In a multi server queuing system, buffer size is often larger than the number of servers.This necessitates queuing and waiting for some customers. Customers become impatient whilewaiting for service. Additionally, they may also become impatient if service is notoffered at the desired rate. This paper analyses a finite buffer multi server queuingsystem with the additional restriction that customers may balk as well as renege. Closedform expressions of a number of performance measures are presented. A design problem isdiscussed to demonstrate the results derived.

The minimum cost network flow problem, (MCNFP) constitutes a wide category of networkflow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) forthe MCNFP has been developed. This algorithm belongs to a special “exterior point simplextype” category. Similar to the classical dual network simplex algorithm (DNSA), thisalgorithm starts with a dual feasible tree-solution and after a number of iterations, itproduces a solution that is both primal and dual feasible, i.e. it isoptimal. However, contrary to the DNSA, the new algorithm does not always maintain a dualfeasible solution. Instead, it produces tree-solutions that can be infeasible for the dualproblem and at the same time infeasible for the primal problem. In this paper, we presentfor the first time, the mathematical proof of correctness of DNEPSA, a detailedcomparative computational study of DNEPSA and DNSA on sparse and dense random probleminstances, a statistical analysis of the experimental results, and finally some newresults on the empirical complexity of DNEPSA. The analysis proves the superiority ofDNEPSA compared to DNSA in terms of cpu time and iterations.

The paper focuses on multi-criteria problems. It presents the interactive compromise hypersphere method with sensitivity analysis as a decision tool in multi-objective programming problems. The method is based on finding a hypersphere (in the criteria space) which is closest to the set of chosen nondominated solutions. The proposed modifications of the compromise hypersphere method are based on using various metrics and analyzing their influence on the original method. Applications of the proposed method are presented in four multi-criteria problems: the assignment problem, the knapsack problem, the project management problem and the manufacturing problem.

In this paper, we develop a supply chain network equilibrium model in which electronic commerce in the presence of both B2B (business-to-business) and B2C (business-to-consumer) transactions, multiperiod decision-making and multicriteria decision-making are integrated. The model consists of three tiers of decision-makers (manufacturers, retailers and consumers at demand markets) who compete within a tier but may cooperate between tiers. Both manufacturers and retailers are concerned with maximization of profit as well as minimization of risk, whereas consumers take both the prices charged by manufacturers and retailers, along with the corresponding costs of transacting, in making their consumption decisions. Increasing relationship levels are assumed to decrease costs of transacting as well as risk costs. Establishing and maintaining these relationship levels incur some costs that have to be borne by the various decision-makers. We study the interaction among different tiers of decision-makers, describe their multicriteria decision-making behavior and derive the optimality conditions as well as the equilibrium conditions which are then shown to satisfy a finite-dimensional variational inequality problem. We then establish qualitative properties of the equilibrium model under some reasonable assumptions and illustrate the model with several numerical examples.