Analysis and solution to the single-level batch production smoothing problem

Many companies use mixed-model production systems running under the Just-in-Time philosophy in order to efficiently meet customer demands for a variety of products. Such systems require demand be stable and production sequence be leveled. The production smoothing problem aims at finding level schedules in which the appearances of products are dispersed over the horizon as uniformly as possible. In this paper, the production smoothing problem is extended to a more general manufacturing environment where a single machine can be identified as either the final or the bottleneck stage of the system and products may have arbitrary non-zero setup and processing time requirements on this single machine. An optimization model is built for the problem and a two phase solution methodology is developed. The first phase problem is shown to be NP-hard and a parametric heuristic procedure is proposed for its solution. In contrast, the second phase problem is shown to be efficiently solvable and currently available solution methods are adopted from the literature. A computational study is designed to test the proposed two phase solution methodology and also the parametric heuristic procedure. Computational results show that the proposed two phase solution methodology enables effective and efficient control of the studied manufacturing system, and the heuristic procedure developed for the first phase problem is time efficient and promises near optimal solutions for a variety of test instances.     

Batch sizes optimisation by means of queueing network decomposition and genetic algorithm

Batch sizes have a considerable impact on the performance of a manufacturing process. Determining optimal values for batch sizes helps to reduce inventories/costs and lead times. The deterministic nature of the available batch size optimisation models reduces the practical value of the obtained solutions. Other models focus only on critical parts of the system (e.g., the bottleneck). In this paper, we present an approach that overcomes important limitations of such simplified solutions. We describe a combination of queueing network analysis and a genetic algorithm that allows us to take into account the real characteristics of the system when benefiting from an efficient optimisation mechanism. We are able to demonstrate that the application of our approach on a real-sized problem with 49 products allows us to obtain a solution (values for batch sizes) with less than 4% relative deviation of the cycle time from the exact minimal value.     

A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand

Numerous production-inventory systems experience significant demand variations from period to period. In many cases, actual demand is random as well. Due to the computational complexity and sensitivity of the optimal solution to the problem of selecting batch sizes, heuristic approaches are often employed. In this paper we propose a method for selecting batch sizes when demand is probabilistic with an unstructured dynamic mean. The procedure is a least period cost approach where the optimal order up to point is found for the desired cycle length.     

Operations planning in a supply chain system with fixed-interval deliveries of finished goods to multiple customers

Raw material ordering policy and the manufacturing batch size for fixed-interval deliveries of finished goods to multiple customers play a significant role in economically managing the supply chain logistics. This paper develops an ordering policy for raw materials and determines an economic batch size for a product at a manufacturing center which supplies finished products to multiple customers, with a fixed-quantity at a fixed time-interval to each of the customers. In this model, an optimal multi-ordering policy for procurement of raw materials for a single manufacturing system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. The carried over inventory of finished goods from the previous cycle is used as initial finished goods inventory, resulting in shifting the production schedule ahead for the next cycle. A closed-form solution to the problem is obtained for the minimal total cost. The algorithm is demonstrated for multiple customer systems.     

Minimising makespan on a single batch processing machine with dynamic job arrivals and non-identical job sizes

Batch scheduling is a prevalent policy in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimising makespan on a single batch processing machine in the presence of dynamic job arrivals and non-identical job sizes. The problem under study is NP-hard. Consequently, we develop a number of efficient construction heuristics. The performance of the proposed heuristics is evaluated by comparing their results to two lower bounds, and other solution approaches published in the literature, namely the first-fit longest processing time-earliest release time (FFLPT-ERT) heuristic, hybrid genetic algorithm (HGA), joint genetic algorithm and dynamic programming (GA+DP) approach and ant colony optimisation (ACO) algorithm. The computational experiments demonstrate the superiority of the proposed heuristics with respect to solution quality, especially for the problems with small size jobs. Moreover, the computational costs of the proposed heuristics are very low.     

Heuristic algorithms for scheduling heat-treatment furnaces of steel casting industries

This paper addresses a research problem of scheduling parallel, non-identical batch processors in the presence of dynamic job arrivals, incompatible job-families and non-identical job sizes. We were led to this problem through a real-world application involving the scheduling of heat-treatment operations of steel casting. The scheduling of furnaces for heat-treatment of castings is of considerable interest as a large proportion of the total production time is the processing times of these operations. In view of the computational intractability of this type of problem, a few heuristic algorithms have been designed for maximizing the utilization of heat-treatment furnaces of steel casting manufacturing. Extensive computational experiments were carried out to compare the performance of the heuristics with the estimated optimal value (using the Weibull technique) and for relative effectiveness among the heuristics. Further, the computational experiments show that the heuristic algorithms proposed in this paper are capable of obtaining near (statistically estimated) optimal utilization of heat-treatment furnaces and are also capable of solving any large size real-life problems with a relatively low computational effort.     

Simultaneous resource scheduling with batching to minimize weighted flow times

This paper examines scheduling problems in which individual tasks require several resources concurrently. We analyze the situation where, in addition to the need to schedule resources concurrently, it is possible to choose the batch sizes of the tasks. Although such situations arise in both manufacturing and service firms, the likely application of these results will be to repetitive batch manufacturing situations. Several formulations for this problem are presented. Both a lagrangian relaxation and a surrogate relaxation are developed. Heuristics based on these relaxations as well as extensive computational experiments are discussed. The simultaneous resource scheduling problem without batching is quite difficult because jobs need to be synchronized so that individual jobs can capture their required simultaneous resources. Nevertheless, if batch size is introduced as an additional variable, we show that the resulting problem is in some sense easier because of the added flexibility provided by the ability to adjust production batch sizes, which allows us to eliminate 'gaps' in the schedule.     

The impact of worker forgetting on production scheduling

Numerous articles suggest using the Japanese manufacturing strategy of minimizing inventories by producing small lot sizes. However, few studies actually have investigated the relative advantages or disadvantages of such a strategy. Worker productivity improvements during production of a batch (learning)and the loss of productivity improvements due to the breaks between batches (forgetting)both influence the optimal lot size for a product. The results of this study indicate that worker forgetting in a batch production environment can substantially increase optimal lot sizes. Since forgetting causes a type of setup cost by penalizing breaks in production, it is intuitive to expect an increase in optimal lot size for forgetting. This study confirms the expectation. What is interesting, however, is that only a small amount of forgetting is required to substantially increase the optimal lot size. The conditions under which lot sizes need to be significantly increased are discussed and illustrated. The results also suggest that special attention must be given to eliminate forgetting due to production disruption when using just-in-time scheduling techniques to reduce lot sizes. The use of automated processes in batch production may overcome the need for large lot sizes by negating the worker forgetting cost, which is a form of setup cost. Robotic technologies or flexible manufacturing systems are types of automated processes which can diminish the forgetting effect in a batch production mode, and therefore, allow efficient production of small lot sizes.     

Decision support for design of reconfigurable rotary machining systems for family part production

To remain competitive in currently unpredictable markets, the enterprises must adapt their manufacturing systems to frequent market changes and high product variety. Reconfigurable manufacturing systems (RMSs) promise to offer a rapid and cost-effective response to production fluctuations under the condition that their configuration is attentively studied and optimised. This paper presents a decision support tool for designing reconfigurable machining systems to be used for family part production. The objective is to elaborate a cost-effective solution for production of several part families. This design issue is modelled as a combinatorial optimisation problem. An illustrative example and computational experiments are discussed to reveal the application of the proposed methodology. Insight gained would be useful to the decision-makers managing the configuration of manufacturing systems for diversified products.     

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.     

Integrated multi-site production-distribution planning in supply chain by hybrid modelling

Allocation of production volumes among multiple manufacturing sites and distribution of products among distribution channels involves many quantitative and qualitative variables and constraints. An integrated multi-product, multi-period, multi-site production-distribution planning subject to the production and distribution constraints, distribution system and local customers demand is considered in this paper. To do this, we took advantage of a hybrid mathematical-simulation model to solve the proposed problem. A mathematical model has been developed to solve the problem, aiming to decrease the costs of set up, production, inventory, distribution and transportation. Because of stochastic factors such as unexpected delays, queuing and machine failure, operation time provided by mathematical model cannot reflect dynamic characteristic of real-world systems and optimal solution of mathematical model is not acceptable in practice. Therefore, we took advantage of a hybrid mathematical-simulation approach to explore the behaviour of the real-world system. Through the computational experiments, we demonstrated that the number of iterations to converge hybrid procedure would lessen when we consider the production-distribution problem in an integrated manner. Also, supply chain overall costs will be reduced through the integration of production and distribution problems. Finally, the solution is a realistically optimal solution for the proposed integrated production-distribution planning problem.     

Lot splitting to minimize average flow-time in a two-machine flow-shop

Lot splitting is a technique for accelerating the flow of work by splitting job lots into sublots, In this paper we investigate the lot splitting scheduling problem in a two-machine flow-shop environment with detached setups and with batch availability. The performance measure considered is the average flow-time which is indicative of the increasingly important manufacturing lead-time. Our contribution is both theoretic and practical for the case of general (not necessarily equal) sublots. We identify properties of the optimal solution and develop a solution procedure to solve the problem. We then present a computational study which indicates that our solution technique is very efficient.     

Grouping parts and tools in flexible manufacturing systems production planning

Batch production in a flexible manufacturing environment is necessary not only to satisfy some technological constraints but also to achieve potential reductions in processing time, to reduce work-in-process and finished goods inventories, and to simplify the production planning process. Central to batch production is the problem of grouping part types and the required tools into families for simultaneous processing. This paper presents a practical and useful algorithm for grouping parts and tools in flexible manufacturing systems (FMSs).This problem is first formulated as a 0-1 linear integer program. A Lagrangian dual formulation is then developed to obtain an upper bound on the optimal objective function value. The Lagrangian dual program is further decomposed into a linear network subproblem and a set of knapsack subproblems. A subgradient algorithm with several enhancement strategies is employed to minimize the upper bound obtained from the dual problem. Computational results for medium and large-scale problems demonstrate that this solution procedure is effective.     

Dynamic programming and mixed integer programming based algorithms for the online glass cutting problem with defects and production targets

In flat glass manufacturing, glass products of various dimensions are cut from a glass ribbon that runs continuously on a conveyor belt. Placement of glass products on the glass ribbon is restricted by the defects of varying severity located on the ribbon as well as the quality grades of the products to be cut. In addition to cutting products, a common practice is to remove defective parts of the glass ribbon as scrap glass. As the glass ribbon moves continuously, cutting decisions need to be made within seconds, which makes this online problem very challenging. A simplifying assumption is to limit scrap cuts to those made immediately behind a defect (a cut-behind-fault or CBF). We propose an online algorithm for the glass cutting problem that solves a series of static cutting problems over a rolling horizon. We solve the static problem using two methods: a dynamic programming algorithm (DP) that utilises the CBF assumption and a mixed integer programming (MIP) formulation with no CBF restriction. While both methods improve the process yield substantially, the results indicate that MIP significantly outperforms DP, which suggests that the computational benefit of the CBF assumption comes at a cost of inferior solution quality.     

Manufacturing lot-sizing,procurement and delivery schedules over a finite planning horizon

In this study, an integrated manufacturing system for technology-related companies whose products are experiencing continuous price decrease during the life cycle is studied for optimal procurement, production and delivery schedules over a finite planning horizon. The model considers the inventory cost both at manufacturing and at delivery from supplier. Since the price is continuously decreasing, a manufacturing firm delivers the finished goods in small quantities frequently. Frequent deliveries in small lots are effective to reduce the total cost of the supply chain. The key for high-tech industries is to reduce the inventory holding time since the component prices are continuously decreasing, and this can only be achieved by implementing an efficient supply chain. Therefore, the main purpose of this paper is to develop an integrated inventory model for high-tech industries in JIT environment under continuous price decrease over finite planning horizon while effectively and successfully accomplishing supply chain integration so that the total cost of the system is minimal. An efficient algorithm is developed to determine the optimal or near-optimal lot sizes for raw material procurement, and manufacturing batch under a finite planning horizon. Finally, the solution technique developed for the model is illustrated with numerical examples.     

Uncapacitated production planning with multiple product types, returned product remanufacturing, and demand substitution

This paper investigates an uncapacitated multi-product production planning problem with returned product remanufacturing and demand substitution, where no backlog and no disposal are allowed. Both the production of new products and the remanufacturing of returned products are considered to meet time-varying demands in a finite time horizon. Setup costs are taken into account when a new product is manufactured or a returned product is remanufactured. The problem is to determine when and how many returned products are remanufactured and new products are manufactured so as to minimize the total cost, including manufacturing, remanufacturing, holding and substitution costs. We first develop an optimization model to formulate the problem. We then propose a dynamic programming approach to derive the optimal solution in the case with large quantities of returned products. We further propose an approximate approach for the general problem to compute a near-optimal solution. The proposed approaches are evaluated by computational experiments and the effectiveness of the approximate approach is verified. Some managerial insights regarding the effects of remanufacturing/substitution are also obtained from the computational studies. This work was partly supported by the National Science Foundation of China under Grant No. 70329001, 70321001, China Postdoctoral Science Foundation under Grant No. 2003034020, 70501014, SRF for ROCS, SEM (2004) and Hong Kong Research Grants Council under Earmarked Grant No. CUHK 4170/03E. We wish to express our sincere appreciation to the Special Issue Editor and the two referees for their constructive comments and suggestions to help improve our paper.     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiproduct Optimal Batch Sizes with In-Process Inventories and Multi Work Centers

In this paper we extend the classical economic batch size model of Camp to situations where a range of products is made to stock and where the products are manufactured in a production shop consisting of a number of work centers of functionally grouped machines. Assuming that the flow times of the batches along the work centers can be modelled as a queueing process, it is shown that the batch sizes influence the batch waiting times in the shop, and the amount of work in process. The cost function to be minimized consists of ordering costs, final inventory holding costs, and work-in-process carrying costs. We show that the cost function is strictly convex and that the optimal batch sizes can be found by means of well-known numerical methods. We present an outline of an iterative procedure in which the batch size optimization procedure is combined with a shop load optimization procedure to achieve a good overall performance. Using a simplified model that assumes that the products are homogeneous in all respects, we also show that there exists an upper limit for the optimal batch size, which is determined by the ordering costs and the work-in-process carrying costs. Finally, we show that not taking into account work-in-process carrying costs may result in substantial errors in both batch size and cost.     

Parallel machine,capacitated lot-sizing and scheduling for the pipe-insulation industry

We develop a solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon. The objective is to determine the product assignment, production quantities, and production sequence on each machine in order to meet demand and maximise the total production amount in a given planning horizon. We study this problem in the context of the manufacturing of pipe insulation, in which multiple features have to be considered simultaneously. The solution procedure combines mathematical programming and a post-processing sequencing heuristic. We also develop a procedure to determine safety stock levels and use Monte Carlo simulation to assess the risk associated with inventory shortages due to stochastic production rates. Computational tests are performed on both real and artificially-generated data.     

离散生产系统车间设施布置优化

分析了离散生产系统车间平面布置的目标函数,生产单元之间的距离计算方法,提出了在非等面积生产单元布置条件下,缩减解空间的两阶段优化布置法。借助计算机的高速运算能力,采用智能最优化算法,对缩减的解空间进行优化搜索,确定出各生产单元的最优位置,在此基础上,根据各生产单元面积比例对车间面积分别按行和列进行分配,确定出初步布置方案,最后对各单元的面积形状进行规整化处理后,得到车间优化布置方案。