Optimization Online



Musa Caglar (mcaglar***at***tulane.edu)
Sinan Gurel (gsinan***at***metu.edu.tr)

Abstract: We consider a project selection problem faced by research councils. The decision maker seeks to construct an optimal subset of projects (i.e. portfolio), which maximizes the expected total score of supported projects subject to the total budget and policy constraints. At the time of funding decisions, exact expenditures of projects are not known. The decision maker selects projects based on approved budgets, which could be higher than exact expenditures. Therefore, the realized total expenditure of the portfolio tends to be lower than the total budget, causing the notion of budgetary slack in a portfolio. In this study, we put a special emphasis on the input modeling of expenditures by considering practical information, and propose a mixture distribution. Then, we develop a chance-constrained stochastic program with policy constraints to enhance the budget utilization. Our study contributes to project portfolio selection literature by elaborating on the input modeling of expenditures along with a chance-constrained stochastic program under policy constraints. Due to the computational intractability of the developed model, we have shown that Normal distribution can be used to approximate the proposed model. However, the decision maker wonders the quality of Normal approximation. Therefore, we quantify the approximation error of our model via a theoretical bound and simulation. We show that Normal distribution gives a good approximation and the theoretical bound is relatively tight for large-scale problems. We find that our model can be solved to optimal (or near optimal) in a reasonable amount of time by a commercial solver such as IBM CPLEX. We also show that the budget utilization rate of 100% is hard to achieve but that of 96-97% is within reach. The proposed approach can increase the budget utilization by 8.0% and 15.2%, which is remarkable for public decision makers. Thereby, more R&D projects could be supported and a higher socio-economic impact can be achieved.

Keywords: project portfolio selection, expenditure uncertainty, input modeling, Normal approximation, chance constrained stochastic programming

Category 1: Applications -- OR and Management Sciences


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Entry Submitted: 04/23/2019
Entry Accepted: 04/23/2019
Entry Last Modified: 02/14/2020

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