Problem Consider a supply chain for fashion products (such as winter shoes). In

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Problem

Consider a supply chain for fashion products (such as winter shoes). In this case, the selling season starts in September and is over by December. The sequence of events in this supply chain is as follows. Production starts 12 months before the selling season, before distributors place any orders with the manufacturer. The distributor places orders with the manufacturer six months after beginning of production. At that time, the manufacturer has completed producing the products while the distributor has received firm orders from retailers. Thus, the manufacturer produces winter shoes prior to receiving distributor orders. Demand for winter shoes follows the following pattern:

?1?The distributor’s pricing and cost information is as follows:

· The distributor sells winter shoes to retailers for $80 per unit.

· The distributor pays the manufacturer $60 per unit. For the manufacturer, we have the following information:

· Fixed cost of production is $75,000.

· The variable production cost per unit equals $50.

· Any winter shoe not purchased by the distributors is sold to a discount store for $25 per pair. How much should the manufacturer produce (consider only the 6 demand values)?

?2? Make-to-Stock (pay-back contract) Refer to Problem 1. Suppose that the distributor offers to pay $15 for each unit produced by the manufacturer but not purchased by the distributor. How much should the manufacturer produce (consider only the 6 demand values)?

?3? Make-to-Stock (cost-sharing contract) Refer to Problem 1. Suppose that the manufacturer and distributor have a cost-sharing contract, in which the manufacturer agrees to decrease the wholesale price from $60 to $50, and in return, the distributor pays 20 percent of the manufacturer’s production cost. How much should the manufacturer produce (consider only the 6 demand values)?

Demand 8,000 10,000 12,000 14,000 16,000 18,000 Probability 0.12 0.15 0.20 0.25 0.18

Explanation / Answer

(1)

Cu = Cost of underage = Payment per item from distributor - variable cost of production = $60 - $50 = $10
Co = Cost of overage = Variable cost of production - Salvage value = $50 - $25 = $25

Critical factor = Cu / (Co+Cu) = 10/(25+10) = 0.286

Optimality will be achieved when the in-stock probability is greater than or equal to the critical factor. In this case, this happens for Demand=12K. So, the optimal production quantity is 12,000 units.

(2)

Cu = $60 - $50 = $10
Co = $50 - $15 = $35

Critical factor = Cu / (Co+Cu) = 10/(35+10) = 0.222

So, the optimal production quantity is 10,000 units as the cumulative probability (0.27) > Critical factor (0.222)

(3)

Cu = $50 - $50*80% = $10
Co = $50*80% - $25 = $15 (the distributor will perhaps share the cost of all items)

Critical factor = Cu / (Co+Cu) = 10/(15+10) = 0.40

So, the optimal production quantity will be 12,000 units (0.47 > 0.40)

Demand Prob Cumulative Prob. 8K 0.12 0.12 10K 0.15 0.27 12K 0.20 0.47 14K 0.25 0.72 16K 0.18 0.90 18K 0.10 1.00

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