A genetic algorithm approach for multi-objective optimization of supply chain networks

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management. It is an important and strategic operations management problem in supply chain management, and usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective SCN design problem. To deal with multi-objective and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. An experimental study using actual data from a company, which is a producer of plastic products in Turkey, is carried out into two stages. While the effects of weight approaches on the performance of proposed solution procedure are investigated in the first stage, the proposed solution procedure and simulated annealing are compared according to quality of Pareto-optimal solutions in the second stage.     

A fuzzy multi-objective covering-based vehicle location model for emergency services

Timeliness is one of the most important objectives that reflect the quality of emergency services such as ambulance and firefighting systems. To provide timeliness, system administrators may increase the number of service vehicles available. Unfortunately, increasing the number of vehicles is generally impossible due to capital constraints. In such a case, the efficient deployment of emergency service vehicles becomes a crucial issue. In this paper, a multi-objective covering-based emergency vehicle location model is proposed. The objectives considered in the model are maximization of the population covered by one vehicle, maximization of the population with backup coverage and increasing the service level by minimizing the total travel distance from locations at a distance bigger than a prespecified distance standard for all zones. Model applications with different solution approaches such as lexicographic linear programming and fuzzy goal programming (FGP) are provided through numerical illustrations to demonstrate the applicability of the model. Numerical results indicate that the model generates satisfactory solutions at an acceptable achievement level of desired goals.     

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals.     

A model of resilient supply chain network design: A two-stage programming with fuzzy shortest path

A supply chain network design needs to consider the future probability of reconfiguration due to some problems of disaster or price changes. The objective of this article is to design a reconfigurable supply chain network by optimizing inventory allocation and transportation routing. A two-stage programming is composed according to Benders decomposition by allocating inventory in advance and anticipating the changes of transportation routings; thus the transportation routing is stochastic in nature. In addition, the fuzzy shortest path is developed to solve the problem complexity in terms of the multi-criteria of lead time and capacity with an efficient computational method. The results and analysis indicate that the proposed two-stage programming with fuzzy shortest path surpasses the performance of shortest path problem with time windows and capacity constraint (SPPTWCC) in terms of less computational time and CPU memory consumption. Finally, management decision-making is discussed among other concluding remarks.     

A multi-objective optimization for green supply chain network design

In this paper, we study a supply chain network design problem with environmental concerns. We are interested in the environmental investments decisions in the design phase and propose a multi-objective optimization model that captures the trade-off between the total cost and the environment influence. We conduct a comprehensive set of numerical experiments. The results show that our model can be applied as an effective tool in the strategic planning for green supply chain. Meanwhile, the sensitivity analysis provides some interesting managerial insights for firms.     

A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007 Chang, C-T. 2007. Binary Behavior of Fuzzy Programming with Piecewise Membership Functions. IEEE Transactions on Fuzzy Systems, 15: 342–349.  [Google Scholar]), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.     

An integrated approach for sustainable supply chain planning

This paper proposes an integrated approach for transposing sustainable development principles to supply chain planning models. Inspired by research on performance measurement, we designed a method that links sustainability performance to supply chain decisions, and allows setting coherent performance measures. By transposing this method to a multi-objective mathematical programming, the supply chain planning is optimized while the economic, environmental and social performances are all coherently integrated into the model. To illustrate our approach, we applied it to a Canadian lumber industry case. We solved the mathematical model by using the weighted goal programming technique, which results in a set of “compromise” solutions allowing the decision maker to choose the alternative that reflects the balance he/she wishes to make regarding the three dimensions of sustainability.     

Hedging an option portfolio with minimum transaction lots: A fuzzy goal programming problem

Options are designed to hedge against risks to their underlying assets such as stocks. One method of forming option-hedging portfolios is using stochastic programming models. Stochastic programming models depend heavily on scenario generation, a challenging task. Another method is neutralizing the Greek risks derived from the Black–Scholes formula for pricing options. The formula expresses the option price as a function of the stock price, strike price, volatility, risk-free interest rate, and time to maturity. Greek risks are the derivatives of the option price with respect to these variables. Hedging Greek risks requires no human intervention for generating scenarios. Linear programming models have been proposed for constructing option portfolios with neutralized risks and maximized investment profit. However, problems with these models exist. First, feasible solutions that can perfectly neutralize the Greek risks might not exist. Second, models that involve multiple assets and their derivatives were incorrectly formulated. Finally, these models lack practicability because they consider no minimum transaction lots. Considering minimum transaction lots can exacerbate the infeasibility problem. These problems must be resolved before option hedging models can be applied further. This study presents a revised linear programming model for option portfolios with multiple underlying assets, and extends the model by incorporating it with a fuzzy goal programming method for considering minimum transaction lots. Numerical examples show that current models failed to obtain feasible solutions when minimum transaction lots were considered. By contrast, while the proposed model solved the problems efficiently.     

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

Ant colony optimization approach to a fuzzy goal programming model for a machine tool selection and operation allocation problem in an FMS

Due to the global competition in manufacturing environment, firms are forced to consider increasing the quality and responsiveness to customization, while decreasing costs. The evolution of flexible manufacturing systems (FMSs) offers great potential for increasing flexibility and changing the basis of competition by ensuring both cost effective and customized manufacturing at the same time. Some of the important planning problems that need realistic modelling and quicker solution especially in automated manufacturing systems have assumed greater significance in the recent past. The language used by the industrial workers is fuzzy in nature, which results in failure of the models considering deterministic situations. The situation in the real life shop floor demands to adopt fuzzy-based multi-objective goals to express the target set by the management. This paper presents a fuzzy goal programming approach to model the machine tool selection and operation allocation problem of FMS. An ant colony optimization (ACO)-based approach is applied to optimize the model and the results of the computational experiments are reported.     

An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design

This paper presents a new multi-objective mathematical model for a multi-modal hub location problem under a possibilistic-stochastic uncertainty. The presented model aims to minimize the total transportation and traffic noise pollution costs. Furthermore, it aims to minimize the maximum transportation time between origin-destination nodes to ensure a high probability of meeting the service guarantee. In order to cope with the uncertainties and the multi-objective model, we propose a two-phase approach, including fuzzy interactive multi-objective programming approach and an efficient method based on the Me measure. Due to the NP-hardness of the presented model, two meta-heuristic algorithms, namely hybrid differential evolution and hybrid imperialist competitive algorithm, are developed. Furthermore, a number of sensitivity analyses are provided to demonstrate the effectiveness of the presented model. Finally, the foregoing meta-heuristics are compared together through different comparison metrics.     

Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment

In this study, an integrated multi-objective production-distribution flow-shop scheduling problem will be taken into consideration with respect to two objective functions. The first objective function aims to minimize total weighted tardiness and make-span and the second objective function aims to minimize the summation of total weighted earliness, total weighted number of tardy jobs, inventory costs and total delivery costs. Firstly, a mathematical model is proposed for this problem. After that, two new meta-heuristic algorithms are developed in order to solve the problem. The first algorithm (HCMOPSO), is a multi-objective particle swarm optimization combined with a heuristic mutation operator, Gaussian membership function and a chaotic sequence and the second algorithm (HBNSGA-II), is a non-dominated sorting genetic algorithm II with a heuristic criterion for generation of initial population and a heuristic crossover operator. The proposed HCMOPSO and HBNSGA-II are tested and compared with a Non-dominated Sorting Genetic Algorithm II (NSGA-II), a Multi-Objective Particle Swarm Optimization (MOPSO) and two state-of-the-art algorithms from recent researches, by means of several comparing criteria. The computational experiments demonstrate the outperformance of the proposed HCMOPSO and HBNSGA-II.     

Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables

Solution procedure consisting of fuzzy goal programming and stochastic simulation-based genetic algorithm is presented, in this article, to solve multiobjective chance constrained programming problems with continuous random variables in the objective functions and in chance constraints. The fuzzy goal programming formulation of the problem is developed first using the stochastic simulation-based genetic algorithm. Without deriving the deterministic equivalent, chance constraints are used within the genetic process and their feasibilities are checked by the stochastic simulation technique. The problem is then reduced to an ordinary chance constrained programming problem. Again using the stochastic simulation-based genetic algorithm, the highest membership value of each of the membership goal is achieved and thereby the most satisfactory solution is obtained. The proposed procedure is illustrated by a numerical example.     

Using binary fuzzy goal programming and linear programming to resolve airport logistics center expansion plan problems

In recent years, the number of direct flights between Taiwan and mainland China has grown rapidly, as charter flights have been turned into regular flights. This important issue has prompted airport ground handling service (AGHS) companies in Taiwan to enhance convenient services for passengers and to invest in airport logistics center expansion plans (ALCEP) to broaden the AGHS market. Due to their budgetary restrictions, AGHS companies need to outsource many of their services to contractors to implement these plans. This study proposes an ALCEP solution procedure to guide AGHS companies in adjusting their priority goals and selecting the best contractor according to their needs. This proposed procedure successfully solves the ALCEP problem and facilitates the assignment of contractors by considering both qualitative and quantitative methods.     

A non-smooth optimization model for a two-tiered supply chain network

A non-smooth optimization model is established for a two-tiered supply chain network where manufacturers are at the upper level and consumers are at the lower level. A supply chain equilibrium model is considered at the lower level while policy interventions are taken into account at the upper level. A mathematical program with equilibrium constraints (MPEC) is established for the two-tiered supply chain network. Numerical illustrations are carried out using a 9-node network and preliminary results are reported.     

A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain

Supply chain management is concerned with the coordination of different parts of the production system. Companies have realized that they must closely collaborate with the suppliers of their strategic components or products. Recently, developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers. In these models some incentives are required from the vendors to motivate the buyer to change his (her) policies to the policy which is optimal for the entire system. Quantity discount policies are used as common incentives in the literature. However, the literature on this problem does not incorporate quantity discount into the coordination model. This paper develops a multi-objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all-unit quantity discount policy for the vendors. Due to the complexity of the problem two well known meta-heuristic algorithms are proposed to solve the problem. An illustrative example is given to show the behavior of the model. Results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions.     

Multi-objective biogeography-based optimization for supply chain network design under uncertainty

This paper proposes a new two-stage optimization method for multi-objective supply chain network design (MO-SCND) problem with uncertain transportation costs and uncertain customer demands. On the basis of risk-neutral and risk-averse criteria, we develop two objectives for our SCND problem. We introduce two solution concepts for the proposed MO-SCND problem, and use them to define the multi-objective value of fuzzy solution (MOVFS). The value of the MOVFS measures the importance of uncertainties included in the model, and helps us to understand the necessity of solving the two-stage multi-objective optimization model. When the uncertain transportation costs and customer demands have joined continuous possibility distributions, we employ an approximation approach (AA) to compute the values of two objective functions. Using the AA, the original optimization problem becomes an approximating mixed-integer multi-objective programming model. To solve the hard approximating optimization problem, we design an improved multi-objective biogeography-based optimization (MO-BBO) algorithm integrated with LINGO software. We also compare the improved MO-BBO algorithm with the multi-objective genetic algorithm (MO-GA). Finally, a realistic dairy company example is provided to demonstrate that the improved MO-BBO algorithm achieves the better performance than MO-GA in terms of solution quality.     

An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty

In this article, we first propose a closed-loop supply chain network design that integrates network design decisions in both forward and reverse supply chain networks into a unified structure as well as incorporates the tactical decisions with strategic ones (e.g., facility location and supplier selection) at each period. To do so, various conflicting objectives and constraints are simultaneously taken into account in the presence of some uncertain parameters, such as cost coefficients and customer demands. Then, we propose a novel interactive possibilistic approach based on the well-known STEP method to solve the multi-objective mixed-integer linear programming model. To validate the presented model and solution method, a numerical test is accomplished through the application of the proposed possibilistic-STEM algorithm. The computational results demonstrate suitability of the presented model and solution method.     

Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic

Sustainability has been considered as a growing concern in supply chain network design (SCND) and in the order allocation problem (OAP). Accordingly, there still exists a gap in the quantitative modeling of sustainable SCND that consists of OAP. In this article, we cover this gap through simultaneously considering the sustainable OAP in the sustainable SCND as a strategic decision. The proposed supply chain network is composed of five echelons including suppliers classified in different classes, plants, distribution centers that dispatch products via two different ways, direct shipment, and cross-docks, to satisfy stochastic demand received from a set of retailers. The problem has been mathematically formulated as a multi-objective optimization model that aims at minimizing the total costs and environmental effect of integrating SCND and OAP, simultaneously. To tackle the addressed problem, a novel multi-objective hybrid approach called MOHEV with two strategies for its best particle selection procedure (BPSP), minimum distance, and crowding distance is proposed. MOHEV is constructed through hybridization of two multi-objective algorithms, namely the adapted multi-objective electromagnetism mechanism algorithm (AMOEMA) and adapted multi-objective variable neighborhood search (AMOVNS). According to achieved results, MOHEV achieves better solutions compared with the others, and also crowding distance method for BPSP outperforms minimum distance. Finally, a case study for an automobile industry is used to demonstrate the applicability of the approach.