连锁门店选址与配送中心选择联合决策的f-MIGP模型

建立了连锁门店选址和配送中心选择联合决策问题的模糊多目标混合整数规划模型．针对该模型的特殊结构。提出一种适用的求解策略：首先确定每个模糊目标的隶属度函数;然后将模糊多目标混合整数规划模型转化为等价的清晰多目标混合整数规划模型,通过最大最小算子求出目标值;最后借助于两阶段算法,求出问题的最优解．通过应用算例进一步说明了该模型的有效性和可行性．     

Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains

This work applies fuzzy sets to integrating manufacturing/distribution planning decision (MDPD) problems with multi-product and multi-time period in supply chains by considering time value of money for each of the operating cost categories. The proposed fuzzy multi-objective linear programming model (FMOLP) attempts to simultaneously minimize total costs and total delivery time with reference to inventory levels, available machine capacity and labor levels at each source, as well as market demand and available warehouse space at each destination, and the constraint on total budget. An industrial case demonstrates the feasibility of applying the proposed model to a realistic MDPD problem and several significant management implications are presented based on computational analysis and comparisons with the existing MDPD methods. The main advantage of the proposed model is that it presents a systematic framework that facilitates fuzzy decision-making for solving the multi-objective MDPD problems with multi-product and multi-time period in supply chains under an uncertain environment, enabling the decision maker to adjust the search direction during the solution procedure to obtain a preferred satisfactory solution.     

A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem

In this paper, we concentrate on developing a fuzzy rough multi-objective decision-making model according to uncertainty theory. We present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method, which is similar to the interactive fuzzy rough satisfying method, in order to obtain a satisfying solution for the decision maker. In addition, the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents. Furthermore, combined with the techniques of fuzzy rough simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi-objective programming problem. Finally, a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm, and then a sensitivity analysis is made.     

A goal programming model for joint decision making of inventory lot-size,supplier selection and carrier selection

In this paper, we address a problem in which a storage space constrained buyer procures a single product in multiple periods from multiple suppliers. The production capacity constrained suppliers offer all-unit quantity discounts. The late deliveries and rejections are also incorporated in sourcing. In addition, we consider transportation cost explicitly in decision making which may vary because of freight quantity and distance of shipment between the buyer and a supplier. We propose a multi-objective integer linear programming model for joint decision making of inventory lot-sizing, supplier selection and carrier selection problem. In the multi-objective formulation, net rejected items, net costs and net late delivered items are considered as three objectives that have to be minimized simultaneously over the decision horizon. The intent of the model is to determine the timings, lot-size to be procured, and supplier and carrier to be chosen in each replenishment period. We solve the multi-objective optimization problem using three variants of goal programming (GP) approaches: preemptive GP, non-preemptive GP and weighted max–min fuzzy GP. The solution of these models is compared at different service-level requirements using value path approach.     

Multi-objective solid transportation problems with budget constraint in uncertain environment

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.     

解约束规划问题的新型多目标粒子群优化算法

给出了一种求解约束规划问题的新解法。新方法将约束规划问题转化成两个目标优化问题,并对转化后的多目标优化问题设计了一种新型多目标粒子群优化算法(MOPSO)。数据实验表明该算法对带约束的规划问题求解是非常有效的。     

热轧带钢批量计划分解算法

针对热轧带钢批量计划问题,提出基于模糊聚类和约束规划的多目标优化分解算法。算法利用模糊C均值聚类将一个轧制单元的板坯划分为若干簇,采用约束规划求解簇内板坯顺序和簇间顺序,合成各簇的解得到轧制单元批量计划。基于生产实际数据和随机数据的实验结果表明算法具有满意的计算效率和效果。     

Multi-objective decision making model under fuzzy random environment and its application to inventory problems

In this paper, we concentrate on developing a fuzzy random multi-objective model about inventory problems. By giving some definitions and discussing some properties of fuzzy random variable, we design a method of solving solution sets of fuzzy random multi-objective programming problems. These are applied to numerical inventory problems in which all inventory costs, purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature, and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers. The exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates. By comparing the results with those from the fuzzy multi-objective models, we believe that the proposed fuzzy random multi-objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life.     

Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview

In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results.     

Two parameter tuned multi-objective evolutionary algorithms for a bi-objective vendor managed inventory model with trapezoidal fuzzy demand

This paper presents a bi-objective vendor managed inventory (BOVMI) model for a supply chain problem with a single vendor and multiple retailers, in which the demand is fuzzy and the vendor manages the retailers’ inventory in a central warehouse. The vendor confronts two constraints: number of orders and available budget. In this model, the fuzzy demand is formulated using trapezoidal fuzzy number (TrFN) where the centroid defuzzification method is employed to defuzzify fuzzy output functions. Minimizing both the total inventory cost and the warehouse space are the two objectives of the model. Since the proposed model is formulated into a bi-objective integer nonlinear programming (INLP) problem, the multi-objective evolutionary algorithm (MOEA) of non-dominated sorting genetic algorithm-II (NSGA-II) is developed to find Pareto front solutions. Besides, since there is no benchmark available in the literature to validate the solutions obtained, another MOEA, namely the non-dominated ranking genetic algorithms (NRGA), is developed to solve the problem as well. To improve the performances of both algorithms, their parameters are calibrated using the Taguchi method. Finally, conclusions are made and future research works are recommended.     

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.     

Reentry Trajectory Optimization for Hypersonic Vehicles Using Fuzzy Satisfactory Goal Programming Method

Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.     

解非线性约束规划问题的新型多目标遗传算法

给出非线性约束规划问题的一种新解法。把带约束的非线性规划问题转化成为两个目标的多目标优化问题,并为转化后的多目标优化模型设计了一种新型多目标遗传算法,数据实验表明该算法对带约束的非线性规划问题求解是非常有效的。     

Application of fuzzy multi-objective linear programming to aggregate production planning

This study develops a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-product aggregate production planning (APP) decision problem in a fuzzy environment. The proposed model attempts to minimize total production costs, carrying and backordering costs and rates of changes in labor levels considering inventory level, labor levels, capacity, warehouse space and the time value of money. A numerical example demonstrates the feasibility of applying the proposed model to APP problem. Its advantages are also discussed. The proposed model yields a compromise solution and the decision maker's overall levels of satisfaction. In particular, in contrast to other APP models, several significant characteristics of the proposed model are presented.     

Applying fuzzy multi-objective linear programming to project management decisions with the interactive two-phase method

The aim of this paper is to develop an interactive two-phase method that can help the Project Manager (PM) with solving the fuzzy multi-objective decision problems. Therefore, in this paper, we first revisit the related papers and focus on how to develop an interactive two-phase method. Next, we establish to consider the imprecise nature of the data by fulfilling the possibilistic programming model, and we also assume that each objective work has a fuzzy goal. Finally, for reaching our objective, the detailed numerical example is presented to illustrate the feasibility of applying the proposed approach to PM decision problems at the end of this paper. Results show that our model can be applied as an effective tool. Furthermore, we believe that this approach can be applied to solve other multi-objective decision making problems.     

A two-phase possibilistic linear programming methodology for multi-objective supplier evaluation and order allocation problems

In this study, an integration of the analytic hierarchy process (AHP) and a multi-objective possibilistic linear programming (MOPLP) technique is developed to account for all tangible, intangible, quantitative, and qualitative factors which are used to evaluate and select suppliers and to define the optimum order quantities assigned to each. A multi-objective linear programming technique is first employed to solve the problem. To model the uncertainties encountered in the integrated supplier evaluation and order allocation methodology, fuzzy theory is adopted. Hence, possibilistic linear programming (PLP) is proposed for solving the problem, as it is believed to be the best approach for absorbing the imprecise nature of the real world. In the supplier evaluation phase, environmental criteria are also considered.     

The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem

This paper develops a fuzzy multi-objective linear programming (FMOLP) model for solving a multi-objective single-machine scheduling problem. The proposed model attempts to minimize the total weighted tardiness and makespan simultaneously. In this problem, a proposed FMOLP method is applied with respect to the overall acceptable degree of the decision maker (DM) satisfaction. A number of numerical examples are solved to show the effectiveness of the proposed approach. The related results are compared with the Wang and Liang's approach. These computational results show that the proposed FMOLP model achieves lower objective functions and higher satisfaction degrees.     

A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints

Traditionally, logistics analysts divide decisions levels into strategic, tactical and operational. Often these levels are considered separately for modeling purposes. The latter may conduce to make non-optimal decisions, since in reality there is interaction between the different levels. In this research, a cross-level model is derived to analyze decisions about inventory control and facility location, specially suited to urban settings, where the storage space is scarce and the vehicles’ capacity is usually restricted. Both conditions, on the one hand make the problem difficult to solve optimally but on the other hand make it more realistic and useful in practice. This paper presents a simultaneous nonlinear-mixed-integer model of inventory control and facility location decisions, which considers two novel capacity constraints. The first constraint states a maximum lot size for the incoming orders to each warehouse, and the second constraint is a stochastic bound to inventory capacity. This model is NP-Hard and presents nonlinear terms in the objective function and a nonlinear constraint. A heuristic solution approach is introduced, based on Lagrangian relaxation and the subgradient method. Numerical experiments were designed and applied. The solution procedure presented good performance in terms of the objective function. One of the key conclusions of the proposed modeling approach is the fact that a reduction of the inventory capacity does not necessarily imply an increase in the number of installed warehouses. In fact, reducing the order size allows the optimal allocation of customers (those with higher variances) into different warehouses, reducing the total system’s cost.     

An integrated three-stage maintenance scheduling model for unrelated parallel machines with aging effect and multi-maintenance activities

We propose an integrated three-stage model for maintenance scheduling of unrelated parallel machines (UPMs) with aging effect and multi-maintenance activities (AEMMAs) using a variety of MODM techniques such as the fuzzy analytic hierarchy process (AHP), the technique for order of preference by similarity to ideal solution (TOPSIS), and goal programming (GP). We use fuzzy AHP in the first stage of the proposed model to account for the inherent ambiguity and vagueness in real-life maintenance scheduling problems. In the second stage, we use TOPSIS to reduce the multi-objective problem into an efficient bi-objective problem. Finally, we use GP to solve the resulting bi-objective problem and develop an optimal maintenance schedule in the third stage of the model. We use a numerical example to demonstrate the applicability of the proposed approach and exhibit the efficacy of the procedures and algorithms.     

A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.