Advanced backtracking search optimization algorithm for a new joint replenishment problem under trade credit with grouping constraint

In the real business situation, suppliers usually provide retailers with forward financing to decrease inventory or increase demand. Moreover, some heterogeneous goods are not allowed to transport together, or a penalty cost is incurred when heterogeneous goods are transported at the same time. This research proposes a practical multi-item joint replenishment problem (JRP) by considering trade credit and grouping constraint in accordance with the practical situation. The JRP aims to find reasonable item replenishment frequencies and each group’s basic replenishment cycle time so that the overall cost can be minimized. Four intelligent algorithms, which include an advanced backtracking search optimization algorithm (ABSA), genetic algorithm (GA), differential evolution (DE) and backtracking search optimization algorithm (BSA), are provided to solve this problem. Findings of contrastive example verify that ABSA is superior to GA, DE, and BSA, which have been validated to be effective algorithms. Randomly generated problems are used to test the performance of ABSA. Results indicate ABSA is more effective and stable to resolve the proposed JRP than the other algorithms. ABSA is a good solution for the proposed JRP with heterogeneous items under trade credits.     

An evolutionary algorithm to solve the joint replenishment problem using direct grouping

There has been much work in establishing a joint replenishment policy to minimize the total cost of inventory replenishment. Most of this work uses the indirect grouping method. Little research has been done with direct grouping methods. In this paper we develop an evolutionary algorithm (EA) that uses direct grouping to solve the joint replenishment problem (JRP). We test the EA and compare these results with results with the best available algorithm. The EA is shown to find a replenishment policy that incurs a lower total cost than the best available algorithm for some problem parameters.     

费用与资源约束双重模糊下的联合采购模型——基于差分进化算法的研究*

针对复杂不确定环境下的联合采购决策难题,用三角模糊数表示不确定的次要订货费用、库存持有费用和资金约束条件,用梯形模糊数表示不确定的存储空间约束,构建了模糊联合采购模型,并采用两种方法对模糊总成本进行去模糊化处理。进而在对差分进化(DE)算法改进并借助典型函数测试性能的基础上,给出了基于改进DE的模糊联合采购模型求解流程,算例证明所设计的DE算法能较好地解决模糊联合采购问题。     

A joint replenishment problem considering multiple trucks with shipment and resource constraints

A joint replenishment problem (JRP) is presented to determine the optimal reordering policy for multi-items with a percentage of defective items. This JRP also has several constraints, such as shipment constraint, budget constraint, and transportation capacity constraint. At the meantime, multiple trucks, each with a fixed transportation cost, are considered and also order quantities of restricted items are not shared among the trucks during the shipment. The objective is to minimize the total expected cost per unit time. A two-dimensional genetic algorithm (GA) is provided to determine an optimal family cycle length and the reorder frequencies. A numerical example is presented and the results are discussed. Extensive computational experiments are performed to test the performance of the GA. The JRP is also solved by using an evolutionary algorithm (EA) and the results obtained from GA and EA are compared.     

Developing a multi-objective,multi-item inventory model and three algorithms for its solution

We develop a multi-objective model in a multi-product inventory system.The proposed model is a joint replenishment problem(JRP) that has two objective functions.The first one is minimization of total ordering and inventory holding costs,which is the same objective function as the classic JRP.To increase the applicability of the proposed model,we suppose that transportation cost is independent of time,is not a part of holding cost,and is calculated based on the maximum of stored inventory,as is the case in many real inventory problems.Thus,the second objective function is minimization of total transportation cost.To solve this problem three efficient algorithms are proposed.First,the RAND algorithm,called the best heuristic algorithm for solving the JRP,is modified to be applicable for the proposed problem.A multi-objective genetic algorithm(MOGA) is developed as the second algorithm to solve the problem.Finally,the model is solved by a new algorithm that is a combination of the RAND algorithm and MOGA.The performances of these algorithms are then compared with those of the previous approaches and with each other,and the findings imply their ability in finding Pareto optimal solutions to 3200 randomly produced problems.     

基于模拟退火的混合差分进化算法及其在联合补货-配送集成优化中的应用

针对差分进化 (Differential evolution, DE)算法搜索效率较低和容易陷入局部最优的缺点,设计了基于SA的混合差分进化算法(SA-based Hybrid DE, SAHDE),以提高DE算法的全局寻优能力。该算法采用自适应变异算子和交叉算子,并结合模拟退火(Simulated Annealing, SA)算法的Metropolis 准则。首先通过标准测试函数对改进的SAHDE进行性能测试,证明了该算法比DE、自适应混合DE (Adaptive Hybrid DE, AHDE)和遗传算法(Genetic Algorithm, GA)更有效。进而将该算法运用到联合补货-配送集成优化(典型NP-hard)问题的求解中,通过大规模的算例分析,证实SAHDE在解决联合补货-配送优化问题比DE、AHDE和GA更有效。     

A sensitivity analysis of solving joint replenishment problems using the RAND method under inaccurate holding cost estimates and demand forecasts

This paper presents a study of solving the joint replenishment problem (JRP) by using the RAND method, a heuristic approach that has been proven to find almost as good as optimal solutions, under uncertain customer demands and inaccurate unit holding cost estimation. The classical JRP deals with the issue of determining a replenishment policy that minimizes the total cost of replenishing multiple products from a single supplier. The total cost considered in the JRP consists of a major ordering cost independent of the number of items in the order, a minor ordering cost depending on the items in the order, and the holding cost. There have been many heuristic approaches proposed for solving the JRP. Most of the research work was done under the assumptions that the demand for each item type and the unit holding cost are known and constant. However, in the real world accurately forecasting customer demands and precisely estimating the unit holding cost are both difficult. Besides, the real values of the demands and the unit holding cost may change over the replenishment horizon. The present study addresses the issue of the uncertain demands and the unit holding cost to the JRP and investigates how misestimates of these demands and holding costs may influence the replenishment policy as determined by the famous JRP heuristic, the RAND method.     

PSO优化在模糊联合补充问题中的应用

对用PSO算法解决需求为不确定的联合补充问题进行了研究。运用模糊规划方法处理需求为模糊变量的联合补充问题,得到了作为求解目标的模糊数学模型;采用PSO思想对该模型进行分析,转化为PSO问题模型,制定出算法流程,并用数值实例验证了提出的粒子群优化模型和求解算法的有效性;对随机生成的大量数据进行处理,结果证明问题规模相同时该算法较遗传算法具有更高的效率。     

联合补货策略下的供应商选择和订货量分配协同优化

分析基于联合补货策略的供应商选择与商品订货量分配协同决策问题,设计一种有效的改进差分进化算法(Improved differential evolution,IDE)进行求解.在考虑商品异质性带来的分组约束基础上,构建一种拓展的供应商选择与订货量分配协同决策新模型.对比算例分析表明,IDE在求解此问题及其扩展问题时优于标准差分进化算法和模拟退火算法,随机生成的大规模算例进一步验证了IDE求解此类复杂问题的优越性.     

Optimizing an integrated inventory-routing system for multi-item joint replenishment and coordinated outbound delivery using differential evolution algorithm

A practical and new joint replenishment and delivery (JRD) problem that considers coordinated outbound delivery policy of multiple items (named JRCD) is studied. The proposed JRCD model aims to balance the joint replenishment, inventory holding, and delivery costs by deciding on the replenishment and outbound delivery schedule of each item. The indirect grouping policy is utilized in the JRCD problem, so items dispatched jointly in each outbound delivery are identified on the basis of the replenishment frequency and delivery frequency. Once the matching of items and retailers in each outbound delivery is confirmed, the optimal route can be subsequently obtained by solving the traveling salesman problem. To solve this complex optimization problem, an intelligent algorithm based on differential evolution is utilized because of its superior performance in handling similar complex problems. Basic and extended numerical examples are used to verify the effectiveness of the proposed algorithm. A comparison between the proposed JRCD and JRD with independent delivery is conducted with examples of varying cost parameters. Results provide interesting insights and useful guidelines for managers to create a reasonable policy for effectively controlling their total cost.     

一种新型混合算法在混流装配调度中的应用

针对含有缓冲区的混流装配中同时存在的生产成本和库存成本问题,提出了一种基于遗传算法和差分进化算法的混合框架,并将其用于混流装配调度的实际问题中。通过融合遗传算法有效处理离散变量及差分进化算法有效处理连续变量的优点,在综合考虑降低生产成本和缓冲区库存的同时,兼顾了每个型号产品生产的顺序及数量。计算机仿真结果表明,与传统算法相比,该算法在混流装配调度上具有收敛速度快、优化能力强、算法可靠等优势。该混合算法可以显著改善多参数、高度非线性问题的优化结果,提高计算效率。     

A supplier-selection model with classification and joint replenishment of inventory items

Since inventory costs are closely related to suppliers, many models in the literature have selected the suppliers and also allocated orders, simultaneously. Such models usually consider either a single inventory item or multiple inventory items which have independent holding and ordering costs. However, in practice, ordering multiple items from the same supplier leads to a reduction in ordering costs. This paper presents a model in capacity-constrained supplier-selection and order-allocation problem, which considers the joint replenishment of inventory items with a direct grouping approach. In such supplier-selection problems, the following items are considered: a fixed major ordering cost to each supplier, which is independent from the items in the order; a minor ordering cost for each item ordered to each supplier; and the inventory holding and purchasing costs. To solve the developed NP-hard problem, a simulated annealing algorithm was proposed and then compared to a modified genetic algorithm of the literature. The numerical example represented that the number of groups and selected suppliers were reduced when the major ordering cost increased in comparison to other costs. There were also more savings when the number of groups was determined by the model in comparison to predetermined number of groups or no grouping scenarios.     

差分进化算法在模糊多资源约束联合补货模型中的应用

本文用三角模糊数表示不确定的资金约束,用梯形模糊数表示不确定的存储空间约束,构建了模糊规划联合补货模型,目标函数为最小化订货成本、库存持有成本和运输成本,决策变量为基本补充周期和每种产品的补充周期。通过对变异算子与选择操作进行变化,设计了改进的差分进化算法对模型进行求解,并通过实例证实了模型与算法的科学合理性。     

A charging-scheme decision model for electric vehicle battery swapping station using varied population evolutionary algorithms

This paper proposes a new battery swapping station (BSS) model to determine the optimized charging scheme for each incoming Electric Vehicle (EV) battery. The objective is to maximize the BSS’s battery stock level and minimize the average charging damage with the use of different types of chargers. An integrated objective function is defined for the multi-objective optimization problem. The genetic algorithm (GA), differential evolution (DE) algorithm and three versions of particle swarm optimization (PSO) algorithms have been implemented to solve the problem, and the results show that GA and DE perform better than the PSO algorithms, but the computational time of GA and DE are longer than using PSO. Hence, the varied population genetic algorithm (VPGA) and varied population differential evolution (VPDE) algorithm are proposed to determine the optimal solution and reduce the computational time of typical evolutionary algorithms. The simulation results show that the performances of the proposed algorithms are comparable with the typical GA and DE, but the computational times of the VPGA and VPDE are significantly shorter. A 24-h simulation study is carried out to examine the feasibility of the model.     

A Joint Replenishment Inventory-Location Model

We introduce a distribution center location model that incorporates joint replenishment inventory costs at the distribution centers. The model is formulated as a Fixed Charge Location Problem (FCLP) which objectively considers not only location specific costs but also inventory replenishment costs. In the joint replenishment problem we consider a single item and several distribution centers in different locations and apply a similar algorithm to the one used to solve the multi-item problem. We propose a Greedy Randomized Adaptive Search Procedure (GRASP) to solve the problem.     

基于自适应差异进化法的电力系统无功优化

差异进化算法（DE）是一种新的进化算法,近年来的研究和应用已经展示出很大的应用潜力,但其中的某些参数需通过试验确定,影响了实用性。提出一种自适应差异进化算法（FADE）,能使算法的控制参数粮据求解问题的不同在优化过程中自适应发生改变,并应用于无功优化问题。通过IEEE-30节点算例系统的仿真结果证明,与DE和GA算法相比,模糊差异进化算法具有很强的自适应性及通用性。     

A new genetic algorithm for the machine/part grouping problem involving processing times and lot sizes

This paper reports a new genetic algorithm (GA) for solving a general machine/part grouping (GMPG) problem. In the GMPG problem, processing times, lot sizes and machine capacities are all explicitly considered. To evaluate the solution quality of this type of grouping problems, a generalized grouping efficacy index is used as the performance measure and fitness function of the proposed genetic algorithm. The algorithm has been applied to solving several well-cited problems with randomly assigned processing times to all the operations. To examine the effects of the four major factors, namely parent selection, population size, mutation rate, and crossover points, a large grouping problem with 50 machines and 150 parts has been generated. A multi-factor (3⁴) experimental analysis has been carried out based on 324 GA solutions. The multi-factor ANOVA test results clearly indicate that all the four factors have a significant effect on the grouping output. It is also shown that the interactions between most of the four factors are significant and hence their cross effects on the solution should be also considered in solving GMPG problems.     

异构云系统中基于智能优化算法的多维资源公平分配

资源分配策略的研究一直是云计算领域研究的热点和难点,针对异构云计算环境下多维资源的公平分配问题,结合基因算法（GA）和差分进化算法（DE）,分别给出了两种兼顾分配公平性和效率的资源分配策略,改进了解矩阵表达式使异构云系统中的主资源公平分配（DRFH）模型转化成为整数线性规划（ILP）模型,并提出了基于最大任务数匹配值（MTM）的初始解产生机制和使不可行解转化为可行解的修正操作,以此提高算法的收敛速度,使其能够快速有效地得到最优分配方案。实验结果表明,基于GA和DE算法的多维资源公平分配策略可以得到近似最优解,在最大化最小主资源份额目标值和资源利用率方面明显优于Best-Fit DRFH和Distributed-DRFH,而且针对不同任务类型的资源需求,具有较强的自适应能力。     

Solving lot-sizing problem with quantity discount and transportation cost

Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.     

A genetic algorithm with proper parameters for manufacturing cell formation problems

One fundamental problem in cellular manufacturing is the formation of product families and machine cells. Many solution methods have been developed for the cell formation problem. Since efficient grouping is the prerequisite of a successful Cellular Manufacturing installation the research in this area will likely be continued. In this paper, we consider the problem of cell formation in cellular manufacturing systems with the objective of maximizing the grouping efficacy. We propose a Genetic Algorithm (GA) to obtain machine-cells and part-families. Developed GA has three different selection and crossover operators. The proper operators and parameters of the GA were determined by design of experiments. A set of 15 test problems with various sizes drawn from the literature is used to test the performance of the proposed algorithm. The corresponding results are compared to several well-known algorithms published. The comparative study shows that the proposed GA improves the grouping efficacy for 40% of the test problems.