Suppose you own an electronics store that sells a video game system, with the po

ID: 3042676 • Letter: S

Question

Suppose you own an electronics store that sells a video game system, with the potential for sales of 0, 1, 2, or 3 units each day with respective probabilities .3, .4, .2, and .1. At the close of business new units can be ordered which will be available when the store opens in the morning. Suppose the sales produce a prot of $12 but it costs $2 per day to keep an unsold unit overnight. Further suppose you decide to reorder up to 3 units only after your inventory reaches 0 units. Compute your expected prots per day with this inventory strategy. (Hint: E[prots] = E[revenue]E[costs]. Be careful when computing average revenue for each day, as sometimes you won’t have enough units to meet demand!)

Explanation / Answer

Let Order Quantity be represented by Q, Demand by D and probability of demand by Pr.

The following Table presents the profit for various Q-D combinations and E(P), the expected profit at each level of Q.

E(P)

-(1 x 2)= - 2

(1 x 12)= 12

7.8

-(2 x 2)= - 4

(1 x 12)-(1 x 2)= 10

(2 x 12)= 24

10.0

-(3 x 2)= - 6

(1 x 12)-(2 x 2)= 8

(2 x 12)-(1 x 2)= 22

(3 x 12)= 36

9.4

0.3

0.4

0.2

0.1

Thus expected profit per day are:

Order Quantity: 0 1 2 3

Expected Profit: 0 7.8 10.0 9.4 ANSWER

Concept Back-up

Profit = 12Q if Q D

= 12D – {2(Q - D)} if Q > D.

DONE