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Passover in Costa Rica Case Solution
During the week of the Passover holiday, Jews all over the world eat a special type of bread called matzah. Costa Rica is a small community in San Rose that consists of approximately 1,000 families. Only one Jewish restaurant in San Jose supplies the matzah bread to the entire Jewish community during the week of Passover. The Jewish restaurant purchases the bread from a Mexican supplier and places the order two months in advance. This report conducts an analysis on the optimal order quantity for the entire supply chain. Furthermore, two different contracts, i.e. revenue sharing, and buyback, have been analyzed in the light of Newsvendor Model.
Following questions are answered in this case study solution
How many boxes of matzah bread should the restaurant order from its Mexican supplier? What would the restaurant’s profit from that order be?
What is the Mexican supplier’s profit from the Costa Rican market? What are the total supply chain profits?
Suppose that the restaurant owner and the supplier were working together to maximize the entire chain’s profits. In that case, what would the optimal ordering quantity of boxes of matzah for the entire supply chain be? What would the total supply chain profits be? What is the supply chain loss (the loss in profit because the supply chain is not coordinated)?
After seeing the results in part (3), the restaurant owner and the supplier would like to create a contractual agreement that will align the incentives in the supply chain with respect to the ordering quantity. The restaurant owner suggests to the supplier that they implement a return policy (buyback contract) in order to reach the supply chain optimum. But the supplier offers a revenue-sharing contract to align the supply chain incentives. Which contract would be better in this case? Why? Assuming they use a revenue-sharing contract, what should be the minimal fraction of revenue the restaurant shares with the supplier for the supplier to prefer this contract to the buyback contract? What would be the buyback price if they used the buyback contract?
Case Analysis for Passover in Costa Rica
1. How many boxes of matzah bread should the restaurant order from its Mexican supplier? What would the restaurant’s profit from that order be?
The demand for matzah bread is expected to lie between 4,000 units to 8,000. The demand probability, as provided in the case study, is shown in Table 1 below. Based on the quantity of demand and the associated probability, the expected value of the demand for the entire season is 6,100 units. Hence, the restaurant should order 6,100 boxes/units of matzah bread from the Mexican supplier.
Moreover, the matzah bread is priced at $20 while the Mexican supplier charges $11 for each box of bread. Hence, the profit for the restaurant from this order would be $54,900. See Table 1 for reference.
2. What is the Mexican supplier’s profit from the Costa Rican market? What are the total supply chain profits?
Since the order quantity from the retailer is 6,100 boxes of bread, the profitability of the Mexican supplier is also calculated using the same quantity. As already mentioned, the price charged by the Mexican supplier is $11. Moreover, the supplier incurs manufacturing cost of $4 while the transportation cost is $1 per box of matzah bread. Hence, the profit to the supplier is $36,600.
Furthermore, the profit to the supply chain would be the end revenue to the retailer minus total cost of material and value additions. As shown in Table 2, the total revenue is $20 x 6,100 = $122,000. Moreover, the overall cost of value addition to the supply chain is $5. This gives the supply chain’s profits as $91,500. It should be noted that the supply chain is also same as the sum of profit to each entity involved in the supply chain. In this case, the supply chain profits of $91,500 is the sum of individual profits to the restaurant and supplier.
3. Suppose that the restaurant owner and the supplier were working together to maximize the entire chain’s profits. In that case, what would the optimal ordering quantity of boxes of matzah for the entire supply chain be? What would the total supply chain profits be? What is the supply chain loss (the loss in profit because the supply chain is not coordinated)?
If the restaurant owner and supplier work together in order to maximize the supply chain profits, the overall supply chain profits will be higher than the uncoordinated supply chain profits. For the purpose of finding the optimal ordering quantity, Newsvendor model of supply chain coordination has been used. Under this model, the selling price and supply chain cost per unit have been taken equal 3 those in the previous question, i.e. $20 and $5 respectively. The salvage value of bread to the retailer is zero (0) as the demand diminishes by the end of the week. Moreover, the overage cost, being the cost of an extra unit of inventory that remains unsold. The overage cost is 5-0 = $5. Furthermore, the underage cost is the cost of each unit of lost sales which is 20-5 = $15 in our case. Using the underage cost of $15 and overage cost of $5, the critical ratio has come out to be 0.75 (underage cost / (underage cost+ overage cost). See Table 3 for reference.
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