# Assignments

Textbook questions are from:

Simchi-Levi, David, Xin Chen, and Julien Bramel. The Logic of Logistics: Theory, Algorithms, and Applications for Logistics and Supply Chain Management. 2nd ed. New York, NY: Springer, 2004. ISBN: 9780387221991.

## Homework

### Assignment 1

Answer textbook questions 6.2 and 6.6 and additional homework questions A-1 and A-2.

### Assignment 3

Answer textbook questions 6.1, 6.5, and 6.7.

### Assignment 4

Answer textbook questions 8.4, 8.5, 8.7 and 8.8.

### Assignment 5

Answer textbook questions 10.2, 10.3, and 10.5.

### Case Study

Power-of-Two (PDF)

A-1) A London based company purchases two raw materials from the same supplier. There is a fixed cost of $2.50 associated with each replenishment order, independent of how many items are involved. The purchasing agent feels that because of relatively high cost, he will always include both items in an order. That is, the item replenishments are coordinated. The characteristics of the items are as follows: The demand for item 1 is 2000 units per year and the inventory holding cost is$0.20 per unit per year. Similarly, demand for item 2 is 1000 units per year and the inventory holding cost is \$0.08 per unit per year.

Under the coordinated control, let T be the time in years between replenishments. Find the best value of T and the order quantity for each item. Assume shortage is not allowed.

A-2) In the classical EOQ model assumes that when we order Q units, we receive our order in two parts. The first part arrives immediately and contains αQ (0 < α ≤ 1) and the second part arrives T units of time after the first part and contains the rest of the order ((1−α)Q). If shortage is not allowed what is the optimal order quantity, Q?

A-3) Prove that the worst-case bound for heuristic developed in class for the single-warehouse multi-item model is tight. That is, construct an example for which the cost of the heuristic is twice the cost of the optimal solution.

A-4) Consider a multi-item model with n products, each of which with parameters, Di, Ki and hi. Let αi be the space taken by one unit of product i. The company needs to lease space and ϒ is the annual leasing cost. The objective is minimize the long run average inventory carrying and ordering cost plus a leasing cost proportional to the space needed for the warehouse. Develop a heuristic and analyze its worst-case performance.

#### Learning Resource Types

assignment Problem Sets
notes Lecture Notes