Optimization is an important tool widely used in formulation of the mathematical model and 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 and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ-constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ-constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.

The present paper addresses the class of two-stage robust optimization problems which can be formulated as mathematical programs with uncertainty on the right-hand side coefficients (RHS uncertainty). The wide variety of applications and the fact that many problems in the class have been shown to be NP-hard, motivates the search for efficiently solvable special cases. Accordingly, the first objective of the paper is to provide an overview of the most important applications and of various polynomial or pseudo-polynomial special cases identified so far. The second objective is to introduce a new subclass of polynomially solvable robust optimization problems with RHS uncertainty based on the concept of state-space representable uncertainty sets. A typical application to a multi period energy production problem under uncertain customer load requirements is described into details, and computational results including a comparison between optimal two-stage solutions and exact optimal multistage strategies are discussed.

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 the interest of the manufacturer to hide this information from the supplier. The precision of the information available to the supplier modifies the rent distribution. The risk of opportunistic behaviour entails a loss of efficiency in the supply chain. The model is extended to the case of a supplier submitting offers to several manufacturers. Some managerial insight through a numerical illustration is provided.

In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method 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 hull sets and geodetic sets of block-cacti are the same, and the minimum geodetic set problem is NP-hard in cobipartite graphs. We conclude by pointing out several interesting research directions.

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

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

In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

In this paper, we propose an industrial symbiosis network equilibrium model by using nonlinear complementarity theory. The industrial symbiosis network consists of industrial producers, industrial consumers, industrial decomposers and demand markets, which imitates natural ecosystem by means of exchanging by-products and recycling useful materials exacted from wastes. The industrial producers and industrial consumers are assumed to be concerned with maximization of economic profits as well as minimization of emissions. We describe the optimizing behavior, derive optimality conditions of the various decision-makers along with respective economic interpretations and establish the nonlinear complementarity model in accordance with the industrial symbiosis network equilibrium conditions. Based on the existence proof of the corresponding nonlinear complementarity model under reasonable assumptions, two groups of numerical examples are given to illustrate the rationality as well as the effectiveness of the model.

Many real-world scheduling problems can be modeled as Multi-mode Resource Constrained Project Scheduling Problems (MRCPSP). However, the MRCPSP is a strong NP-hard problem and very difficult to be solved. The purpose of this research is to investigate a more efficient alternative based on ant algorithm to solve MRCPSP. To enhance the generality along with efficiency of the algorithm, the rule pool is designed to manage numerous priority rules for MRCPSP. Each ant is provided with an independent thread and endowed with 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 routes based on the branch and bound method. The algorithm is tested on the well-known benchmark instances in PSPLIB. The computational results validate the effectiveness of the proposed algorithm.

We address a queueing control problem considering service times and conversion times following normal distributions. We formulate the multi-server queueing control problem by constructing a semi-Markov decision process (SMDP) model. The mechanism of state transitions is developed through mathematical derivation of the transition probabilities and transition times. We also study the property of the queueing control system and show that optimizing the objective function of the addressed queueing control problem is equivalent to maximizing the time-average reward.