An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity,Periodic Delivery Policy

A manufacturing system which procures raw materials from suppliers and processes them to convert to finished products is considered here. This paper develops an ordering policy for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both supplier (of raw material) and buyer (of finished products) sides. This model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. The total cost is found to be a piece-wise convex cost function. An interval that contains the optimal solution is first determined followed by an optimization technique to identify the exact solution from this interval.     

Controlling a Production Scheduling System

When using an automatic production scheduling system management require the system to respond to different overall policies, such as clear all arrears or minimize average lateness weighted by job importance. In many commercial scheduling packages there is no quantitative explanation of how to achieve this response. A successfully implemented scheduling system is introduced here where each policy or objective is obtained by selecting the appropriate criterion on which to sort the jobs. An analytical relationship between the policy and the sorting criterion is established. A new type of lateness penalty is developed heuristically, which is basically an exponential function. The sorting criterion to minimise this lateness penalty turns out to be simply sorting by least slack.     

Optimizing a Production System with a Fixed Delivery Schedule

This note considers a model in which a manufacturing company purchases a raw material, manufactures a product (at a finite rate) and ships a fixed quantity of the product to a single customer at fixed and regular intervals of time, as specified by the customer. In general there are several shipments made during each production run. The objective is to determine a purchasing and production schedule which minimises the total cost of purchasing, manufacturing and stockholding. It extends previously published work by considering the possibility that a single raw material purchase provides stock for several production runs or that several raw material purchases provide stock for a single production run.     

Bounds and Tabu Search for a Cyclic Max-Min Scheduling Problem

A cyclic scheduling problem with applications to transport efficiency is considered. Given a set of regular polygons, whose vertices represent regularly occurring events and are lying on a common circle line, the objective is to maximize the distance between the closest vertices of different polygons on the circle line. Lower and upper bounds for the optimal solution of this NP-hard scheduling problem are presented. They are used to improve the quality of a procedure which is applied to solve this problem heuristically. It consists of a greedy starting algorithm and a Tabu Search algorithm. The numerical results show the efficiency of the procedure proposed.     

Batch Delivery Scheduling on a Single Machine

The problem of partitioning a set of independent and simultaneously available jobs into batches and sequencing them for processing on a single machine is presented. Jobs in the same batch are to be delivered together, upon completion of the last job in the batch. Jobs finished before this time have to wait until delivery. There are a delivery cost depending on the number of batches formed and an earliness cost for jobs finished before delivery. The dynamic programming approach to minimizing the total cost is considered, yielding two pseudopolynomial algorithms when the number of batches has a fixed upper bound. A polynomial algorithm for a special case of the problem is also presented.     

A Production Lot-Size Model for Perishable Items Under Two Level Trade Credit Policy for a Retailer with a Powerful Position in a Supply Chain System

This paper investigates a production lot-size inventory model for perishable items under two levels of trade credit for a retailer to reflect the supply chain management situation. We assume that the retailer maintains a powerful position and can obtain full trade credit offered by supplier yet retailer just offers the partial trade credit to customers. Under these conditions, retailer can obtain the most benefits. Then, we investigate the retailer’s inventory policy as a cost minimization problem to determine the retailer’s inventory policy. A rigorous mathematical analysis is used to prove that the annual total variable cost for the retailer is convex, that is, unique and global-optimal solution exists. Mathematical theorems are developed to efficiently determine the optimal ordering policies for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain a lot of managerial phenomena.     

Optimal Operating Policy for a Random Additional Service Facility

This paper studies the steady state behaviour of a Markovian queue wherein there is a regular service facility serving the units one by one. A search for an additional service facility for the service of a group of units is started when the queue length increases to K (0 < K < L), where L is the maximum waiting space. The search is dropped when the queue length reduces to some tolerable fixed size L - N. The availability time of an additional service facility is a random variable. The model is directed towards finding the optimal operating policy (N,K) for a queueing system with a linear cost structure.     

Single Machine Scheduling with a Common Delivery Window

In this paper we consider the single machine scheduling problem of minimizing the mean absolute deviation (MAD) of job completion times from a restricted common delivery window. This problem is NP-hard. A Lagrangian relaxation procedure is proposed to solve the problem. Two efficient heuristics are also proposed. An experimental study on randomly generated problems is carried out to test the performance of the proposed methods. The computational results show that the obtained lower bounds are very good and the proposed heuristics generate near-optimal solutions.     

Optimal Production and Setup Scheduling: A One-Machine, Two-Product System

This paper studies the scheduling problem for two products on a single production facility. The objective is to specify a production and setup policy that minimizes the average inventory, backlog, and setup costs. Assuming that the production rate can be adjusted during the production runs, we provide a close form for an optimal production and setup schedule. Dynamic programming and Hamilton–Jacobi–Bellman equation is used to verify the optimality of the obtained policy.     

可变环境下的离散时间单部件可修系统

研究离散时间可修系统,讨论了一个可在不同环境下工作的单部件可修系统,其所处环境的改变服从马尔可夫更新过程;利用马尔可夫更新理论,得到了系统的可用度, 故障频度和可靠度等各项指标．     

多阶段生产系统最优生产批量和原材料订购决策模型

Sarker和Parija(1996)建立了生产系统最优生产批量和原材料订购决策模型。然而他们的模型仅局限于单阶段生产系统,本文将他们的模型扩展到多阶段生产系统,我们首先建立了使整个多阶段生产系统总成本最小的各阶段最优生产批量、原材料订购批量及阶段之间的运输批量模型,然后分析了原材料订购费、半成品运费及设备安装费的敏感性。最后,我们结合实例综合分析了原材料订购费、半成品运输费和设备安装费的变化及最小值点取整后对原材料订购决策、最优生产批量和总成本的影响。     

金属矿山企业生产计划优化方法

针对金属矿山企业的单位开采与运输成本大、优化求解结果偏差大问题, 首先, 依据金属矿山企业编制开采计划的基本原则, 以矿石开采与运输成本最小化为优化目标, 利用整数规划方法, 构建了金属矿山企业生产计划数学模型, 其次, 为了精准快速求解金属矿山企业生产计划模型, 提出了改进的量子粒子群优化算法, 采用进化速度和聚集度因子对算法中的惯性权重进行动态调整, 并设计了双层可行域搜索策略, 提高了算法的局部和全局搜索能力。最后, 以某大型金属矿山企业采运生产作业为案例, 通过与矿山实际生产指标、非线性规划结果以及粒子群优化结果进行比较分析。结果表明:在相同经济指标和参数环境下, 本文算法优于其它两种优化方法, 且每吨矿石的开采和运输成本减少了0.05元左右, 降低了金属矿山企业的开采运输成本, 提高了企业的整体经济效益。     

An Efficient Implementation of a Two-stage Production Scheduling Algorithm

In this paper, a most efficient implementation of Johnson's two-stage algorithm is presented. An illustration with numerical example and computational results is also included.     

Scheduling a Multi-Product Single Machine System

This paper describes an easy method of determining the economic manufacturing schedule of a multi-product single machine system on a repetitive basis. An example has been solved to illustrate the method reported in the paper.     

An Exact Solution Algorithm for a Class of Production Planning and Scheduling Problems

This paper presents a formulation and an exact solution algorithm for a class of production planning and scheduling problems. The problem is one of optimally specifying production levels for each product in each period of the planning horizon. The objective is to minimize the sum of the set-up, regular time production, overtime and inventory holding costs. The problem has been formulated as a variation of fixed charge transportation problem. The problem discussed here is NP-hard in computational complexity. A numerical example is presented for better understanding of the algorithm.     

Determination of Optimum Production Quantity for a Two-Stage Production System

In this paper, a method is given for determining the optimum production quantity for a two-stage production system. The method assumes that a lot size is manufactured through two production stages with only one set-up at each stage. A production lot is manufactured in a number of sub-batches of sizes which reduce the total manufacturing cycle time of a production lot. The production quantity is considered 'optimum' when the sum of all the costs is minimized.     

Optimal Ordering Policy for a Multi-item,Single-supplier System with Constant Demand Rates

This paper develops optimal inventory-management rules for an n-item system supplied by a common vendor and with constant demand rates for the various items. The model allows planned stockouts, whose optimal values are determined on the basis of the total cost minimization.     

A Genetic Approach for Solving a Scheduling Problem in a Robotized Analytical System

We consider a robotized analytical system in which a chemical treatment has to be performed on a given set of identical samples. The objective is to carry out the chemical treatment on the whole set of samples in the shortest possible time. All constraints have to be satisfied since a modification of the chemical process could create unexpected reactions.We have developed a new robust method governed by a genetic algorithm to solve this scheduling problem. The crossover mechanism of this evolutionary method is based on an extension of the uniform crossover introduced by Syswerda (1989).The proposed approach can be adapted to other combinatorial problems where decisions, based on rules, have to be taken at each step of a constructive method.