Multi-objective optimization is an optimization problem with some conflicting objectives to be attained, simultanously. This paper reviewed literature about multi-objective optimization problems for supply chain management. The review aimed to provide the lastest research views and recomendations for further studies. We discussed the lastest ten years publications about multi-objective optimization for supply chain management. The scope of this review was classified into five categories i.e. problem statements, multi-objective frameworks, mathematical formulation modeling, optimization techniques, and representation of supply chain. Multi-objective optimization approaches, both classical and metaheuristic approaches, were discussed, accordingly. In this review, we conducted conclusion and recomendations about likelihood research directions in future.

The present work proposes a multi-objective improved teaching-learning based optimization (MO-ITLBO) algorithm for unconstrained and constrained multi-objective function optimization. The MO-ITLBO algorithm is the improved version of basic teaching-learning based optimization (TLBO) algorithm adapted for multi-objective problems. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions (i.e. Pareto front) maintained in an external archive. The performance of the MO-ITLBO algorithm is assessed by implementing it on unconstrained and constrained test problems proposed for the Congress on Evolutionary Computation 2009 (CEC 2009) competition. The performance assessment is done by using the inverted generational distance (IGD) measure. The IGD measures obtained by using the MO-ITLBO algorithm are compared with the IGD measures of the other state-of-the-art algorithms available in the literature. Finally, Lexicographic ordering is used to assess the overall performance of competitive algorithms. Results have shown that the proposed MO-ITLBO algorithm has obtained the 1st rank in the optimization of unconstrained test functions and the 3rd rank in the optimization of constrained test functions.

This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm.

Reliability is one of the most important characteristics of the electrical and mechanical systems with applications in the space communication industries, internet networks, telecommunication systems, power generation systems, and productive facilities. What adds to the importance of reliability in these systems are system complications, nature of competitive markets, and increasing production costs due to failures. This paper investigates availability optimization of a system using both repairable and non-repairable components, simultaneously. The availability-redundancy allocation problems involve the determination of component availability (i.e., life time and repair time of the components) and the redundancy levels that produce maximum system availability. These problems are often subject to some constraints on their components such as cost, weight, and volume. To maximize the availability and to minimize the total cost of the system, a new Mixed Integer Nonlinear Programming (MINLP) model is presented. To solve the proposed model, an improved version of the genetic algorithm is designed as an efficient meta-heuristic algorithm. Finally, in order to verify the efficiency of the proposed algorithm, a numerical example of a system is presented that consists of both repairable and non-repairable components.

In hierarchical production planning system, Aggregate Production Planning (APP) falls between the broad decisions of long-range planning and the highly specific and detailed short-range planning decisions. This study develops an interactive Multi-Objective Genetic Algorithm (MOGA) approach for solving the multi-product, multi-period aggregate production planning (APP) with forecasted demand, related operating costs, and capacity. The proposed approach attempts to minimize total costs with reference to inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor, machine and warehouse capacity. Here several genetic algorithm parameters are considered for solving NP-hard problem (APP problem) and their relative comparisons are focused to choose the most auspicious combination for solving multiple objective problems. An industrial case demonstrates the feasibility of applying the proposed approach to real APP decision problems. Consequently, the proposed MOGA approach yields an efficient APP compromise solution for large-scale problems.

Most of the time, the government of the affected country cannot handle the entire relief operations. Under such conditions, international organizations act independently but are obliged to obey the law of the country. In this paper, we propose a dynamic multi-level programming where the affected country and international organizations dynamically change their roles, being leader or follower, according to a game. The application of the proposed model is investigated for a case problem where real data are utilized to design a network for humanitarian logistics during potential earthquakes. The advantages of using multi-level modeling against considering just one player's point of view are provided to guide decision-makers under a variety of conditions. The results show for the first three periods, the gov-ernment of the affected area cannot handle the demand for the rescue operation. Thus, the international suppliers act as the leader for the first three periods. However, by decreasing the demand for the rescue operation in the last three periods, the government can manage the evacuation operation properly.

This paper presents a multi-objective location problem in a three level supply chain network under uncertain environment considering inventory decisions. The proposed model of this paper considers uncertainty for different parameters including procurement, transportation costs, supply, demand and the capacity of various facilities. The proposed model presents a robust optimization model, which specifies locations of distribution centers to be opened, inventory control parameters (r, Q), and allocation of supply chain components, concurrently. The resulted mixed-integer nonlinear programming minimizes the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. The model also minimizes the variability of the total cost of relief chain and minimizes the financial risk or the probability of not meeting a certain budget. We use the ?-constraint method, which is a multi-objective technique with implicit trade-off information given, to solve the problem and using a couple of numerical instances, we examine the performance of the proposed approach.

Inconel 600 is a super alloy known for its properties like low thermal conductivity and work hard-ening. The work hardening property of this alloy makes it harder and harder during successive passes of the tool during machining. Therefore, machining of this type of material demands inno-vation in tool material, selection of proper combination of parameters and their levels for economical machining. Coated carbide tool inserts are most widely used for machining Inconel alloys. These inserts are coated with special materials by PVD or CVD technique to reduce flank wear, improve surface finish of machined components and increase the material removal rate (MRR). In this work carbide insert coated with nanocomposite coatings like AlTiN and TiAlSiN commercially known as Hyperlox and HSN2 were used and their performance during machining of Inconel 600 was studied. As improper selection of process parameter influences on the quality of products and productivity, it is important to identify the optimum combination of input process parameters. Most of the time the influence of the input process parameters on the output parameters like MRR, surface roughness and flank wear is studied independently. Information obtained through single objective optimization may not be sufficient because industries desire to optimize all the output parameters, simultaneously. Multi-objective optimization is the only solution to satisfy the requirements of industries and genetic algorithm based multi-objective optimization is adopted in this work in order to get the optimum combination of input process parameters to obtain maximum material removal rate, minimum surface roughness and minimum flank wear simultaneously.

In this paper, we have modeled a decision making problem of a tea industry as a multi-objective optimization problem in interval environment. The goal of this problem is to maximize the overall profit as well as to minimize the total production cost subject to the given resource constraints depending on budget, storage space and allotted processing times in different machines. For this purpose, the problem has been formulated as a multi-objective integer linear programming problem with interval objectives. To solve the problem, we have proposed extended elitist non-dominated sorting genetic algorithm (ENSGA-II) for integer variables with interval fitness, crowded tournament selection, intermediate crossover, one neighborhood mutation and elitism. To develop this algorithm, we have proposed modified non-dominated sorting and crowding distance based on interval mathematics and interval order relations. Finally, to test the performance of the proposed algorithm, a numerical example has been solved.

Group scheduling problem in cellular manufacturing systems consists of two major steps. Sequence of parts in each part-family and the sequence of part-family to enter the cell to be processed. This paper presents a new method for group scheduling problems in flow shop systems where it minimizes makespan (Cmax) and total tardiness. In this paper, a position-based learning model in cellular manufacturing system is utilized where processing time for each part-family depends on the entrance sequence of that part. The problem of group scheduling is modeled by minimizing two objectives of position-based learning effect as well as the assumption of setup time depending on the sequence of parts-family. Since the proposed problem is NP-hard, two meta heuristic algorithms are presented based on genetic algorithm, namely: Non-dominated sorting genetic algorithm (NSGA-II) and non-dominated rank genetic algorithm (NRGA). The algorithms are tested using randomly generated problems. The results include a set of Pareto solutions and three different evaluation criteria are used to compare the results. The results indicate that the proposed algorithms are quite efficient to solve the problem in a short computational time.