The capacitated lot sizing problem with setup carry-over

Although there is a significant amount of literature on the capacitated lot sizing problem, there has been insufficient consideration of planning problems in which it is possible for a lot size, or production run, to continue over consecutive time periods without incurring multiple setups. While there are papers that consider this feature, they typically restrict production to at most one product in each period. We present a set of mixed integer linear programs for the capacitated lot sizing problem that incorporate setup carry-over without restricting the number of products produced in each time period. Efficient reformulations are developed for finding optimal solutions, and a Lagrangian decomposition heuristic is provided that quickly generates near-optimal solutions. The computational results demonstrate that incorporating setup carry-over has a significant effect on both cost and lot sizes.     

Hierarchical production control for a flow shop with dynamic setup changes and random machine breakdowns

In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.     

Sequence-to-customer goal with stochastic demands for a mixed-model assembly line

A mixed-model assembly line comprises a set of workstations in serial and a conveyor moving at a constant speed, which can assemble variety products in different models during a working shift or a working day. Initial-units that belong to different models are successively fed onto the conveyor at a given cycle time length to get into the assembling operations as semi-products. The conveyor moves semi-products to pass through the workstations gradually to complete the assembling operations for generating finished products. A set of warehouses stores finished products, and each model has a specified warehouse. Customers arrive at the warehouses to demand finished products with stochastic demand forms. A daily scheduling task is the determination of the sequence that specifies the feeding order of the models, which must be set out at the beginning of each day. This paper deals with a new goal, ‘sequence-to-customer’, with stochastic customer demands. An optimization problem is formulated with the objective of minimizing the system cost that includes the holding cost for finished products and the penalty cost for backordered customers during a decision horizon. A lower bound of the system cost is found, which is useful in verifying the optimality of any solution. A heuristic algorithm is proposed to solve the optimization problem, which can obtain optimal solutions or near-optimal solutions with almost ignorable relative errors to optimal solutions. By using the algorithm, the behaviour of the system cost with respect to the variation in customer demands is also investigated to provide insights into management of a mixed-model assembly line.     

Economic lot scheduling with lost sales and setup times

We introduce a new modeling framework for the classic economic lot scheduling problem that permits lost sales if they lead to higher profits. The model also accounts for setup times at a facility, but assumes no explicit incremental setup cost in the objective. Despite assumptions of deterministic demands, production rates and setup times, the cost of carrying inventory may make lost sales during a cycle economically attractive. Statistical analysis on randomly generated problems ranging in size from 100 to 1000 products indicates that the computation time grows by the square of the number of products.     

异质车辆配送可重复装货易腐品库存—路径模型

研究了易腐品的订货、配送和车辆选型一体化决策问题。在一个供应商供应单一产品给多个零售商的供应链中,产品在运输阶段存在腐败,采用运行温度、车辆相关成本和腐败率有差异的异质车辆进行配送,联合决策模型的目标是确定每个零售商的配送车辆类型、配送路径及配送周期使得总成本最小。通过建立数学模型,证明了给定车辆类型和行驶路径后,单一车辆存在最优配送周期,由此设计了改进的节约算法嵌套对车辆类型的遍历对问题进行求解,结合实际企业背景,通过数值算例说明了易腐品配送车辆的选型问题,并得出了对企业的管理启示。     

Economic Lot Scheduling for Two-Product Problem

In this paper we propose an algorithm for the two-product single machine Economic Lot Scheduling Problem (ELSP). Past research on this problem has relied heavily on the assumption that both products are produced cyclically. In particular Boctor's algorithm provides optimal solution to the two-product problem under such assumption. We first simplify Boctor's algorithm and then propose an algorithm which allows for the unequal cycle time for the more frequently manufactured product. We show that the cost corresponding to our solution is either less than 1.015 times the cost obtained from the Independent Solution, which is a lower bound of the optimal solution, or is better than that obtained by Boctor's algorithm. An example is used to show that the difference in cost can be as much as 24%.     

Scheduling The Production Of Components At A Common Facility

We formulate a problem dealing with the manufacture of components at a single facility for subsequent assembly into end products. Each product requires both unique components and common components, and each production batch requires a setup. An optimal schedule for mean completion time is found by means of an algorithm which combines a sequencing procedure and a dynamic programming procedure.     

The economic lot and delivery scheduling problem: the common cycle case

We analyze the interface between a supplier and an assembly facility, where direct shipments are made from one to the other. The final manufacturing step at the supplier involves multiple components produced on a single machine or production line. The assembly facility uses these components at a constant rate. The supplier incurs a sequence-independent setup cost and/or setup time each time the production line is changed over from one component to another. On the other hand, setup costs and times for the assembly facility are negligible. We consider two types of delivery cost: a fixed charge for each delivery, and a fixed-charge-per-truck cost.

We develop a heuristic procedure to find a 'just-in-time' schedule in which one production run of each product and a subsequent delivery of these products to the assembly facility occur in each cycle. The objective is to find the cycle duration that minimizes the average cost per unit time of transportation, inventory at both the supplier and the assembly facility, and setup costs at the supplier. We also develop an error bound for this procedure, and use some of the insights gained from the analysis to explain how delivery schedules can influence the attractiveness of reductions in production setup costs.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

A Heuristic for a Class of Production Planning and Scheduling Problems

This paper describes a solution technique for a general class of problems referred to as aggregate planning and master scheduling problems. The technique is also applicable to multi-item single level capacitated lot sizing problems. The solution technique presented here is a heuristic that is practical for large problems e.g. 9 products and 36 periods. We have tested it for problems with varying number of time periods, number of products, setup costs, holding costs, overtime costs and capacity levels. For those problems that we could solve exactly using a branch and bound algorithm, the solutions produced by the heuristic were all within 1 % of optimality. For problems that we could not solve exactly, we are able to compute a lower bound on the optimal cost. Using the bound we are able to show that our heuristic solutions were within 2.93% of optimality on the average. Except for those problems having very high setup cost or problems with extreme seasonality, the algorithm produced solutions that were within 1 % of optimality on average.     

The product cycling problem under increasing yield rates

We investigate the product cycling problem (also known as the common cycle scheduling problem) when there are economies of scale due to increasing yield rates. Increasing yield rates are characteristic of production processes in which the percentage of acceptable parts increases with the duration of the production run, usually owing to adjustments made during the initial portion of the production run. We develop a solution procedure that is optimal for a wide range of production cost functions under very mild conditions. We then compare optimal solutions with those obtained from the commonly used 'fixed-plus-linear' approximation of costs. Computational results suggest that the 'fixed-plus-linear' approximation generally performs well, but may result in substantial errors under certain extreme conditions.     

Modeling and analysis of the product assignment problem in single stage electronic assembly systems

Consider the production of an evolving family of similar products, each having a well-defined life cycle. The fundamental production resources are inherently flexible, i.e., reconfigurable and reprogrammable. Two distinct strategies can be followed in configuring production facilities: (1) focused facilities, where a facility is dedicated to one product at a time, but may be reassigned; and (2) nonfocused facilities, where setup operations permit a variety of products to be produced during a given planning period. When focused facilities are used, which is a common strategy in some electronics companies, products must be assigned to specific facilities. If facilities are not identical, and capacity is limited, then changing production requirements may force reassignment of products from one facility to another. Thus, the product assignment/reassignment decision may have a significant impact on the production capacity required. This paper concentrates on the product assignment/reassignment decision when a pure focused facility strategy is used. This problem is analyzed and a number of insights are developed. Based on this analysis, the problem is reformulated and an optimal solution procedure based on a multi-commodity network flow model is presented and tested for the product assignment/reassignment decision     

On the optimal lot-sizing and scheduling problem in serial-type supply chain system using a time-varying lot-sizing policy

In this paper, we solve the optimal sequencing, lot-sizing and scheduling decisions for several products manufactured through several firms in a serial-type supply chain so as to minimise the sum of setup and inventory holding costs while meeting given demand from customers. We propose a three-phase heuristic to solve this NP-hard problem using a time-varying lot- sizing approach. First, based on the theoretical results, we obtain candidate sets of the production frequencies and cycle time using a junction-point heuristic. Next, we determine the production sequences for each firm using a bin-packing method. Finally, we obtain the production times of the products for each firm in the supply chain system by iteratively solving a set of linear simultaneous equations which were derived from the constraints. Then, we choose the best solution among the candidate solutions. Based on the numerical experiments, we show that the proposed three-phase heuristic efficiently obtains feasible solutions with excellent quality which is much better than the upper-bound solutions from the common cycle approach.     

Analysis of partial setup strategies for solving the operational planning problem in parallel machine electronic assembly systems

In this paper, we analyse the operational planning problem in an electronic assembly system with multiple placement machines operating in parallel. The partial setup strategy is proposed as an effective methodology for this problem. This strategy attempts to determine the balance between processing time and changeover time during system operation. The Tour primary issues are determining the assignment of products to machines, the sequence of products on each machine, the assignment of components to feeder locations for each product, and the component placement sequence for each product. Four solution procedures for unique and partial setup strategies are developed and tested. The computation results show that for low to medium volume high mix environments, the partial setup procedures offer significant improvement over the unique setup strategies. The results also show that no single fixed strategy dominates in all scenarios, and therefore, an adaptable procedure that will choose the best solution for each set of requirements is needed.     

Production planning with stochastic seasonal demandand capacitated production

We consider a production/inventory problem with stochastic seasonal demand. A scarce resource limits production in each time period, and setup time is negligible. Linear and stationary costs are assessed for production, holding inventory, and stock-outs. The calculation of optimal solutions is difficult so heuristics are used. The heuristics used in business practice are shown to cost an average of 30% above optimal policy costs. A superior heuristic is constructed utilizing an analytic approximation for optimal policies that costs an average of 2% over optimal policy costs.     

Balancing manual mixed-model assembly lines using overtime work in a demand variation environment

This study deals with the balancing problem of a manual mixed-model assembly line, where the production volume or the product mix changes from shift to shift during the planning horizon. The unstable demand can be characterised by several representative scenarios, and the line uses overtime work to meet the demand variation. The balancing problem concerns how to assign assembly tasks to stations and determine the amount of overtime in each possible demand scenario. The objective is to satisfy the demand in each possible scenario with the minimum labour costs paid for both normal shifts and overtime work. A lower bound on the labour costs is proposed, and a heuristic algorithm is developed to quickly find a feasible solution. A branch, bound and remember (BB&;R) algorithm is then proposed to find better solutions. These solution methods are tested on 765 instances. The BB&;R algorithm obtains optimal solutions for 510 instances and gives high-quality solutions for the remaining 255 instances within 60?s. The experimental results show that the use of overtime work and adjustable cycle times significantly reduces the labour costs, especially when the demand or task processing time variations are large.     

Order-oriented cooperative sequencing optimisation in multi-mix-model assembly lines

Order-oriented products assembly sequence among different assembly lines becomes a critical problem for mass customisation manufacturing systems. It significantly affects system productivity, delivery time, and manufacturing cost. In this paper, we propose a new approach to extend the traditional products sequencing from mixed model assembly line (MMAL) to multi-mixed model assembly lines (MMMALs) to obtain the optimal assembly sequence with the objectives of minimising consumption waviness of each material in the lines, assembly line setup cost, and lead-time. A multi-objective optimisation algorithm based on variable neighbourhood search methods (VNS) is developed. We perform an industrial case study in order to demonstrate the practicality and effectiveness of the proposed approach.     

Production and subcontracting control for an unreliable manufacturing system with setups

This paper deals with the problem of joint production, setup and subcontracting control of unreliable manufacturing systems producing two product types. The production requires setups each time it switches from one product type to another. Subcontracting is an integral part of the decision-making process due to limited production capacity in existing facility. The objective is to propose an effective control policy for the considered system which simultaneously manages production, setup and subcontracting activities. The complexity of the problem lies in the interaction between internal manufacturing decisions and subcontracting that outsource a part of the production, in a dynamic and stochastic environment. An experimental optimisation approach is adopted to determine the optimal control parameters which minimise the average total cost. Extensive sensitivity analyses are performed to illustrate the robustness and the usefulness of the adopted approach. An in-depth study comparing five control policies across a wide range of system parameters is also conducted. Extended cases closer to reality are also investigated considering elements such as the preventive maintenance and the production of non-conforming products. The best control policy in terms of economic performance is then obtained. Valuable insights providing a better understanding of interactions involving production, setup, and subcontracting are discussed.     

基于货架寿命的乳制品配送车辆路径优化研究

目的 基于货架寿命对库存和配送进行优化研究,降低冷链过程中的乳制品损耗,保证乳制品的质量,降低企业成本,提高消费者的满意度。方法 考虑到货架寿命对配送的影响,在研究货架寿命的基础上,建立乳制品货损率与货架寿命的关系式。在时间窗约束下,以总成本最小为目标,分别构建未考虑货架寿命的配送车辆路径优化模型和考虑货架寿命的配送车辆路径优化模型,并通过改进遗传算法对2种模型进行求解分析。结果 对比2种模型的最优结果,发现在1个配送周期内,基于货架寿命配送的总成本比不考虑货架寿命的运输总成本低3.71%。结论 该研究在一定程度上可以为物流企业减少配送成本,提高企业的经济效益。     

A note on resource allocation scheduling with group technology and learning effects on a single machine

In this article, single-machine group scheduling with learning effects and convex resource allocation is studied. The goal is to find the optimal job schedule, the optimal group schedule, and resource allocations of jobs and groups. For the problem of minimizing the makespan subject to limited resource availability, it is proved that the problem can be solved in polynomial time under the condition that the setup times of groups are independent. For the general setup times of groups, a heuristic algorithm and a branch-and-bound algorithm are proposed, respectively. Computational experiments show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions.