[SOLVED] MJ Logistics has decided to build a new warehouse to support | SolutionInn

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Problem Overview

MJ Logistics must choose between building a large ($8 million) or small ($3 million) warehouse. Profitability depends on high or low future demand, with a 60% chance of high demand according to company assessment.

Decision Tree Analysis

A decision tree will help MJ Logistics to visualize and analyze the potential outcomes of each decision (building a large or small warehouse), given the probabilities of high and low demand and the corresponding profits.

Expert Opinion

An economic expert is consulted, offering a 70% chance of high demand, with a 75% accuracy rate for upside predictions and a 90% accuracy rate for downside predictions. This expert opinion will refine the decision-making process. The best strategy will be determined based on whether the expert predicts economic improvement or deterioration.

Probability Revision

The probability of high volume demand needs to be recalculated, considering the expert's prediction and the accuracy rates of their forecasts. Bayes' theorem or a similar method will be needed for this.

Question: MJ Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse

MJ Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse or a small one. Construction costs for the large facility are $ 8 million versus $ 3 million for the small facility. The profit ( excluding construction cost) depends on the volume of work the company expects to contract for in the future. This is summarized in the following table ( in millions of dollars):

The company believes that there is a 60% chance that the volume of demand will be high. a. Construct a decision tree to identify the best choice.

b. Suppose that the company engages an economic expert to provide an opinion about the volume of work based on a forecast of economic conditions. Historically, the expert’s upside predictions has been 75% accurate, whereas the downside predictions have been 90% accurate. In contrast to the company’s assessment, the expert believes that the chance for high demand is 70%. Determine the best strategy if their predictions suggest that the economy will improve or will deteriorate. Given the information, what is the probability that the volume will be high?

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Large warehouse Small warehouse High Volume $35 $25 Low Volume $20 $15