An International Manufacturer Of Electronic Products Is Cont

An International Manufacturer Of Electronic Products Is Contemplating

An international manufacturer of electronic products is contemplating introducing a new type of compact disk player. After some analysis of the market, the president of the company concludes that, within 2 years, the new product will have a market share of 5%, 10%, or 15%. The subjective probabilities of these events are .15, .45, and .40, respectively. If the product captures only a 5% market share, the company will lose $28 million. A 10% market share will produce a $2 million profit, and a 15% market share will produce an $8 million profit. If the company decides not to begin production of the new compact disk player, there will be no profit or loss. Based on the expected value decision, what should the company do? b. The owner of a clothing store must decide how many men’s shirts to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt; if she orders 200 shirts, her cost is $9 per shirt; and if she orders 300 or more shirts, her cost is $8.50 per shirt. Her selling price for the shirt is $12, but any shirts that remain unsold at the end of the season are sold at her famous “half-price, end-of-season sale.” For the sake of simplicity, she is willing to assume that the demand for this type of shirt will be 100, 150, 200, or 250 shirts. Of course, she cannot sell more shirts than she stocks. She is also willing to assume that she will suffer no loss of goodwill among her customers if she understocks and the customers cannot buy all the shirts they want. Furthermore, she must place her order today for the entire season; she cannot wait to see how the demand is running for this type of shirt. a. Construct the payoff table to help the owner decide how many shirts to order. b. Draw the decision tree.

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Introduction

The decision-making processes in business environments often involve analyzing potential risks and benefits of different strategic options. This paper explores two case studies that exemplify such decision-making scenarios: one involving a company contemplating the launch of a new electronic product, and the other concerning a clothing retailer deciding on inventory levels for seasonal shirts. Both cases require the application of decision analysis tools such as expected value and decision trees to optimize outcomes and mitigate potential losses.

Case Study 1: Launching a New Electronic Product

The first scenario involves an international manufacturer considering launching a new compact disk (CD) player. The company’s president estimates three possible market share outcomes within two years: 5%, 10%, or 15%, with subjective probabilities of 0.15, 0.45, and 0.40, respectively. The financial implications are significant: a 5% market share yields a loss of $28 million, a 10% share results in a $2 million profit, and a 15% share leads to an $8 million profit. If the company chooses not to produce the product, the profit or loss is zero.

To determine the optimal decision, the expected monetary value (EMV) is calculated for the launch option. The EMV is obtained by multiplying each outcome by its probability and summing these products:

\[

EMV = (0.15 \times -28) + (0.45 \times 2) + (0.40 \times 8) = -4.2 + 0.9 + 3.2 = -0.1\text{ million dollars}

\]

Since the EMV is slightly negative, the company might consider not launching the product, which guarantees no profit or loss. Nonetheless, decision-makers should also consider other factors such as strategic positioning and market potential beyond the expected monetary value.

Case Study 2: Inventory Decision for Shirts

The second scenario involves a clothing store owner deciding how many shirts to order for a new season. Orders are made in discrete quantities: 100, 200, or 300 shirts, each with different costs per shirt ($10, $9, and $8.50, respectively). The selling price is fixed at $12. The owner faces uncertainty regarding demand, which could be 100, 150, 200, or 250 shirts. Since demand cannot exceed stock, unsold shirts are sold at half-price, but Poisson’s law of demand indicates that the number of shirts sold cannot surpass stock levels, with shortages not harming customer goodwill.

A payoff table is constructed by calculating revenues and costs based on these variables, considering all combinations of order quantities and demand levels. The profit depends on whether shirts are sold at full, half-price, or remain unsold. For example:

- Ordering 100 shirts:

- Demand of 100: profit is 100 \times ($12 - $10) = $200

- Demand of 150 or more: profit is 100 \times ($12 - $10) = $200, with leftover stock sold at half-price.

- Ordering 200 shirts:

- Demand of 150: profit is calculated based on sold shirts at full price and unsold at half-price.

- Demand of 200: profit is 200 \times ($12 - $9) = $600, and so on.

The complete payoff table encompasses all combinations, illustrating the potential profit outcomes for each order quantity across varying demand levels.

Decision Tree Construction

Drawing the decision tree involves mapping out the initial decision node—choosing order quantity—and subsequent chance nodes representing demand scenarios. For each choice, branches emanate to depict demand outcomes, with associated probabilities. The expected value of each path is calculated, guiding the owner toward the optimal order quantity.

Discussion and Implications

Both cases underscore the importance of probabilistic analysis and decision trees in managerial decision-making. The first case illustrates the utility of expected value calculations in product launch decisions, highlighting how potential gains and losses influence strategic choices. The second emphasizes inventory management under uncertainty, demonstrating how constructing payoff tables and decision trees can help maximize expected profits while managing risks associated with stockouts and excess inventory.

Conclusion

Decision analysis tools such as expected monetary value and decision trees are vital in navigating uncertain business environments. They enable managers to quantitatively evaluate options, compare outcomes, and make informed decisions that align with corporate strategies and financial objectives. Practical applications, as demonstrated by the case studies, reinforce the importance of systematic analysis in achieving optimal business performance.

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