Question

Mildford Trucking inc is located in Chicago, has request to haul 2 shipment, one to st Louis and one to Detroit. Because of a scheduling problem, Mildford will only be able to select one of the assignments. The st Louis customer has guaranteed a return shipment, but the Detroit customer has not.Thus if the management at mildford accept the detroit shipment and cannot find a detroit-to-Chicago return shipment, the truck will return to Chicago empty. The net profit for the st louis round trip is 4,600. the net profit for detroit round trip is 6,000 if there is a return shipmemt, and is 2,000 if there is no return shipmet? the probability of getting a detroit return shipment is 60%( should the management choose the st louis shipment or the detroit shipment)

a) construct a decisin table to represent this problem. which destination should management select 1) be risk prone (optimistic) St louis or Detroit 2) be risk averse(pessimistic) st Louis or detroit 3) maximize value the expected (value) of the payoff? st louis or detroit b) if Detroit is selected and there is no return shipment, what is the opportunity loos to the company? c) if management knew whether or not it could obtain a return shipment from detroit( should the truck go there?) before it had to make its decision, how much would this add to profitability on average?

d)Mildford management can phone a detroit dispatch center and determine if the general detroit shipping activity is BUSY or SLOW(if the report is BUSY, the chances of obtaining a return shipment will increse). the probability of a BUSY response is 60%, Given a Busy response the probability of a return shipment is 75%, given a SLOW response the probability of a return shipment is a 37.5%( should managenet pay the 100 fee for this report? Draw a tree with all payoffs and probabilities to represent this problem.

Answer 1

1. Decision Table

Route	Probability	Profit
St.Louis	100%	4600
Detroit (If return shipment)	60%	6000
Detroit (If no return shipment)	40%	2000

Expected Payoff - StLouis	100%*4600	4600
Expected Payoff-Detroit	60%*6000+40%*2000	4400

1. Risk Prone – Optimistic

If Management is Optimistic, it’ll expect the Detroit route to get return shipment as profit is greater. If it gets return shipment, profit will be 6000. So choose DETROIT route if OPTIMISTIC.

1. Risk Averse – Pessimistic

If Management is Pessimistic, it’ll expect the Detroit route to not get return shipment as probability of return shipment is lower than St.Louis. So choose ST.LOUIS route if PESSIMISTIC.

1. Maximize value of expected Payoff

In this case, we multiply probabilities of outcome with profit of the outcome. For St.Louis its – 100%*4600 = 4600 , while for Detroit its 60%*6000+40%*2000= 4400. Management will choose St.Louis to maximize the Payoff.

1. Opportunity Loss if NO RETURN from DETROIT

In this case, Opportunity loss would be profit it could’ve made on St.Louis trip by getting guaranteed shipment on return rather than returning without shipment from Detroit.

It will be = 4600-2000 = 2600

1. If Management knew whether or not a return shipment will be available

If no return from Detroit = Choose St.Louis = Payoff = 4600

If return from Detroit = Choose Detroit = Payoff = 6000

Currently, it has two alternatives (Detroit/St.Louis) = Probability of each event = 0.5

Detroit has further two alternatives (Return Shipment/No return Shipment)=Probability (0.6/0.4)

From Payoff diagram we see Expected Payoff currently = 4500 (0.5*4600-forSt.Louis + 0.5*4400-forDetroit)

So, it adds on average = (6000+4600)/2-4500= 800

D. If can determine Detroit BUSY or SLOW

BUSY - 0.6*.75*6000= 2700

SLOW- 0.4*.375*6000= 900

Total ExpectedPayoff from return shipment = 3600.

Total Payoff = 3600+800(.4*2000-from Empty Return)= 4400

Since, Detroit route payoff hasn't increased, Management shouldn't pay anything for this report.