Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem: A Heuristic Implementation

The multi-item capacitated lot-sizing problem consists of determining the magnitude and the timing of some operations of durable results for several items in a finite number of processing periods so as to satisfy a known demand in each period. The subgradient algorithm implemented to minimize the processing costs is based on a Lagrangean relaxation of the capacity constraints imposed on the resources. The method incorporates a primal partitioning scheme—with a network flow subproblem—to obtain good feasible solutions.     

A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints

A heuristic algorithm is presented for solving the scheduling of several items in parallel under capacity constraints with setup and carrying costs. The method is based upon finding a lower bound solution for these costs, securing the feasibility of the solution, and improving the feasible solution so obtained until no further improvements can be made. Comparison of the performance of the proposed heuristic algorithm to that of an exact mixed-integer programming model showed that best solution costs found by the heuristic deviated on an average by 1% from the optimal values, while the computing time was on an average 1/140 of that required by the exact method.     

The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity

This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the “forward-pass” concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.     

成组单元生产批量计划问题的知识进化算法

有资源约束的成组单元生产批量计划问题是一个NP难题,为有效求解该问题,提出了一种知识进化算法求解方案,并阐明了知识进化算法的具体实现过程。通过对仿真实例的计算和结果比较,表明了该算法在寻优能力等方面都明显优于遗传算法。     

基于改进粒子群算法求解单级多资源约束生产批量计划问题

本文提出了用于求解单级多资源约束的生产批量计划问题的改进二进制粒子群算法,阐明了算法的具体实现过程。通过对其它文献中的例子进行计算和结果比较,表明了该算法在寻优能力、求解速度和稳定性方面都明显优于文献中的传统遗传算法和退火惩罚混合遗传算法。     

A Dual-Cost Heuristic For The Capacitated Lot Sizing Problem

This paper examines a mathematical programming method of accounting for capacity costs for the deterministic, multi-item, single operation lot sizing problem. With the capacity constraints of CLSP removed with Lagrangian relaxation, the problem decomposes into a set of uncapacitated single product lot sizing problems which are solved with dynamic programming. The Lagrangian dual costs are updated by subgradient optimization. Feasible solutions (production plans within the capacity limitations) are constructed with a heuristic smoothing procedure. The dual-cost heuristic gave solutions which were better on average than the other algorithms tested (and was faster than some comparable algorithms).     

Heuristic Procedures for the Single Operation, Multi-Item Loading Problem

This paper considers the planning of individual machine groups or work centers producing many different products such as components, subassemblies or assemblies. The deterministic multi-item lot size problem with limited capacity has attracted much attention during the past two decades but no efficient optimization techniques are available up to now. We therefore suggest an efficient heuristic which is an extension of the Eisenhut heuristic. The resulting production programs always adhere to the characteristics of the dominant schedules. Special attention is given to the characterization of these dominant schedules.     

基于改进蚁群算法的一类运输能力约束的生产-运输批量问题求解

针对生产与运输两个过程的联合决策,通过分析一类生产-运输批量优化问题,建立的混合0-1整数规划模型整合了多产品多阶段能力约束批量生产和产品运输。其中运输成本由运输工具使用数量决定,当企业内部运输能力不能满足运输需求时可将运输外包,但需支付更高的运输成本。根据此问题的特点,构造改进蚁群算法求解,令其信息素和启发信息都存在0和1两种状态下的不同取值,通过转移概率确定0-1生产准备矩阵,进一步得到生产矩阵和运输计划。仿真实验结果表明在生产批量决策的同时考虑运输,可以减少运输成本,令总费用最小,通过将实验结果与其他优化算法比较,所构造的蚁群算法寻优概率是100%,平均进化10代,平均耗时小于1 s,稳定性和求解效率均高于其他算法,是求解这类问题一种有效与适用的算法。     

Capacitated Multiple Item Ordering Problem with Quantity Discounts

Purchasing managers face a complex problem when determining order quantities for multiple items in the presence of quantity discounts and resource limitations. In this paper, the problem is formulated as a mathematical programming model. An efficient solution algorithm is developed utilizing the Lagrangian relaxation approach. Extensive computational experiments are performed and the results are presented.     

The Stochastic Uncapacitated Facility Location Problem: A New Formulation and Extensions to the Capacitated Problem

This note presents an alternative formulation of the deterministic location model which Tcha and Yoon have recently developed to approximate the stochastic uncapacitated facility location problem. The model, besides being more compact and easier to handle than their model, has the distinct advantage of having a tighter LP relaxation. Also suggested is how the new formulation can be implemented in Van Roy's Cross Decomposition method for solving a more general stochastic capacitated problem.     

多资源约束批量计划问题的分散搜索算法

为求解多资源有资源约束的生产批量计划问题,提出了一种基于分散搜索算法(Scatter Search,SS)和能力调整方法(Capacity Adjusting Methods,CAM)相结合的方法,阐明了该方法的具体实现过程。在对不可行解进行资源能力调整的实施阶段,采用"先顺序-再逆序"的方式进行处理。通过对文献中的仿真算例进行计算和结果比较,表明了该算法在寻优能力、求解速度和稳定性方面的优势。     

带装载能力的需求依背包拆分车辆路径问题

以最小化总的旅行时间为优化目标,以单车场、单车型、装载能力和需求依背包拆分等为约束条件,将以往客户需求不可拆分的条件松弛为依背包来离散拆分,建立了带装载能力的需求依背包拆分VRP（CVRPSDB）的单目标数学模型。设计了一个自适应禁忌搜索算法（ATSA）对模型进行求解。该算法采用了自适应惩罚机制,构建了一个多邻域结构体,并针对客户点与背包都设计了相应的邻域操作算子,较好地适应了客户需求量的离散拆分程度。经算例测试与文献对比,验证了所设计模型与算法的有效性。     

Economic Lot-Sizing with Remanufacturing Options

We study a production planning problem with remanufacturing. We provide the problem's general formulation and assess its computational complexity under various cost structures. We prove that the problem is NP-complete for general concave-cost structures. When costs are linear, we obtain an 0(T³) algorithm based on transforming the problem into the transportation problem in a special way. Finally, we suggest linearizing costs as an alternative for solving the problem in the real world.     

混合智能算法在CVRPTW中的应用

考虑到遗传算法本身存在易"早熟收敛"的缺陷,提出将模拟退火算法中的Metropolis接受准则引入到遗传算法的群体更新策略中,并将其应用于物流管理中的带容量约束和时间窗的车辆路径问题(CVRPTW).针对Solomon提出的几个标准问题,从数值计算上探索了遗传算法和模拟退火算法融合后的优化能力,获得了满意的效果.     

具有时间窗约束累积性车辆路径问题的禁忌搜索优化算法

基于对中国实际物流运输中成本计算方法的研究,考虑到我国高速公路系统计价方式的特殊性,提出了具有时间窗约束的累积性车辆路径问题。以降低实际车辆运输成本为目标,设计了新型的禁忌搜索算法对问题进行有效求解;算法中嵌入多种邻域搜索方法,允许同时在可行和不可行解空间内进行邻域搜索,同时采用Nagata提出的时间窗违反量计算方法[1-2]对解的时间窗约束违反进行评估。针对提出的新型问题的数值试验证明了所采用的时间窗违反量计算方法的时间节约性和有效性;同时由于该问题可以覆盖传统的累积性车辆路径问题,对后者的数值实验以及与其他优化算法的对比验证了所提出算法的优良求解效果。     

Lotsizing in Multi-Item Multi- Machine Job Shops

A great many manufacturing facilities can be described as closed job shops which process multiple items through multiple work centers for stock or for assembly. The performance of these shops is strongly dependent on the batching policies employed for work in the shop. In particular, waiting time in queue and total manufacturing lead time for batches are functions of lotsizes. In turn these affect work-in-process costs, safety stock requirements, schedule performance and part coordination for assembly. The relationship between lot-sizing and shop performance is represented using a queueing network model which is then embedded in an optimization routine that searches for optimal lot sizes.     

Multi-Item Inventory Management with Monetary Objective Function

This paper summarizes an actual multi-item periodic-review inventory control study where the “order-up-to-S” policy is employed. The objective function is expressed in monetary terms and is optimized subject to a budgetary limit on the maximum amount of money that can be tied up in inventories. The optimal solution is obtained by employing the generalized Lagrange multipliers method. Findings indicate that it is possible to decrease by at least 37.5% the amount of money currently invested in inventories while maintaining an 85-90% service level to customers. In this study a considerable amount of effort is also spent on the estimation of cost parameters, especially the shortage cost.     

Column Generation Based Heuristic Algorithm for Multi-Item Scheduling

The column generation algorithm for the multi-item lot-size scheduling problem under resource constraints is examined and improved upon by augmenting simpler heuristic routines in place of the time-consuming Wagner-Whitin dynamic programming routine. The heuristic algorithms thus developed are tested by controlling problem size, setup time, demand variability, and capacity change costs in test problems. The empirical results indicate that the proposed heuristic algorithms reduce CPU time as well as the number of iterations with only a slight loss in optimality.     

Analysis of Constrained, One-Time, Multi-Item Discount Offers

This article develops optimal ordering policies for a group of inventory items when a supplier offers a one-time discount for the group. The objective of such policies is to reduce total inventory costs within a firm's warehouse space or funds-availability constraints. Several models are developed to reflect the characteristics of suppliers' offers and the models are analyzed using both Lagrangian and linear programming methods.