Optimization is an important tool widely used in formulation of the mathematical modeland design of various decision making problems related to the science and engineering.Generally, the real world problems are occurring in the form of multi-criteria andmulti-choice with certain constraints. There is no such single optimal solution existwhich could optimize all the objective functions simultaneously. In this paper,ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used tosolve multi-objective Geometric programming problems(MOGPP) for searching a compromisesolution. To find the suitable compromise solution for multi-objective Geometricprogramming problems, a brief solution procedure using ϵ-constraint method hasbeen presented. The basic concept and classical principle of multi-objective optimizationproblems with KKT condition has been discussed. The result obtained by ϵ-constraint method withhelp of KKT condition has been compared with the result so obtained by Fuzzy programmingmethod. Illustrative examples are presented to demonstrate the correctness of proposedmodel.

The present paper addresses the class of two-stage robust optimization problems which canbe formulated as mathematical programs with uncertainty on the right-hand sidecoefficients (RHS uncertainty). The wide variety of applications and the fact that manyproblems in the class have been shown to be NP-hard, motivates the search for efficientlysolvable special cases. Accordingly, the first objective of the paper is to provide anoverview of the most important applications and of various polynomial or pseudo-polynomialspecial cases identified so far. The second objective is to introduce a new subclass ofpolynomially solvable robust optimization problems with RHS uncertainty based on theconcept of state-space representable uncertainty sets. A typicalapplication to a multi period energy production problem under uncertain customer loadrequirements is described into details, and computational results including a comparisonbetween optimal two-stage solutions and exact optimal multistage strategies arediscussed.

We study the pricing problem between two firms when the manufacturer’s willingness to pay(wtp) for the supplier’s good is not known by the latter. We demonstrate that it is in theinterest of the manufacturer to hide this information from the supplier. The precision ofthe information available to the supplier modifies the rent distribution. The risk ofopportunistic behaviour entails a loss of efficiency in the supply chain. The model isextended to the case of a supplier submitting offers to several manufacturers. Somemanagerial insight through a numerical illustration is provided.

In this paper, we develop a divide-and-conquer approach, called block decomposition, tosolve the minimum geodetic set problem. This provides us with a unified approach for allgraphs admitting blocks for which the problem of finding a minimum geodetic set containinga given set of vertices (g-extension problem) can be efficiently solved. Ourmethod allows us to derive linear time algorithms for the minimum geodetic set problem in(a proper superclass of) block-cacti and monopolar chordal graphs. Also, we show that hullsets and geodetic sets of block-cacti are the same, and the minimum geodetic set problemis NP-hard in cobipartite graphs. We conclude by pointing out several interesting researchdirections.

In this paper, we show how optimization methods can be used efficiently to determine theparameters of an oscillatory model of handwriting. Because these methods have to be usedin real-time applications, this involves that the optimization problems must be rapidelysolved. Hence, we developed an original heuristic algorithm, named FHA. This code wasvalidated by comparing it (accuracy/CPU-times) with a multistart method based on TrustRegion Reflective algorithm.

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.

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 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.

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.