1200 units per month. You can keep the product in inventory, and your maximum end-of-month inventory capacity is 900 units. For each month, your inventory cost is $0.55 times the month's average inventory (which you calculate as the average of the month's beginning and ending inventory). It is now the beginning of month 1, and you have 430 units in inventory. To give yourself some leeway in meeting unknown demands after month 6, you want to end month 6 with at least 200 units in inventory.

Determine how to meet all six month's customer demand at the lowest possible total cost. Note that the inventory cost calculation in this model is somewhat more complicated than the similar model covered in class.