15. Jill, the office manager of a desktop publishing outfit, stocks replacement

Question

15. Jill, the office manager of a desktop publishing outfit, stocks replacement toner cartridges for laser printers. Demand for cartridges is approximately 30 per year and is quite variable (i.e., can be represented by the Poisson distribution). Cartridges cost $100 each and require 3 weeks to obtain from the vendor. Jill uses a (Q, r) approach to control stock levels. (a) If Jill wants to restrict replenishment orders to twice per year on average, what batch size Q should she use? Using this batch size, what reorder point r should she use to ensure a service level (i.e., probability of having the cartridge in stock when needed) of at least 98 percent?

Explanation / Answer

One of the performance measure of a (Q,r) model is

Average Order Frequency F(Q,r) = D/Q.

Where Q = Order Quantity and D = Demand.

1) Using this above equation of Average Order Frequency F we can solve and get the Batch Size as per the problem given as follows.

Given that, D = 30/year, F = 2/year

Therefore, Q = D/F = 30/2 = 15 Quantities.

2) But, if Jill wants to restrict replenishment orders to 6 times per year on average, then the batch size Q should be as follows.

D = 30/year, F=6/year

Then, Q = D/F = 30/6 = 5 Quantities.

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