Iranian Journal Of Operations Research
Volume:5 Issue: 1, Winter and Spring 2014

Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. It is proved that nonsmooth complementary approximate Karush-Kuhn-Tucker conditions are stronger than nonsmooth approximate gradient projection conditions. Sufficiency for differentiable generalized convex programming is established.

In traditional data envelopment analysis (DEA) the uncertainty of inputs and outputs is not considered when evaluating the performance of a unit. In other words, effects of uncertainty on optimality and feasibility of models are ignored. This paper introduces a new model for measuring the efficiency of decision making units (DMUs) having interval inputs and outputs. The proposed model is based on interval DEA (IDEA) in which the inputs and outputs are limited to be within uncertainty bounds. In this model, the inputs and outputs take fixed values for each DMU such that the sum of efficiencies is maximized. The DMUs are evaluated by the same production possibility set (PPS). The efficiency is measured based on the proposed conservatism level for each input and output. Indeed, the inputs and outputs are defined by the presented conservatism level. The proposed model is integrated measuring all the DMUs efficiencies simultaneously. These efficiency scores lie between the optimistic and pessimistic cases introduced by Despotis and Similar (2002) [11].

Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-state probabilities along with partial fraction decomposition as a simple algebraic procedure, the problem reduces to the solution of a system of linear equations.

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to deterministic demands. A mixed integer linear fractional programming (MILFP) model is formulated and a solution approach for MILFP is discussed. Product distribution and allocation of different customers along with sensitivity of the key parameters and performance of the model are discussed through a numerical example. The results illustrate that profit achieved by the MILFP model is slightly higher than mixed integer programming (MIP) model. It is observed that increase in the opening cost decreases the profit obtained by both MILFP and MIP models. If the opening cost of a location decreases or increases, the demand and capacity of the location changes accordingly. The opening cost dramatically changes the demand rather than the capacity of the product. Finally, a conclusion is drawn in favor of the MILFP model as a relevant approach in a logistic model searching for the optimum solution.

Most of data in a multi attribute decision making (MADM) problem are unstable and changeable, and thus sensitivity analysis can effectively contribute to making proper decisions. Here, we offer a new method for sensitivity analysis of multi-attribute decision making problems so that by changing one element of decision making matrix, we can determine changes in the results of a decision making problem. An analysis is made for simple additive weighting method (SAW) technique, a mostly used multi-attribute decision making techniques, and the corresponding formulas are obtained.