In this paper we give necessary and sufficient optimality conditions for a vectoroptimization problem over cones involving support functions in objective as well asconstraints, using cone-convex and other related functions. We also associate a unifieddual to the primal problem and establish weak, strong and converse duality results. Anumber of previously studied problems appear as special cases.

This work aims to fill a lacunae in the project-oriented production systems literatureproviding a formal analytic description of the rework effects formulae and thedetermination of the extended design time due to a certain degree of overlapping in a pairof activities. It is made through the utilization of concepts of workflow constructionwith hidden (semi) Markov models theory and establishing a way to disaggregate activitiesinto sub-activities, in order to determine the activity parameters used by the projectscheduling techniques. With the aim to make a correlation between the entropy of the statetransitions and the probability of changes, the information theory is also used, and theconcept of impact caused by the probability of changes is provided. Numerical examples areshown for the purpose to demonstrate the applicability of the concepts developed, and oneexample of overlapping of two activities is shown. The original contributions of this workare shown on the last section.

We present a non-cooperative union-firm wage bargaining model in which the union mustchoose between strike and holdout if a proposed wage contract is rejected. The innovativeelement that our model brings to the existing literature on wage bargaining concerns theparties’ preferences which are not expressed by constant discount rates, but by sequencesof discount factors varying in time. First, we determine subgame perfect equilibria if thestrike decision of the union is exogenous. We analyze the case when the union is committedto strike in each disagreement period, the case when the union is committed to strike onlywhen its own offer is rejected, and the case of the never strike exogenous decision. Acomparison of the results is provided, among the cases of the exogenous strike decisions.Next, we consider the general model with no assumption on the commitment to strike. Wefind subgame perfect equilibria in which the strategies supporting the equilibria in theexogenous cases are combined with the minimum-wage strategies, provided that the firm isnot less patient than the union. If the firm is more impatient than the union, then thefirm is better off by playing the no-concession strategy. We find a subgame perfectequilibrium for this case.

The object of this research in the queueing theory is a theorem about theStrong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserveropen queueing network. SLLN is known as a fluid limit or fluid approximation. In thiswork, we prove that the long-term average rate of growth of the queue length process of amultiserver open queueing network under heavy traffic strongly converges to a particularvector of rates. SLLN is proved for the values of an important probabilisticcharacteristic of the multiserver open queueing network investigated as well as the queuelength of jobs.

In this short note, we investigate the framework where agents or players have some uncertainties upon their payoffs or losses, the behavior (or the type, number or any other characteristics) of other players. More specifically, we introduce an extension of the concept of Nash equilibria that generalize different solution concepts called by their authors, and depending on the context, either as robust, ambiguous, partially specified or with uncertainty aversion. We provide a simple necessary and sufficient condition that guarantees its existence and we show that it is actually a selection of conjectural (or self-confirming) equilibria. We finally conclude by how this concept can and should be defined in games with partial monitoring in order to preserve existence properties.

This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities à la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing.

This paper analyses an M/G/1 retrial queue with working vacation and constant retrial policy. As soon as the system becomes empty, the server begins a working vacation. The server works with different service rates rather than completely stopping service during a vacation. We construct the mathematical model and derive the steady-state queue distribution of number of customer in the retrial group. The effects of various performance measures are derived.

In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic decomposition, which shows the relationship with that of the classical MX/M/ 1 queue without vacation or breakdown. Besides, we also give the Laplace-Stieltjes transform (LST) of the stationary waiting time distribution of an arbitrary customer in a batch. Finally, some numerical examples are given to illustrate the effect of the parameters on the system performance measures.

Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization technique is used to obtain an optimal solution to this parametric problem. This optimal solution will also be the fuzzy optimal solution for the original problem. An example is also provided to illustrate the algorithm.