A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Integrated production scheduling and distribution planning in dairy supply chain by hybrid modelling

In this paper we address the production scheduling and distribution planning problem in a yoghurt production line of the multi-product dairy plants. A mixed integer linear programming model is developed for the considered problem. The objective function aims to maximize the benefit by considering the shelf life dependent pricing component and costs such as processing, setup, storage, overtime, backlogging, and transportation costs. Key features of the model include sequence dependent setup times, minimum and maximum lot sizes, overtime, shelf life requirements, machine speeds, dedicated production lines, typically arising in the dairy industry. The model obtains the optimal production plan for each product type, on each production line, in each period together with the delivery plan. The hybrid modelling approach is adopted to explore the dynamic behavior of the real world system. In the hybrid approach, operation time is considered as a dynamic factor and it is adjusted by the results of the simulation and optimization model iteratively. Thus, more realistic solutions are obtained for the scheduling problem in yoghurt industry by using the iterative hybrid optimization-simulation procedure. The efficiency and applicability of the proposed model and approach are demonstrated in a case study for a leading dairy manufacturing company in Turkey.     

Evaluating focused factory benefits with queuing theory

In this paper, we study the benefits of a focused factory using lead-time as a performance measure. Specifically, we model a production process, using multi-class (multiple product types), general interarrival and processing time distributions with multiple machines (GI/G/c) queuing models for deriving each product’s mean lead-time. We also perform simulations for estimating the standard deviation of lead times. There are two product types: a standard and a customized product. The customized product has a more variable demand pattern than the standard product, and also requires additional processing time (setup and run time) in its production process. We assume that management is willing to sacrifice the lead-time performance of the customized product in favor of improved performance for the standard product. The paper shows that focusing the factory is more attractive for plants operating at higher utilization, and manufacturing products that have higher processing time and demand variability differentials between product types.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

Some Problems Associated with the Distribution of Consumer Products

The distribution problem is considered as a whole. The interconnexions are shown between various subproblems: factory siting, warehouse (or depot) siting, subdepot siting, allocation of production resources to factory sites and minimization of costs. It is suggested that the results obtained for certain products distributed nationally through grocery outlets are valid (with qualifications) for any nationally marketed consumer product. The use of traditional operational research techniques, where appropriate, is referred to but not in great detail. A logical approach to siting problems, particularly the siting of a large number of subdepots, is outlined. The aim of this approach is to obtain the correct answers with the minimum amount of work. The implications for marketing are discussed with particular reference to costs: the cost of distributing goods to certain areas may be unduly high; the cost of customer service may rise disproportionately as the level of service given rises. A balance must be struck which is in line with the company's aims but which may mean modifying production, distribution and sales objectives.     

A Dynamic Programming Approach to Determine Optimal Manpower Recruitment Policies

The manpower planning models available in the literature have dealt with how changes take place in a manpower planning system, under various operating and policy constraints. However, none of these models has identified the manpower system costs. In this paper we have identified various manpower system costs. Further, we have developed a manpower planning model with the objective of minimizing the manpower system costs. The model has been found to be analogous to the Wagner-Whitin model in production/inventory management. A numerical example has been given to illustrate the model.     

An Interactive Planning Model for the New Zealand Dairy Industry

A long-term planning model for a large New Zealand dairy company is described. The model presents an integrated view of the company's operation, including transportation and processing. The model used is based on a network formulation, NETPLAN, developed by the authors to carry out the optimisation. NETPLAN is highly flexible, interactive and provides graphical output of the results. The optimisation maximises net revenue based on product prices, variable process costs and variable transport costs subject to factory capacity, product demand and raw material supply constraints.     

A stochastic programming approach for multi-site aggregate production planning

Production planning problems play a vital role in the supply chain management area, by which decision makers can determine the production loading plan—consisting of the quantity of production and the workforce level at each production plant—to fulfil market demand. This paper addresses the production planning problem with additional constraints, such as production plant preference selection. To deal with the uncertain demand data, a stochastic programming approach is proposed to determine optimal medium-term production loading plans under an uncertain environment. A set of data from a multinational lingerie company in Hong Kong is used to demonstrate the robustness and effectiveness of the proposed model. An analysis of the probability distribution of economic demand assumptions is performed. The impact of unit shortage costs on the total cost is also analysed.     

Several methods usable in production systems prediction

In this paper, we describe three methods based on the use of a dynamical system, the use of neural networks with rough sets, and the use of a fuzzy-logic method in order to predict the behavior of data processing extracted from a highly automated factory.The work presented here is a preliminary study done in order to develop a decision aid system for a highly automated factory in southern France (Merlin-Gérin). This factory produces low cost electrical circuit breakers in high volumes with short order delays. The aim is to predict the occurrence of ruptures in the production system where a rupture corresponds to a missed delivery date.The aim of our research is to model the global behavior of manufacturing systems, and then to correlate production tactical choices with their effects. We would like then to clarify the existing relations between some sectors of the enterprise. More precisely, the work carried out at Merlin-Gérin consists in a prediction of their nondelivery ratio, which is evaluated according to an analysis of historical data provided by production processing.     

集团分布式制造模式下生产调配优化模型研究及算法设计

基于分布式概念的集团分布式制造生产管理模式在市场中占据着越来越重要的地位,此种运营模式由制造型企业向服务型企业蔓延的趋势也越来越明显,然而针对这一具有自身特点的集团分布式概念下的生产管理模型的调度研究却很少。研究针对此生产管理模式下集团级的生产调配问题建立数学模型,综合考虑客户订单的分散情况、各分厂日生产能力限制和产品品种多样性的特点,采用改进的遗传算法求解该模型,提出一种基于订单和工厂的两段式非负整数染色体编码方法,保证了生产能力约束和订单约束,采用PMX交叉算法避免不合法染色体的出现。选取W集团一定计划期内的客户订单数据进行实例分析,验证了该生产调配模型和算法的有效性。     

An Expert System Framework for Economic Evaluation of Machining Operation Planning

Recognising the importance of combining manufacturing and management systems for machining operation planning, this paper presents a new methodology for the evaluation of economic aspects in an operation plan. To ensure that the quality of machined parts satisfies the required specifications, the manufacturing system acts as an alternative generator that provides meaningful and practical plans. Through cost analysis, the variable, fixed, and total costs associated with the machining operation are quantitatively determined. The management system, which functions as an evaluation mechanism, then selects the optimal plan based on the defined goal. The proposed methodology has been applied in the framework design of an expert system. The program establishes a sequence of machining operation planning and searches for the optimal plan. This optimal plan integrates considerations from both managers and production engineers, and balances their needs for efficient machining of a quality product.     

A robust optimization model for production planning of perishable products

In this study, a robust optimization model is developed to solve production planning problems for perishable products in an uncertain environment in which the setup costs, production costs, labour costs, inventory costs, and workforce changing costs are minimized. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilize the resources. By adjusting penalty parameters, decision-makers can determine an optimal production loading plan and better utilize resources while considering different economic growth scenarios. A case from a Hong Kong plush toy company is studied and the characteristics of perishable products are discussed. Numerical results demonstrate the robustness and effectiveness of the proposed model. An analysis of the trade-off between solution robustness and model robustness is also presented.     

Structuring production planning systems for computer applications

Activities in a job shop type mechanical company can be split in production, product cycle and production cycle. The corresponding flow in each of these are materials, manufacturing specifications and product requirements. Production planning will plan and control these flows. Basic data structures are a product model and a corresponding hierarchy linked to production resources. A planning system may be designed by combining a set of operation or building blocks. These are three types: user communication, data base management and basic operations. The basic operations cover all processing necessary in production planning and represent the fundamental building blocks. A list of basic operations is suggested.     

A production planning model for an unreliable production facility: Case of finite horizon and single demand

We study a two-level inventory system that is subject to failures and repairs. The objective is to minimize the expected total cost so as to determine the production plan for a single quantity demand. The expected total cost consists of the inventory carrying costs for finished and unfinished items, the backlog cost for not meeting the demand due-date, and the planning costs associated with the ordering schedule of unfinished items. The production plan consists of the optimal number of lot sizes, the optimal size for each lot, the optimal ordering schedule for unfinished items, and the optimal due-date to be assigned to the demand. To gain insight, we solve special cases and use their results to device an efficient solution approach for the main model. The models are solved to optimality and the solution is either obtained in closed form or through very efficient algorithms.     

Scheduling of brand production and shipping within a sugar supply chain

The Australian sugar industry exports about 90% of its five million tonne annual sugar production on the open market to customers in several countries, who request various brands of raw sugar. In planning at this interface of the sugar supply chain, an objective is to schedule the brands of sugar each mill produces throughout the annual harvest season, along with the ports that each ship loads at, to minimize total costs of sugar production and shipping. The complexity of such planning for the sugar industry has been overcome through the development and solution of a mixed-integer programming model to perform the task. The model is used as an annual planning tool to obtain a base schedule, as well as a rescheduling tool to revise the plan during the year as mill production rates and shipments change. Using the Australian sugar industry as a case study, this paper focuses on the mathematical model and solution using two known meta-heuristics based on local search. Using the 2002/2003 and 2003/2004 financial years, a comparison is made between the schedules produced in practice using manual methods and those using the model, which show a total potential cost savings of up to AU$4.0?M for the 2 years.     

Balancing capacity and lot sizes

In many companies there is an on-going discussion about capacity, capacity utilization and capital tied up in inventories. However, traditional models such as the EOQ model only include capacity considerations in the set-up cost, or in the cost of a replenishment order. This implies e.g. that they do not consider the set-up time as a capacity constraint. Furthermore, in these models the set-up cost is usually treated as a constant, even though the opportunity cost for capacity in general is dependent upon the capacity utilization.The purpose of this paper is to derive an analytical model for the balancing of capacity and lot sizes. The model includes costs for capacity, work-in-process (queueing, set-up, and processing time), and finished goods inventory. The total costs are minimized with respect to capacity. Then, the corresponding, recommended lot sizes are determined. The model was tested with data from a Swedish manufacturing company. The results turned out to coincide with experiences of the company in many important respects. The model offers production management an opportunity to discuss the relationship between capacity, work-in-process, and lot sizes.     

A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs

In this paper, we develop a three-step heuristic to address a production scheduling problem at a high volume assemble-to-order electronics manufacturer. The heuristic provides a solution for scheduling multiple product families on parallel, identical production lines so as to minimize setup costs. The heuristic involves assignment, sequencing, and time scheduling steps, with an optimization approach developed for each step. For the most complex step, the sequencing step, we develop a greedy randomized adaptive search procedure (GRASP). We compare the setup costs resulting from the use of our scheduling heuristic against a heuristic previously developed and implemented at the electronics manufacturer that assumes approximately equal, sequence-independent, setup costs. By explicitly considering the sequence-dependent setup costs and applying GRASP, our empirical results show a reduction in setups costs for an entire factory of 14–21% with a range of single production line reductions from 0% to 49%.     

A Method of Dealing with Certain Non-Linear Allocation Problems Using the Transportation Technique

An investigation was carried out to establish a method of determining the allocation between certain factories of a known production requirement so as to minimize the total expense of production. Each factory was made up of a number of departments or services whose total expense varied non-linearly with production level.The method was to divide the production range of each department in each factory into regions of approximate linear expense, and consider the associated total company expense connected with the optimum allocation for each possible group of regions (one region in each department). In theory the simplex technique could be applied to each group to find its optimum allocation, but as the number of groups is prodigious for quite simple problems this is not practicable. (In the actual problem for which the method was produced there was of the order of 100,000 groups.)A procedure was devised using the transportation technique together with various lemmas proved in the text and feasibility considerations, by which it was possible to reduce rapidly the number of groups needed to be considered in detail to just a few.Other problems should be amenable to this method provided they are similar to the one above in two respects.(1) The departmental variation of expense with production from one region to the next is in general continuous with decreasing rate of change of expense, i.e. the variation is concave.(2) It should be possible to put the requirements into one of the units of capacity usage in which there are important physical or maximum capacity restrictions.In addition, the method is particularly suitable when the number of factories is not large.As the method required repeated applications of the transportation model, a technique was devised for obtaining an optimum solution to this model more quickly than by the usual techniques. This technique will be described in another paper.An example of a whole problem is given after the Appendix. A full solution of this problem is shown in which occur most of the points dealt with in the text.The problem for which the method was devised, was one of minimizing the total expense of production of twenty common products between three factories. Each factory had seven departments or services, in most of which two regions were required to describe satisfactorily a department's variation of expense with production, in linear terms. A complete solution was obtained in a few days using the method described without recourse to an electronic computer (not counting the initial computations of costs, etc. required).     

钢管定购和运输的策略优化

本文为图 1主管道和图 2树形管道的定购和运输计划给出了一个最优化模型 .通过解这一个最优化模型得到钢管的定购和运输的最优策略 .同时 ,分析了哪个钢厂钢管销价的变化对图 1主管道购运计划和总费用影响最大 ,哪个钢厂钢管产量的上限的变化对购运计划和总费用影响最大     

准时制下非核心企业最佳生产数学模型研究

通常,研究订单生产企业的生产计划求解模型往往只解决排产问题,制作的计划不能顾及各个方面的生产成本.其主要原因在于两个方面:一是,没有对由计划引发的成本作全面的考虑;二是,缺乏有效的成本表达方式,尤其是任意时间段内的各个产品的负荷总和以及能力波动费用的数学表达.研究了一种特殊的订单生产——准时制下非核心企业的生产,分析了计划范围内的成本,并分别就各种成本给出求解公式,尤其在能力波动费用的求解上,引进了符号函数,解决了在任意单位时间段内能力累计的数学表达以及能力波动费用的数学求解,在以上基础上给出了最佳生产的数学模型,给出了求解方法,讨论了最优解的存在条件,最后,讨论了在APS(A dvance P lan System)中的应用前景.