Passover in Costa Rica Case Solution

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.