Iranian Journal Of Operations Research
Volume:3 Issue: 2, Summer and Autumn 2012

Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functions and we prove that the new barrier functions are locally self-concordant. In many cases, the (local) complexity numbers of the new barrier functions along the central path are better than the complexity number of the logarithmic barrier function by a factor between 0.5 and 1.

We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality conditions for the problem.

In today’s highly competitive market, the pressure on organizations to find a better way to create and deliver value to customers is mounting. The decision involves many quantitative and qualitative factors that may be conflicting in nature. Here, we present a new model for transportation problem with consideration of quantitative and qualitative data. In the model, we quantify the qualitative data by using the weight assessment technique in the fuzzy analytic hierarchy process. Then, a preemptive fuzzy goal programming model is formulated to solve the proposed model. The software package LINGO is used for solving the fuzzy goal programming model. Finally, a numerical example is given to illustrate that the proposed model may lead to a more appropriate solution.

We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the uncertain data, classical robust optimization approaches cannot be applied directly to construct its robust counterpart. We exploit the problem structure to develop exact solution methods and present some computational results.

We present a new mathematical model for a permutation flowshop scheduling problem with sequence-dependent setup times considering minimization of two objectives, namely makespan and weighted mean total earliness/tardiness. Only small-sized problems with up to 20 jobs can be solved by the proposed integer programming approach. Thus, an effective multi-objective immune system (MOIS) is specially proposed to solve the given problem. Finally, the computational results are reported showing that the proposed MOIS is effective in finding solutions of large-sized problems.

We deal with the relationship termination problem in the context of individual-level customer relationship management (CRM) and use a Markov decision process to determine the most appropriate occasion for termination of the relationship with a seemingly unprofitable customer. As a particular case, the beta-geometric/beta-binomial model is considered as the basis to define customer behavior and it is explained how to compute customer lifetime value when one needs to take account of the firm’s choice as to whether to continue or terminate relationship with unprofitable customers. By numerical examples provided by simulation, it is shown how a stochastic dynamic programming approach can be adopted in order to obtain a more precise estimation of the customer lifetime value as a key criterion for resource allocation in CRM.