3. (20 points) A highly perishable dairy product is ordered daily at a particula
ID: 396373 • Letter: 3
Question
3. (20 points) A highly perishable dairy product is ordered daily at a particular super market. The product, which costs S1.19 per unit, sells for S1.65 per unit. If units are unsold at the end of the day, the supplier will accept returns for a refund of $1 per unit. Daily demand is assumed to be normally distributed with a mean of 150 units and a standard deviation of 30 units. a. What daily order quantity would you recommend to the super market? b. What is the probability that the super market will sell out of the item? c. How many units would the super market order if the supplier offered only $025 as a d. How would the supplier's and retailer's profits change as the refund changes from S1 to It may be questioned why the supplier has chosen to offer almost a full refund for the product. refund? Or no refund, $0? $0.25 to $0? (use specific numbers to fuel your answer here and assume a supplier production cost of $0. The numbers used can by hypothetical. The interest is in seeing what direction profits move in as the refund amount changes) Which refund amount would you recommend for the supplier'?Explanation / Answer
Co = Overage cost = cost - salvage value = 1.65-1.19 =0.46
Cu= Underage cost = price -cost = 1.19-1 =0.19
Critical ratio = Cu / Co+Cu = 0.19 /0.46+0.19 = 0.19 / 0.65 = 0.2923
z =-0.54 corresponding to this critical ratio.
a. Optimum quantity = mu+zxsigma
= 150+(-0.54)x30 = 133.8 =134
b. Probability that supermarket will sell out of item is (1-0.2923) = 0.7077
c. If the supplier gave only 0.25 as refund
Cu = 1.19-0.25 = 0.94
Co= 1.65-1.19 = 0.46
Critical ratio = Cu / Cu+Co = 0.94 /1.4 = 0.6714
which corresponds to z=0.45
Units to be ordered = 150+0.45x30 =163.5 =164
With no refund. the critical ration will be
1.19 / 1.19+0.46 = 1.19 /1.65 =0.7212
which corresponds to z=0.59
Units to be ordered now is
= 150+0.59x30 = 168
d.
Assuming that suplier's production cost is 0, the profit of retailer with supplier refunding $1 is
Retailer's profit = 0.46 x every unit sold - 0.19 x every unit unsold
Supplier's profit = 1.19 xevery unit sold +0.19 x every unit unsold
Case Ii When supplier refund 0.25 only
Retailer's profit = 0.46 xevery unit sold - 0.94 xevery unit unsold
Supplier's profit = 1.19x every unit sold + 0.94 x every unit unsold
Case III When supplier does not refund anything for unsold items
Retalier's profit = 0.46 x every unit sold -1.19 x every unit unsold
Supplier' profit = 0.1.19xevery unit sold + 1.19x every unit unsold
It can be seen that with refund amount decreasing from 1 to 0, the supplier's profit increases and becoes maximum ( and constant )at no refund policy. The retailer's profit declines with every unsold unit when the refund rates are low.
case I
when 134 units are bought and suppose 130 are sold
Retailer's profit = 130x0.46-0.19x4 = 59.04
Supplier's profit = 130 x1.19 +0.19x4 = 155.46
Case II - When 164 units are ordered and 160 sold then
Retailer's profit = 160x.46 -0.94x4 =69.84
Supplier's profit = 160x1.19 + 0.94x4 =194.16
Case III when 168 units are ordered and 164 sold
Retailers' profit = 164x0.46-1.19x4 = 70.68
Supplier's profit = 168x1.19 =199.92
The supplier needs to give zero refund to achieve the maximum profitability.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.