Activity: building the exchange curve as a class
Chapter 4, Multi-Item and Constrained Systems
Work in pairs, then as a class. 20 minutes.
Names: ______________________________________________
The group. Five items the storeroom buys under one carrying charge, \(\gamma = 0.20\) a year, and one ordering cost \(k\) for all five. Demand is constant and known.
| Item | \(\lambda_j\), a year | \(c_j\) |
|---|---|---|
| P-1 | 2,000 | $20.00 |
| P-2 | 900 | $25.00 |
| P-3 | 4,000 | $2.50 |
| P-4 | 160 | $40.00 |
| P-5 | 1,440 | $2.50 |
Your pair’s ordering cost. The instructor gives your pair a letter.
| Pair | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| \(k\) | $2.50 | $10.00 | $22.50 | $40.00 | $90.00 | $160.00 |
Part A. Predict
Pair D’s ordering cost is four times pair B’s. How will pair D’s cycle stock compare with pair B’s, and its number of orders a year?
Part B. Your point
- For each item compute \(Q_j = \sqrt{2k\lambda_j/(\gamma c_j)}\), the cycle stock \(c_jQ_j/2\) and the orders a year \(\lambda_j/Q_j\).
- Sum to the aggregate cycle stock \(\bar{I}^{a}\) and the aggregate replenishments \(N^{a}\). Check: \(\bar{I}^{a}/N^{a}\) must equal \(k/\gamma\).
- Post your point on the class plot, and mark every pair’s point on the grid.
Plot on graph paper, with \(N^{a}\) from 0 to 120 across and \(\bar{I}^{a}\) from 0 to $12,000 up.
Part C. The storeroom’s practice
The storeroom places 40 orders a year across this group and carries $6,000 of cycle stock.
- Is its point on the class curve? Compute \(\bar{I}^{a}N^{a}\) for the curve and for the practice.
- At 40 orders a year, how much stock does the curve need? At $6,000, how many orders? What can the storeroom gain, and what must it give up?
- A colleague reads the practice as \(k/\gamma = 6{,}000/40 = 150\). What is wrong with that reading?
- Purchasing puts \(k\) at $40. Where on the curve should the storeroom operate, and what would it save a year in ordering plus holding cost?
Part D, if you have time. A second storeroom
Another storeroom with the same five items sits on the curve at 59 orders and $2,950. What ordering cost does its practice imply? Its purchasing department says $40 an order. Which way should it move, and what is the move worth a year?
Exit ticket (tear off and hand in)
Name: ____________________
- On the curve, why can a storeroom not order more often without holding less stock?
- True or false, and why: a storeroom above its curve must accept more orders to carry less stock.