Esra Köktener Karasakal

Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making

In this paper, we address the problem of generating a discrete representation of the nondominated frontier in multiple objective linear problems. We find a surface that approximates the shape of the nondominated frontier. Utilizing the surface, we generate a set of discrete points that is representative of the frontier. Our experience on randomly generated problems demonstrates that the approach performs well in terms of both the quality of the representation and the computation time.

A Simulated Annealing Approach to Bicriteria Scheduling Problems on a Single Machine

In this paper, we apply a simulated annealing approach to two bicriteria scheduling problems on a single machine. The first problem is the strongly NP-hard problem of minimizing total flowtime and maximum earliness. The second one is the NP-hard problem of minimizing total flowtime and number of tardy jobs. We experiment on different neighbourhood structures as well as other parameters of the simulated annealing approach to improve its performance. Our computational experiments show that the developed approach yields solutions that are very close to lower bounds and hence very close to the optimal solutions of their corresponding problems for the minimization of total flowtime and maximum earliness. For the minimization of total flowtime and number tardy, our experiments show that the simulated annealing approach yields results that are superior to randomly generated schedules.

Incorporating wealth information into a multiple criteria decision making model

Abstract We describe how a multiple criteria decision making (MCDM) modelling framework can be extended to account for one of the behavioral ramifications of a decision making activity, namely, the decision maker’s (DM’s) perception of his/her current wealth status, referred to as decisional wealth . Within the MCDM framework, decisional wealth reflects the relative achievements of each of the objectives in a given efficient solution. It is our argument that a DM’s preferences and the importance of his/her objectives, vary depending on the decisional wealth. Therefore, we use the wealth information and trade-off analysis to guide the search for preferred outcomes. We identify efficient solutions that satisfy a DM’s wealth-dependent preferences, and we illustrate the proposed modelling framework with an example.

R&D Project Performance Evaluation With Multiple and Interdependent Criteria

In this study, we develop an approach based on analytic network process (ANP) and data envelopment analysis (DEA) to evaluate the performance of Research and Development projects. We identify a set of criteria and subcriteria having interdependencies among themselves. Interdependency is treated using a hybrid ANP model consisting of both hierarchy and network. The interval pairwise comparison matrices are constructed in a group decision-making process. ANP is extended to obtain interval weights from the interval pairwise comparison matrices. Interval weights are formulated as assurance region constraints in a super-efficiency DEA model, through which the project ranking is obtained. The super-efficiency DEA model is also modified to handle missing data. The approach is applied to a real case study on performance evaluation of the ongoing projects in a Defense Research and Development Institute.

An interactive approach for multiobjective decision making

We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations.

An interactive solution approach for a bi-objective semi-desirable location problem

In this study, we consider a semi-desirable facility location problem in a continuous planar region considering the interaction between the facility and the existing demand points. A facility can be defined as semi-desirable if it has both undesirable and desirable effects to the people living in the vicinity. Our aim is to maximize the weighted distance of the facility from the closest demand point as well as to minimize the service cost of the facility. The distance between the facility and the demand points is measured with the rectilinear metric. For the solution of the problem, a three-phase interactive geometrical branch and bound algorithm is suggested to find the most preferred efficient solution. In the first two phases, we aim to eliminate the parts of the feasible region the inefficiency of which can be proved. The third phase has been suggested for an interactive search in the remaining regions with the involvement of a decision maker (DM). In the third phase, the DM is given the opportunity to use either an exact or an approximate procedure to carry out the search. The exact procedure is based on the reference point approach and guarantees to find an efficient point as the most preferred solution. On the other hand, in the approximate procedure, a hybrid methodology is used to increase the efficiency of the reference point approach. The approximate procedure can be used when the DM prefers to see locally efficient solutions so as to save computation time. We demonstrate the performance of the proposed method through example problems.

Mixed integer programming-based solution procedure for single-facility location with maximin of rectilinear distance

In this paper, we study the 1-maximin problem with rectilinear distance. We locate a single undesirable facility in a continuous planar region while considering the interaction between the facility and existing demand points. The distance between facility and demand points is measured in the rectilinear metric. The objective is to maximize the distance of the facility from the closest demand point. The 1-maximin problem has been formulated as an MIP model in the literature. We suggest new bounding schemes to increase the solution efficiency of the model as well as improved branch and bound strategies for implementation. Moreover, we simplify the model by eliminating some redundant integer variables. We propose an efficient solution algorithm called cut and prune method, which splits the feasible region into four equal subregions at each iteration and tries to eliminate subregions depending on the comparison of upper and lower bounds. When the sidelengths of the subregions are smaller than a predetermined value, the improved MIP model is solved to obtain the optimal solution. Computational experiments demonstrate that the solution time of the original MIP model is reduced substantially by the proposed solution approach.

A probabilistic multiple criteria sorting approach based on distance functions

A new distance-based sorting method is proposed for multicriteria sorting problems.Several distance norms for aggregation are compared for different data sets.Distance to ideal point is shown to be a good indicator for class identification.Optimistic and pessimistic positions are determined for each class.Optimistic and pessimistic probabilities are calculated for each alternative. In this paper, a new probabilistic distance based sorting (PDIS) method is developed for multiple criteria sorting problems. The distance to the ideal point is used as a criteria disaggregation function to determine the values of alternatives. These values are used to sort alternatives into the predefined classes. The method also calculates probabilities that each alternative belong to the predefined classes in order to handle alternative optimal solutions. It is applied to five data sets and its performance is compared with two well-known methods from literature. Computational experiments show that the PDIS method performs better than the other methods.

An Interactive Partitioning Approach For Multiobjective Decision Making Under A General Monotone Utility Function

We develop an interactive partitioning approach for solving the multiobjective decision making problem of a decision maker (DM) who has an implicit general monotone utility function. The approach reduces feasible solution space using the DMs preferences. Hypothetical solutions called partition ideals (PIs) that dominate portions of the efficient frontier are generated and those that are inferior to a feasible solution are used to eliminate the dominated regions. We investigate the issues in representation of the reduced feasible solution space. We develop procedures for locating PIs and measuring the size of feasible solution space. We incorporate these ideas into an approach that converges to a neighborhood of the most preferred solution of the DM. We demonstrate the approach on an example problem.