Calculate expected profit and decision tree, Econometrics

It was shortly before noon. Mr. Zhi-Long Chen, director of Overnight Delivery Operations at Capital Crab and Lobster, Inc.(CCL) in Washington DC, anxiously watched the Weather Channel on his office television. A fall storm was rapidly moving along the Atlantic coast towards DC. If the storm front continued to move north at its current speed, the storm would hit DC at around 5 pm. However many such storms change direction and move out to sea before they reach DC, leaving DC with only minor precipitation. The weather forecaster predicted a 50% chance that the storm would hit DC (at around 5pm) and a 50% chance that the storm would move out to sea and miss DC and the rest of the northern Atlantic states. Zhi-Long Chen was not the only one watching the Weather Channel so attentively. Because there was a chance that DC Regan airport might have to shut down operations if the storm hit, many business travelers were nervously awaiting further weather information as well. Historically, when storms of this magnitude hit DC, one in five are accompanied by severely strong winds that force Regan to close down its operations almost immediately.

CLL and Lobsters

A major part of Capital Crab and Lobster business is overnight delivery of lobsters to restaurants, caterers and consumers in the Northeastern United States. The management at CCL believes that customer service is critical for the success of any business in the food sector and maintaining an excellent reputation for customer service has always been a high priority.

Lobster is so perishable that it must be cooked live. After death, an uncooked lobster's meat rapidly deteriorates. For this reason, lobsters must always be transported live, and this adds significantly to their cost. Live lobsters are packed in special boxes for transport and can live in these special boxes for 36 to 48 hours. It is therefore always necessary transport lobster by overnight air or truck delivery to ensure that it is delivered live to its recipient.

Overnight delivery operations

Customers can order lobsters for next-day delivery any time prior to 5pm on the day before delivery. A typical day's orders amount to approximately 3,000 lobsters that need to be delivered to customers. The staff of the CCL process and pack lobster during the day. At 5:30pm, delivery trucks from the Express Delivery Service (EDS) pick up the packed lobsters and truck them to the Regan airport facility. A special delivery plane takes off from Regan at 6:30pm and flies the packages to a central processing and sorting facility near Boston, MA. At this facility all packages (including the packages from CCL) are sorted and classified by their final destination and transported by air and then local trucks during the night, typically arriving at their destination by 10:30am the following morning.

The price that CCL charges its customers is $30 per lobster. When CCL ships a lobster using EDS, its unit contribution to earnings is close to $10 per lobster. If for any reason due to weather, CCL is not able to deliver a customer's lobster order, it is CCL's policy to notify the customer, to refund the purchase price of the lobster, and to give the customer a $20 discount coupon per lobster, which can be used towards the purchase of a lobster form CCL at any time in the next twelve months. Marketing data has shown that approximately 70% of customers who receive such coupons eventually redeem them. When this happens, customers are typically disappointed that they will not receive their lobster order, but they usually understand the relationship between delivery and weather conditions, and they appreciate the discount coupon.

In the case that CCL cancels their order; the direct cost of canceling the orders is approximately $0.75 per lobster (this includes the cost of contacting customers and part of the packaging that is thrown out). This is in addition to the expected cost from the coupon program.

Plan B

Serous coastal storms that have the potential to close down Regan airport hit DC about ten times per year. However, these storms virtually never threaten inland transportation operations on the ground or in the air. For this reason, CCL has often in the past relied on the services of Maryland air Freight (MAF), which operates out of Gaithersburg Maryland. If contacted before 5:30 pm, MAF will pick up the packaged lobsters from CCL in DC, deliver them by truck to Dulles airport and then fly them to EDS's sorting facility in Boston MA, whereupon EDS will take over the further routing and eventual delivery of the lobsters to customers. The cost of using MAF is variable, but has averaged around $15 per lobster.

CCL has one more option if storms close down Regan, they could use a truck delivery company. However they need to notify the company; Easter Parcel Delivery (EPD) by noon in order for them to hold trucks for CCL. There are two issues with using EPD. First, CCL would need to commit to using trucks by noon, well before they would know additional information about the storm. Second, truck delivery via EPD is more costly than delivery via air using EDS. The additional incremental cost of using EPD over EDS is $3.

The decision scenario

It is now 11:30am. If Zhi-Long were to choose to transport the lobsters by truck using EPD, he would have to make the arrangements almost immediately. If he chose not to use EPD, he could wait and see if the storm hit DC, and if the storm forced Regan to close down. If the storm were to hit DC, it would do so at around 5pm and Regan would either close immediately or not at all, depending on the severity of the winds.

If the storm were not to hit DC and/or the storm were not to close down Regan, Zhi-Long would presumably know this by 5:30 and could go ahead with CCL's regular plan of using EDS. If the storm closes Regan, Zhi-Long would also know this by 5:30pm and he would then face the decision of whether to cancel the customers' deliveries altogether, or to transport the lobsters via MAF to Dulles Airport and on to EDS sorting facility.

The assignment:

a) What is CCL's profit per lobster if they deliver using EPD?

b) What is CCL's profit per lobster if they need to utilize MF (in addition to EDS) for the delivery of lobsters?

c) Construct a decision tree in Precision Tree for the analysis of this decision scenario. Include a printout (or a drawing if you prefer to implement the tree by hand) of the full tree, marked as Exhibit 1-A. (HINT: Base your tree on a single lobster).

d) What is the expected profit per lobster given the current weather conditions?

e) Describe in a few words the optimal policy below. Include a printout of the optimal policy, marked as    

f) What should be CCL's long term strategy when faced with weather conditions similar to those described in the case?

Posted Date: 3/7/2013 5:11:16 AM | Location : United States

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