Question

Question 1. (Selling grills) Smith and Jackson Inc. (SJ) sells an outdoor grill to Cusano’s Hardware Store. SJ’s wholesale price

for the grill $185. (The wholesale price includes the cost of shipping the grill to Cusano.) Cusanosells the grill for $250 and SJ’s variable cost per grill is $100. Suppose Cusano’s forecast for seasonsales can be described as a Normal distribution with mean 9 and standard deviation 3. Furthermore, Cusano plans to make only one grill buy for the season. Grills left over at the end of the season are sold at a 75 percent discount (on the selling price).

1. How many grills should Cusano order?

2. What is Cusano’s expected profit given Cusano’s order in part a?

3. What is SJ’s expected profit given Cusano’s order in part a?

4. To maximize the supply chain’s total profit (SJ’s profit plus Cusano’s profit), how many

   grills should be shipped to Cusano’s Hardware?

Suppose SJ were to accept unsold grills at the end of the season: SJ gives Cusano a 90 percent credit for each returned grill, that is, SJ pays Cusano $166.50 for each returned grill. Cusano incurs a $15 cost to ship each grill back to SJ. Among the returned grills, SJ finds out that 45 percent of them are damaged and SJ cannot resell them the following season, but the remaining 55 percent can be resold to some retailer for the full wholesale price of $185.

5. How many grills Cusano order to maximize his profit?

6. What is Cusano’s expected profit given Cusano’s order in part e?

7. What is SJ’s expected profit given Cusano’s order in part e?

Answer 1

1)

For Cusano

Unit underage cost, Cu = selling price - wholesale price

= 250 - 185

= $ 65

Unit overage cost, Co = wholesale price - discounted price

= 185 - 250*(1-75%)

= $ 122.5

Critical ratio = Cu/(Cu+Co)

= 65/(65+122.5)

= 0.3467

z-value = NORMSINV(0.3467)

= -0.3943

Number of grills Cusano should order = mean demand + z * std dev of demand

= 9 + (-0.3943)*3

= 7.82

~ 8   (rounded-off)

2)

For order quantity, Q = 8   (as determined in part 1)

z-value = (8-9)/3 = -0.3333

I(z) = 0.2542   (from standard normal table)

Expected unsold inventory, V = 3*0.2542 = 0.76

Expected sales, S = Q - V = 8 - 0.76 = 7.24

Expected profit = S*Cu - V*Co

= 7.24*65-0.76*122.5

= $ 377.5

3)

SJ's profit = Q*(wholesales price - SJ's variable cost)

= 8*(185-100)

= $ 680

4)

For integrated supply chain,

Unit underage cost, Cu = selling price - Sj's variable production cost

= 250 - 100

= $ 150

Unit overage cost, Co = variable production cost - discounted price

= 100 - 250*(1-75%)

= $ 37.5

Critical ratio = Cu/(Cu+Co)

= 150/(150+37.5)

= 0.8

z-value = NORMSINV(0.8)

= 0.8416

Number of grills Cusano should order = mean demand + z * std dev of demand

= 9 + 0.8416*3

= 11.52

~ 12    (rounded-off)

For order quantity, Q = 12,

z-value = (12-9)/3 = 1

I(z) = 1.0833 (from standard normal table)

Expected unsold inventory, V = 3*1.0833 = 3.25

Expected sales, S = Q - V = 12 - 3.25 = 8.75

Expected supply chain profit = S*Cu - V*Co

= 8.75*150-3.25*37.5

= $ 1,190.63