EMGT 3310 OPERATIONS AND PRODUCTION MANAGEMENT FALL 2017 HOMEWORK # 6 (Due at th

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EMGT 3310 OPERATIONS AND PRODUCTION MANAGEMENT FALL 2017 HOMEWORK # 6 (Due at the beginning of class on Tuesday, 11/14) Question 1 ABC is a retailer that carries Easter eggs. The entire demand for Easter eggs occurs within a few days of Easter. ABC buys eggs from a supplier at Sc per egg and sells them at Sp per egg. After Easter, the supplier buys back a fraction fof unsold eggs at Sb per egg. (For example, iff 0.4 and ABC ends up with 100 unsold eggs, then the supplier will pay ABC 40b.) The remaining fraction, l-f, of unsold eggs goes to waste. Assume bcc. a) What is the unit underage cost (cu)? b) What is the unit overage cost (co)? c) Suppose p-1 1, c-3, b=2 andf .5. Also, assume that the demand for Easter eggs is given by the following discrete demand distribution. How many eggs should ABC stock? Demand Probabil 0.2 0.2 0.2 0.2 0.2 10 d) What is the expected number of eggs that ABC will sell to consumers? e) What is the expected leftover of eggs? f) What is ABC's expected profit?

Explanation / Answer

a) cu = $ p - $ c (selling price - cost price)

b) co= $ c - (f * $b) (cost price - salvage cost)

c) Critical ratio = cu / (cu + co)

Q= quantityto store = std dev * z + mean

z calculated from z score table (probaility for z score is the critical ratio calculated by above formula)

Using these formulas:

HEnce, ABC should stock = 2 eggs (rounding off)

d) e)

Expected (lost sales=shortage) in a season = E(max{Demand in a seasonQ, 0}). When the demand is normally distributed with mean m and standard deviation s, the expected lost sales is s×L(z),where z=(Qm)/s and L(z)=normdist(z, 0, 1, 0)z(1normdist(z, 0, 1, 1))

expected demand = m = expected sales+expected lost sales

expectde sales

f) expected sales = 1.13 eggs = 1 egg (rounding off)

storage =2 eggs

cost of 2 eggs = 2* $3 = $6

sales form 1 egg = $ 11

salvage no of eggs = 0.5 * 1 =0.5 = 0 (rounding off)

hence, profit = sakes - cost = 11 - 6 = $5

deamnd probability expected demand (demand*prob) 2 0.2 0.4 4 0.2 0.8 6 0.2 1.2 8 0.2 1.6 10 0.2 2 mean 1.2 std dev 0.63 Critical ratio 0.8 z 0.84 Q 1.731262647

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