A New Model for Probabilistic Multi-Period Multi-Objective Project Selection Problem

Abstract

The project selection problem is considered as one of the most imperative decisions for investor organizations. Due to non-deterministic nature of some criteria in the real world projects in this paper, a new model for project selection problem is proposed in which some parameters are assumed probabilistic. This model is formulated as a non-linear, multi-objective, multi-period, zero-one programming model. Then the epsilon constraint method and an algorithm are applied to check the Pareto front and to find optimal solutions. A case study is conducted to illustrate the applicability and effectiveness of the approach, with the results presented and analysed. Since the proposed model is more compatible with real world problems, the results are more tangible and trustable compared with deterministic cases. Implications of the proposed approach are discussed and suggestions for further work are outlined.Keywords: Project selection, multi objective programming, chance constraint, epsilon constraint method. INTRODUCTIONDecision making about selection or rejection of a project is considerable from both theoretical and practical aspects and it depends on satisfaction of financial and nonfinancial constraints of the problem. In the real world project selection problems there are normally more than one objective function. This makes the solution algorithm more complicated and time consuming. The purpose of this paper is decision making about selection of N projects in T periods of time such that the profit gets maximum and total cost of equipment, human resources and used raw materials become minimum. In real world problems many of parameters are unlikely to be deterministic and ignoring the stochastic model can lead to unreliable results. In this paper a new framework is proposed for modeling a project selection problem relying on the concept of risk and by applying a linear approximation on probabilistic constraints. The mentioned model is called "Mean-Risk" model which the main idea of it is maximizing the expected profit of selecting a project such that risk curve of this selection always be below of the confidence curve. Here without loss of generality and just for simplification, the confidence is assumed a linear function. Since some parameters are probabilistic, the constraints include these parameters are also probabilistic constraints. Chance constrained programming was developed as a means of describing constraints in the form of probability levels of attainment. Consideration of chance constraints allows the decision maker to consider objectives in terms of their attainment probability. This approach changes constraints with stochastic parameters to constraints with a confidence level as the threshold of decision maker, using variance-covariance matrix. If α is a predetermined confidence level desired by the decision maker, the implication is that a constraint will have a probability of satisfaction of α. After transforming the problem from probabilistic mode to deterministic mode, the resulting model i...