A typical project consists of many activities. Logical dependencies cause some of them to be critical and some non-critical. While critical activities have a strict start time, in some projects the problem of selecting the start time of a non-critical activity may arise. Usually, it is possible to use the “as soon as possible” or “as late as possible” rules. Sometimes, however, the result of such a decision depends on external factors, e.g., an exchange rate. In this paper, we consider the multi-criteria problem of determining the start time of a non-critical activity. We assume that the earliest start and the latest start times of the activity have been identified using the critical path method, but the project manager is free to select the time when the activity will actually be started. This decision, however, cannot be changed later, as it is associated with the allocation of key resources. The criteria that are usually considered in such a situation are cost and risk. We assume that the cost depends on an exchange rate. We also consider the risks of project delay and a decrease in quality. This paper formulates the selection of the start time for a non-critical activity as a discrete dynamic multicriteria problem. We solve it using an interactive procedure based on the analysis of trade-offs.
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The paper considers a discrete stochastic multicriteria problem. This problem can be denned by a finite set of actions A, a set of attributes X and a set of evaluations E. It is assumed that the performance probability distributions for each action on each attribute are known. A new procedure for such a problem is proposed. It is based on two concepts: stochastic dominance and interactive approach. Stochastic dominance is employed for comparing evaluations of actions with respect, to attributes. The STEM methodology is employed in the dialogue procedure between decision maker and decision model. In each step a candidate action a_i is generated. The decision maker examines evaluations of a_i, with respect to attributes and selects the one that satisfies him/her. Then the decision maker defines the limit of concessions, which can be made on average evaluations with respect to this attribute. The procedure continues until a satisfactory action is found.
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