Money Back Guarantees

Money-back guarantees

In case returns are allowed in the supply chin, two different scenarios are considered. First, the manufacturer offers to the final customers in case that they are not satisfied with the product to return it directly to the manufacturer (see diagram below). If the customer decide to return the product, he receives partial refund of a*r, where 0 ≤ a ≤ 1. The probability that the customer will return the product is θ. For this scenario, the part of returned products to the manufacturer is θX.

Second, the retailer allows the customers to return the product in case that they are unsatisfied with it (see diagram below). For this case the refund that the customer retains is as in previous case a*r, where 0 ≤ a ≤ 1. After the return of the product to the retailer, the retailer obtains a salvage value for the product from the manufacturer. The expected number of returned products is θX.

It is assumed that the demand is a random variable distributed between 1 and 5. The probabilities for each demand value are given (see table below). The expected demand for the product is calculated in the table E(X) = 1200.

1 2 3 4 5 Expected demand

Xi 1000 1100 1200 1300 1400

qi 0,1 0,2 0,4 0,2 0,1

Product 100 220 480 260 140 1200

In order to find the equilibrium fort he both scenarios, the profits have to be calculated, which the manufacturer, retailer and the channel as a whole would obtain in the both cases.

It is assumed that production costs for the manufacturer are 90. The price for which the product is sold to the final customer is 120. Therefore, the manufacturer has to set his price in the range between 90 ≤ w ≤ 120. It is considered that the probability that the customer would be unsatisfied with the product and would return is 10% (see table below). Two scenarios are assumed, the customer obtains full refund for the returned products (a = 1) and partial refund of the half of the price (a = 0,5).

I) Full refund (a = 1)

The data conserning this case is included in the table below:

Variable Value

c 90

r 120

a 1

a*r 120

teta 0,1

s 90

1) In case that the products are returned directly to the manufacturer, the profits of the participants in the supply chain are as follows:

w Profit OEM Profit R Total Profit

90 -14400 36000 21600

91 -13200 34800 21600

92 -12000 33600 21600

93 -10800 32400 21600

94 -9600 31200 21600

95 -8400 30000 21600

96 -7200 28800 21600

97 -6000 27600 21600

98 -4800 26400 21600

99 -3600 25200 21600

100 -2400 24000 21600

101 -1200 22800 21600

102 0 21600 21600

103 1200 20400 21600

104 2400 19200 21600

105 3600 18000 21600

106 4800 16800 21600

107 6000 15600 21600

108 7200 14400 21600

109 8400 13200 21600

110 9600 12000 21600

111 10800 10800 21600

112 12000 9600 21600

113 13200 8400 21600

114 14400 7200 21600

115 15600 6000 21600

116 16800 4800 21600

117 18000 3600 21600

118 19200 2400 21600

119 20400 1200 21600

120 21600 0 21600

The break even point fort he manufacturer is w = 102. With other words, he