Minimizing sum of the due date assignment costs,maximum tardiness and distribution costs in a supply chain scheduling problem

In production systems, manufacturers face important decisions that affect system profit. In this paper, three of these decisions are modelled simultaneously: due date assignment, production scheduling, and outbound distribution scheduling. These three decisions are made in the sales, production planning and transportation departments. Recently, many researchers have devoted attention to the problem of integrating due date assignment, production scheduling and outbound distribution scheduling. In the present paper, the problems of minimizing costs associated with maximum tardiness, due date assignment and delivery for a single machine are considered. Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Programming (MIP) are used for the solution. This problem is NP-hard, so two meta-heuristic algorithms, an Adaptive Genetic Algorithm (AGA) and a Parallel Simulated Annealing algorithm (PSA), are used for solution of large-scale instances. The present paper is the first time that crossover and mutation operators in AGA and neighbourhood generation in PSA have been used in the structure of optimal solutions. We used the Taguchi method to set the parameters, design of experiments (DOE) to generate experiments, and analysis of variance, the Friedman, Aligned Friedman, and Quade tests to analyse the results. Also, the robustness of the algorithms was addressed. The computational results showed that AGA performed better than PSA.     

贪心核加速动态规划算法求解折扣{0-1}背包问题

针对现有动态规划算法求解折扣{0-1}背包问题（D{0-1}KP）缓慢的问题，基于动态规划思想并结合新型贪心修复优化算法（NGROA）与核算法，通过缩小问题规模加速问题求解来提出一种贪心核加速动态规划（GCADP）算法。首先利用NGROA对问题进行贪心求解，得到非完整项；然后通过计算得到模糊核区间的半径和模糊核区间范围；最后对于模糊核区间内的物品及同一项集内的物品利用基础动态规划（BDP）算法求解。实验结果表明：GCADP算法适用于求解D{0-1}KP，且在求解速度上相比BDP算法平均提升了76.24%，相比FirEGA算法平均提升了75.07%。     

A tabu search procedure for coordinating production,inventory and distribution routing problems

This paper addresses the problem of optimally coordinating a production‐distribution system over a multi‐period finite horizon, where a facility production produces several items that are distributed to a set of customers by a fleet of homogeneous vehicles. The demand for each item at each customer is known over the horizon. The production planning determines how much to produce of each item in every period, while the distribution planning defines when customers should be visited, the amount of each item that should be delivered to customers and the vehicle routes. The objective is to minimize the sum of production and inventory costs at the facility, inventory costs at the customers and distribution costs. We also consider a related problem of inventory routing, where a supplier receives or produces known quantities of items in each period and has to solve the distribution problem. We propose a tabu search procedure for solving such problems, and this approach is compared with vendor managed policies proposed in the literature, in which the facility knows the inventory levels of the customers and determines the replenishment policies.     

基于遗传算法的战略供应链集成研究

在战略供应链研究中,考虑供应链的三个主要阶段,采购、生产、配送和它们之间的相互作用,不同客户需求,设施配对关系,供应商优先权以及现有供应链设计模型的局限性,建立了混合整数非线性规划（MINLP）模型。为有效地解决这种大规模混合整数非线性规划模型的约束,采用自适应遗传算法（AGA）对该模型进行求解优化。实验结果表明,所提混合整数非线性规划模型能够有效解决战略供应链设计中的供应链协同优化问题,并能得到较优的供应链设计方案。     

Coupling genetic algorithm with a grid search method to solve mixed integer nonlinear programming problems

A new hybrid algorithm is being introduced for solving Mixed Integer Nonlinear Programming ( ) problems which arise from study of many real-life engineering problems such as the minimum cost development of oil fields and the optimization of a multiproduct batch plant. This new algorithm employs both the Genetic Algorithm and a modified grid search method interfacing in such a way that the resulting hybrid algorithm is capable of solving many problems efficiently and accurately. Testings indicate that this algorithm is efficient and robust even for some ill-conditioned problems with nonconvex constraints.     

改进修复策略遗传算法求解折扣{0-1}背包问题

第一遗传算法（FirEGA）在求解折扣{0-1}背包问题（D{0-1}KP）过程中对非正常编码的修复未能较好运用物品折扣关系,影响修复效果,导致求解结果不理想。针对该问题,对FirEGA中的贪心修复与优化算法（GROA）进行修正：传统贪心修复按照价值密度对项进行选取,当出现同一项集中两个项均被选取时,文中不再选取价值密度较大项,而是选择价值较大项,得到处理非正常编码个体的新的贪心修复优化算法（NGROA）。在FirEGA中采用NGROA,构成求解D{0-1}KP新的第一遗传算法（NFirEGA）。最后,利用NFirEGA求解四类大规模D{0-1}KP问题,结果表明,NFirEGA在求解精度上明显优于FirEGA。     

Optimization of mixed integer nonlinear economic lot scheduling problem with multiple setups and shelf life using metaheuristic algorithms

This paper addresses the economic lot scheduling problem where multiple items produced on a single facility in a cyclical pattern have shelf life restrictions. A mixed integer non-linear programming model is developed which allows each product to be produced more than once per cycle and backordered. However, production of each item more than one time may result in an infeasible schedule due to the overlapping production times of various items. To eliminate the production time conflicts and to achieve a feasible schedule, the production start time of some or all the items must be adjusted by either advancing or delaying. The objective is to find the optimal production rate, production frequency, cycle time, as well as a feasible manufacturing schedule for the family of items, in addition to minimizing the long-run average cost. Metaheuristic methods such as the genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO), and artificial bee colony (ABC) algorithms are adopted for the optimization procedures. Each of such methods is applied to a set of problem instances taken from literature and the performances are compared against other existing models in the literature. The computational performance and statistical optimization results shows the superiority of the proposed metaheuristic methods with respect to lower total costs compared with other reported procedures in the literature.     

The economic lot scheduling problem: A pure genetic search approach

The economic lot scheduling problem (ELSP) is the challenge of accommodating several products to be produced on a single machine in a cyclical pattern. A solution involves determining the repetitive production schedule for N$N$ products with a goal of minimizing the total of setup and holding costs. We develop the genetic lot scheduling (GLS) procedure. This method combines an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure. We maintain efficient solution feasibility determination, a problematic part of ELSP solution generation and a weakness of several other methods, by employing simple but effective sequencing rules that create “nested” schedules. We create a binary chromosomal representation of the new problem formulation and utilize a genetic algorithm to efficiently search for low cost ELSP solutions. The procedure is applied to a benchmark problem suite from the literature, including Bomberger's stamping problem [Bomberger, A dynamic programming approach to a lot scheduling problem. Management Science 1966; 12:778–84], a problem that has been under investigation since the mid 1960's. The genetic lot scheduling procedure produces impressive results, including the best solutions obtained to date on some problems.     

Soft computing for scheduling with batch setup times and earliness-tardiness penalties on parallel machines

A model for scheduling grouped jobs on identical parallel machines is addressed in this paper. The model assumes that a set-up time is incurred when a machine changes from processing one type of component to a different type of component, and the objective is to minimize the total earliness-tardiness penalties. In this paper, the algorithm of soft computing, which is a fuzzy logic embedded Genetic Algorithm is developed to solve the problem. The efficiency of this approach is tested on several groups of random problems and shows that the soft computing algorithm has potential for practical applications in larger scale production systems.     

Tabu search with path relinking for an integrated production–distribution problem

This paper deals with the problem of integrating production and distribution planning over periods of a finite horizon. We consider a capacity-constrained plant that produces a number of items distributed by a fleet of homogenous vehicles to customers with known demand for each item in each period. The production planning defines the amount of each item produced in every period, while the distribution planning defines when customers should be visited, the amount of each item that should be delivered to customers, and the vehicle routes. The objective is to minimize production and inventory costs at the plant, inventory costs at the customers and distribution costs. We propose two tabu search variants for this problem, one that involves construction and a short-term memory, and one that incorporates a longer term memory used to integrate a path relinking procedure to the first variant. The proposed tabu search variants are tested on generated instances with up to ten items and on instances from the literature involving a single item.     

模糊环境下多周期多决策生鲜闭环物流网络

针对生鲜品因易腐易损性而产生的高频次物流配送及不确定需求与退货量的问题，提出了模糊环境下多周期生鲜闭环物流网络系统，以实现最小系统成本、最优设施选址与最佳配送路径的多决策安排。为求解系统对应的模糊混合整数线性规划（FMILP）模型，首先将生鲜需求量和退货量设定为三角模糊值，其次运用模糊机会约束规划方法将模糊约束等价变换为清晰式，最后利用遗传算法（GA）和粒子群优化（PSO）算法搜索案例的最优解。实验结果表明，多周期闭环系统比单周期更能兼顾多决策规划，同时三角模糊量的置信水平变化对企业最优运作有着显著影响，进而为相关决策者提供借鉴。     

Batching work and rework processes with limited deterioration of reworkables

We study a deterministic problem of planning the production of new and recovering defective items of the same product manufactured on the same facility. Items of the product are produced in batches. The processing of a batch includes two stages. In the first work stage, all items of a batch are manufactured and good quality items go to the inventory to satisfy given demands. In the second rework stage, some of the defective items of the same batch are reworked. Each reworked item has the required good quality. While waiting for rework, defective items deteriorate. There is a given deterioration time limit. A defective item, that is decided not to be reworked or cannot be reworked because its waiting time will exceed the deterioration time limit, is disposed of immediately after its work operation completes. Deterioration results in an increase in time and cost for performing rework processes. It is assumed that the percentage of defective items is the same in each batch, and that they are evenly distributed in each batch. A setup time as well as a setup cost is required to start batch processing and to switch from production to rework. The objective is to find batch sizes and positions of items to be reworked such that a given number of good-quality items is produced and total setup, rework, inventory holding, shortage and disposal cost is minimized. A polynomial dynamic programming algorithm is presented to solve this problem.     

Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs

This paper addresses a production scheduling problem in an injection molding facility. It appears to be the first attempt to schedule parallel machines for multiple items in presence of multiple capacitated resource constraints with sequence-dependent setup costs and times. The objective is to meet customer demands while minimizing the total inventory holding costs, backlogging costs and setup costs. We present a mathematical formulation of the problem. The computational complexity associated with the formulation makes it difficult for standard solvers address industrial-dimensioned problems in reasonable solution time. To overcome this, a two-phase workcenter-based decomposition scheme has been developed in this paper. The computational results for different problem sizes demonstrate that this scheme is able to solve industrial-dimensioned problems within reasonable time and accuracy.     

A planar single facility location and border crossing problem

In this study, we tackle the problem of locating a facility in a region where a fixed line barrier divides the region into two. The resulting subregions communicate with each other through a number of passage points located on the line barrier. Our contribution is threefold. First, we formulate the problem as a Mixed Integer Nonlinear Programming (MINLP) model and provide an optimal solution methodology based on an Outer Approximation (OA) algorithm. Second, we discuss the minimax version of this problem for locating an emergency facility and use the OA algorithm to solve the problem. We then provide simple example problems and extensive computational results for both problems. Finally, we propose a one-infinity approximation approach for the latter problem which yields a linear model. Practical uses of the models have been discussed in the border crossing context.     

A hybrid Lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times

This paper examines the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such problems are quite common in the semiconductor manufacturing industry. In particular, this paper pays special attention to the chipset production in the semiconductor Assembly and Test Manufacturing (ATM) factory and constructs a Mixed Integer Programming (MIP) model for the problem. The primal problem is decomposed into a lot-sizing subproblem and a set of single-machine scheduling subproblems by Lagrangian decomposition. A Lagrangian-based heuristic algorithm, which incorporates the simulated annealing algorithm aimed at searching for a better solution during the feasibility construction stage, is proposed. Computational experiments show that the proposed hybrid algorithm outperforms other heuristic algorithms and meets the practical requirement for the tested ATM factory.     

Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem

Generalised Assignment Problems (GAP), traditionally solved by Integer Programming techniques, are addressed in the light of current Constraint Programming methods. A scheduling application from manufacturing, based on a modified GAP, is used to examine the performance of each technique under a variety of problem characteristics. Experimental evidence showed that, for a set of assignment problems, Constraint Logic Programming (CLP) performed consistently better than Integer Programming (IP). Analysis of the CLP and IP processes identified ways in which the search was effective. The insight gained from the analysis led to an Integer Programming approach with significantly improved performance. Finally, the issue of collaboration between the two contrasting approaches is examined with respect to ways in which the solvers can be combined in an effective manner.     

Multiobjective optimization of MPLS-IP networks with a variable neighborhood genetic algorithm

This paper presents a Genetic Algorithm for the optimization of multiple indices of Quality of Service of Multi Protocol Label Switching (MPLS) IP networks. The proposed algorithm, the Variable Neighborhood Multiobjective Genetic Algorithm (VN-MGA), is a Genetic Algorithm based on the NSGA-II, with the particular feature that solutions are encoded defining two different kinds of neighborhoods. The first neighborhood is defined by considering as decision variables the edges that form the routes to be followed by each request, whilst the second part of solution is kept constant. The second neighborhood is defined by considering the request sequence as decision variable, with the first part kept constant. Comparisons are performed with: (i) a VNS algorithm that performs a switch between the same two neighborhoods that are used in VN-MGA; and (ii) the results obtained with an integer linear programming solver, running a scalarized version of the multiobjective problem. The results indicate that the proposed VN-MGA outperforms the pure VNS algorithm, and provides a good approximation of the exact Pareto fronts obtained with Integer Linear Programming (ILP) approach, at a much smaller computational cost. Besides potential benefits of the application of the proposed approach to the optimization of packet routing in MPLS networks, this work raises the theoretical issue of the systematic application of variable encodings, which allow variable neighborhood searches, as generic operators inside general evolutionary computation algorithms.     

A new evolutionary clustering search for a no-wait flow shop problem with set-up times

This paper addresses the m-machine no-wait flow shop problem where the set-up time of a job is separated from its processing time. The performance measure considered is the total flowtime. A new hybrid metaheuristic Genetic Algorithm–Cluster Search is proposed to solve the scheduling problem. The performance of the proposed method is evaluated and the results are compared with the best method reported in the literature. Experimental tests show superiority of the new method for the test problems set, regarding the solution quality.     

需求随机的变质性产品生产计划模型

研究了能力约束的有限计划展望期生产计划问题,各周期的需求随机,库存产品存在变质且变质率为常数。建立了问题的期望值模型,目标函数为极小化生产准备成本、生产成本、库存成本的期望值。提出了随机模拟、遗传算法和启发式算法相结合的求解算法。用数值实例对模型和算法进行了验证,优化结果表明模型和算法是有效的。     

Tractable Fragments of Presburger Arithmetic

In this paper we introduce a problem called Quantified Integer Programming, which generalizes the Quantified Satisfiability problem (QSAT). In a Quantified Integer Program (QIP) the program variables can assume arbitrary integral values, as opposed to the boolean values that are assumed by the variables of an instance of QSAT. QIPs naturally represent two-person integer matrix games. The Quantified Integer Programming problem is PSPACE-hard in general, since the QSAT problem is PSPACE-complete. Quantified Integer Programming can be thought of as a restriction of Presburger Arithmetic, in that we allow only conjunctions of linear inequalities. We focus on analyzing various special cases of the general problem, with a view to discovering subclasses that are tractable. Subclasses of the general QIP problem are obtained by restricting either the constraint matrix or quantifier specification or both. We show that if the constraint matrix is totally unimodular, the problem of deciding a QIP can be solved in polynomial time. We also establish the computational complexities of Oblivious strategy games and Clairvoyant strategy games.