In this paper, a solution procedure is proposed to solve fuzzy linear fractionalprogramming (FLFP) problem where cost of the objective function, the resources and thetechnological coefficients are triangular fuzzy numbers. Here, the FLFP problem istransformed into an equivalent deterministic multi-objective linear fractional programming(MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFPproblem is reduced single objective linear programming (LP) problem. The proposedprocedure illustrated through a numerical example.

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.

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set ofunit-time operations subject to time delays with respect to the makespan. This problem isknown to be \hbox{${\cal NP}$}𝒩𝒫-hard in the strong sense. We propose an algorithm basedon a branch and bound enumeration scheme. This algorithm includes the implementation ofnew lower and upper bound procedures, and dominance rules. A computer simulation tomeasure the performance of the algorithm is provided for a wide range of testproblems.

This paper analyzes a discrete-time finite buffer renewal input queue with multipleworking vacations where services are performed in batches of maximum size “b”. The service times bothduring a regular service period and vacation period and vacation times are geometricallydistributed. Employing the supplementary variable and imbedded Markov chain techniques, wederive the steady-state queue length distributions at pre-arrival, arbitrary and outsideobserver’s observation epochs. Based on the queue length distributions, some performancemeasures and waiting time distribution in the queue have been discussed. Finally,numerical results showing the effect of model parameters on the key performance measuresare presented.

Data envelopment analysis (DEA) has been widely used to measure the performance of theoperational units that convert multiple inputs into multiple outputs. In many real worldscenarios, there are systems that have a two-stage network process with shared inputs usedin both stages of productions. In this paper, the problem of evaluating the efficiency ofa set of specialized and interdependent components that make up a large DMU is considered.In these processes the first stage consists of two parallel components which are connectedserially with the process in the second stage. The paper develops a DEA approach formeasuring efficiency of decision processes which can be divided into two stages. Thisapplication of parallel-series production process involves shared resources and the paperdetermines an optimal split of shared resources among two components.

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 propose a nonlinear multi-objective optimization problem whoseparameters in the objective functions and constraints vary in between some lower and upperbounds. Existence of the efficient solution of this model is studied and gradient based aswell as gradient free optimality conditions are derived. The theoretical developments areillustrated through numerical examples.

In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines.The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs isassociated with one agent. The K agents compete to perform their jobs on commonresources. The objective is to find a schedule that minimizes a global objective functionf 0, while maintaining the regularobjective function of each agent, f k, at a level nogreater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This problem is a multi-agent schedulingproblem with a global objective function. In this study, we consider the casewith preemption and the case without preemption. If preemption is allowed, we propose apolynomial time algorithm based on a network flow approach for the unrelated parallelmachine case. If preemption is not allowed, we propose some general complexity results anddevelop dynamic programming algorithms.

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.

In this paper, we propose an industrial symbiosis network equilibrium model by usingnonlinear complementarity theory. The industrial symbiosis network consists of industrialproducers, industrial consumers, industrial decomposers and demand markets, which imitatesnatural ecosystem by means of exchanging by-products and recycling useful materialsexacted from wastes. The industrial producers and industrial consumers are assumed to beconcerned with maximization of economic profits as well as minimization of emissions. Wedescribe the optimizing behavior, derive optimality conditions of the variousdecision-makers along with respective economic interpretations and establish the nonlinearcomplementarity model in accordance with the industrial symbiosis network equilibriumconditions. Based on the existence proof of the corresponding nonlinear complementaritymodel under reasonable assumptions, two groups of numerical examples are given toillustrate the rationality as well as the effectiveness of the model.

In general, traditional production-inventory systems are based on a number of simplifying– but somewhat unrealistic – assumptions, including constant demand rate, constant holdingcost, and instantaneous order replenishment. These assumptions have been individuallychallenged in numerous variations of production-inventory models. Finite production ratemodels, such as economic production quantity (EPQ) systems consider gradual orderreplenishment. Stock-dependent demand models assume the demand rate to be an elasticfunction of the inventory level. Variable holding cost models assume the holding cost perunit per time period to be a function of the time spent in storage. In this paper, thethree simplifying assumptions are simultaneously relaxed in a new production-inventorysystem with a finite production rate, stock-level dependent demand rate, and variableholding cost. Mathematical models and optimum solution procedures, including nonlinearprogramming, are presented for two functional forms of holding cost variability. The maincontribution of this paper is the formulation and solution of a new production-inventorymodel that more closely represents real-world situations. The realistic assumptions andefficient solution algorithms should make the model practical and useful for industrialapplications.

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.

Many real-world scheduling problems can be modeled as Multi-mode Resource ConstrainedProject Scheduling Problems (MRCPSP). However, the MRCPSP is a strong NP-hard problem andvery difficult to be solved. The purpose of this research is to investigate a moreefficient alternative based on ant algorithm to solve MRCPSP. To enhance the generalityalong with efficiency of the algorithm, the rule pool is designed to manage numerouspriority rules for MRCPSP. Each ant is provided with an independent thread and endowedwith the learning ability to dynamically select the excellent priority rules. In addition,all the ants in the ant algorithm have the prejudgment ability to avoid infeasible routesbased on the branch and bound method. The algorithm is tested on the well-known benchmarkinstances in PSPLIB. The computational results validate the effectiveness of the proposedalgorithm.

We address a queueing control problem considering service times and conversion timesfollowing normal distributions. We formulate the multi-server queueing control problem byconstructing a semi-Markov decision process (SMDP) model. The mechanism of statetransitions is developed through mathematical derivation of the transition probabilitiesand transition times. We also study the property of the queueing control system and showthat optimizing the objective function of the addressed queueing control problem isequivalent to maximizing the time-average reward.