QUESTION 2 [25 Marks] Since the operations analyst comes across different types of problems, it is a good idea to classify them into some groups. This will make it easier to select models and criteria to use in the analysis. There can be two ways of classifying problems: by the degree to which the outcome is uncertain, and by the degree to which the decisions are independent. UNCERTAINTY OF OUTCOMES When we know for sure what the outcome of each decision will be, we are dealing with a problem under control of certainty. When a decision has more than one possible outcome and we know the likelihood of each outcome, we are dealing with a problem under conditions of risk. Finally, when a decision has more than one possible outcome and we do not know the likelihood of each outcome, we are dealing with a problem under conditions of uncertainty. Some examples may clarify these conditions of certainty, risk, and uncertainty. 2.1 A chain of supermarkets is going to open a new store at one of four possible locations. Management wishes to select the location that will maximize profitability over the next ten years. An extensive analysis was performed to determine the costs, revenues, and profits for each alternative. The results are shown below. Location 1 10 year amual profit (S millions) 0.70 0.95 0.60 0.84 Management has a high degree of confidence in these figures. The decision criterion (profit) has been explicitly identified and accurately calculated for each alternative. Advise management on the optimal location to select to achieve the identified objective. 2.2 Further analysis of the supermarket chain's problem reveals that the profit associated with each location is not known for sure. Management is convinced that the ten-year profitability of each location will depend upon regional population growth. Therefore, management cannot predict the outcome with certainty. Three possible rates of population growth were identified: low, medium, and high. The profitability ($ millions) associated with each location and each rate of population growth was calculated, as shown below. Rate of population growth Location Law (3% or less) Medium (above 3% brei below 10%) High (10% or more) 1 0.3 million $ 0.8 million $ 0.9 million S 2 (1.2 01.6 1.1 3 0.4 0.5 0.6 + 0.6 0.7 0.8 Probability (p) 0.2 0.3 0.5 The figures at the bottom of the table gives the probability (likelihood) of each rate of population growth. Decision strategy in this situation is more difficult than it is under conditions of certainty. The choice is not so easy. It is not known which location will be best because the rate of future population growth is not known for certain. Prepare a brief report for management to determine which alternative is the best. 2.3 Even further analysis has cast doubt on the probability of the rates of population growth. New management doesn't know the probabilities of low, medium, or high growth, and is faced with a problem under conditions of uncertainty. Obviously, strategy is much harder to come by in this case. Discuss the approaches from a set of several options that analysts use in the situation of uncertainty.