Question: Safty Circuits Inc. stocks and sells small electronics products using an (R, S) type of control system. A manager reviews the stock monthly. The supplier

Safty Circuits Inc. stocks and sells small electronics products using an (R, S) type of control system. A manager reviews the stock monthly. The supplier delivers at their location following a lead time of 10 days. Inventory carrying charge is 0.12 $/$/year. The manager has observed that demand for the XRL line is as follows:

Item (i) Demand (Di) (Packs/year) i,1 (Packs)
XLR-1

1200

35
XLR-2

350

50
XLR-3

700

40

where i,1 is the standard deviation of yearly demand for item i. Suppose that a TSS of $1,200 is to be allocated among the three items. Consider the following service measures:

1. Same k for the 3 items

2. Same P1 for the 3 items

3. Same TBS for the 3 items

4. Same B1 for the 3 items

5. Same B2 for the 3 items

For each, determine:

a. How the $1,200 is allocated among the three items?

b. ETSOPY (expected total #stock-outs per year)

c. ETVSPY (expected total value short per year)

Note: Assume that forecast errors are normally distributed and the same r value is applicable to all three items. Negative safety factors are not permitted.

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