Draw a decision tree and recommend a decision strategy

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Reference no: EM133684370

Business Analytics and Data Intelligence

Learning Outcome 1: Demonstrate advanced and integrated understanding of business and data Intelligence for organisational decision-making.
Learning Outcome 2: Analyse critically, reflect on and synthesise techniques of data visualisation and data mining.

Assignment Description:

The assignment is designed to allow you to demonstrate effective business analytics skills using optimisation methods. You will need to use linear programming and decision making skills to conduct the analytics and obtain the solutions. This is and individual assignment and each student will work independently.

Problem 1:

ABC is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium- and high-priced golf bags standard and deluxe (S and D). The two main operations needed to make the bags are cutting and sewing. For each S bag cutting takes 5 hours, sewing takes 8 hours, and 9 ounces of leathers is required. For each D bag, cutting takes 4 hours, sewing takes 6 hours, and 15 ounces of leathers is required. The estimated profit for each S bag and each D bag sold are $250 and $110, respectively.

ABC estimates that for one of their stores each hour of overtime for cutting will cost $14 and each hour of overtime for sewing will cost $15. The overtime cannot exceed 250 hours for this store. The available time for cutting and sewing are 450 hours and 680 hours, respectively. The amount of leather available is 2,600 ounces. For this store, the minimum demand for S and D bags are 100 units and 95 units, respectively.

ABC, aims to maximise the profit from selling in their new store. Sensitivity analysis table produced after solving the problem is as below:

Given above information answer the following questions:

Formulate the LP model for ABC

Define shadow price in your own words. Why are some shadow prices equal to 0 in the sensitivity analysis report?

If the company decides to increase 20 hours for either cutting or sewing, which one should they choose? Why?

If ABC's supplier could only deliver 90% of the leathers, what would be the impact on the optimal solution?

Based on the sensitivity analysis report, identify two ways that ABC can increase the total profit without adjusting any objective function coefficients?

Problem 2

Market Fresh Melbourne is considering signing a new contract with A or with a local B farm for daily supplies of fresh vegetables. Market Freshmust decide to sign the contract with A or signing a contract with B, but if company signs with B, profits will not be as high in comparison to A. If any contract is rejected, it is assumed that there will be a quantifiable cost to the store. Market Fresh Melbourne wants to maximise the profits as are summarised in the following payoff table (in thousands of Australian dollars).

Apply the Opportunity Loss Approach (with the minimax regret criterion) to recommend a decision to Fresh Food Melbourne.

Market Fresh Melbourne made an initial assessment on what A and B may do and came up with the following probabilities:

A: P(Reject) = 0.4, P(3 Years) = 0.4, P(5 Years) = 0.2 B: P(Reject) = 0.1, P(3 Years) = 0.2, P(5 Years) = 0.7

Draw a decision tree and recommend a decision strategy on whom she should sign the contract with. Show your calculations and provide a justification for your decision strategy.

If Market Fresh Melbourne wants to get more information from the market it will cost $2,000. Overall chances of a favourable outcome to Market Fresh Melbourne is denoted by F, and unfavourable review by
U. The following conditional probabilities are realistic.

Apply Bayes' Theorem to compute the posterior probabilities for both the Favourable and Unfavourable review cases.

Draw the decision tree, determine the recommended decision strategy and the expected value for the case where Fresh Food Melbourne has already decided to conduct the review on A. Make the assumption that after the review, Fresh Food Melbourne only has two options: it can sign the contract with either A or B.

Draw the decision tree with clear labels, show all your calculations and, Provide justification(s) for your decision strategy.

Reference no: EM133684370

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