A robust optimisation model for aggregate and detailed planning of a multi-site procurement-production-distribution system

The planning problem in the context of a multi-site procurement-production-distribution system (MSPPDS) considered in this paper is motivated from a real life case of a multinational consumer goods company. A robust optimisation model considering model robustness and solution robustness in the objective function is developed for integrated planning in three dimensions. Detailed production, procurement and distribution plans are integrated; countrywide aggregate production plan is integrated with a detailed plan. Similarly the detailed production plans from the previous planning cycle are integrated with current production plans. Constraints on storage space, production capacity and the time lag between procurement, production and distribution activities are captured in the model. Procurement and production plans are treated as ‘here-and-now’ decisions and the distribution plans are treated as ‘wait-and-see’ decisions to be implemented based on the realised demand scenario. The model is illustrated using an example problem and also successfully applied to the data of a consumer goods company involving 104,000 variables (with 832 integer variables) and 21,000 constraints.     

高频直缝电阻焊管企业多阶段生产计划建模及管理信息系统设计

生产计划是企业生产管理的重要起点和依据。为避免以往采用人工排产方式所导致的资源浪费,达到最优排产策略,基于高频直缝电阻焊管（Electric Resistance Welding,ERW）企业的生产特点,针对多阶段生产计划建立了提前/拖期惩罚数学模型。考虑了交货期窗口、库存影响、企业产能、维修停机等约束条件,以惩罚费用最小作为优化生产计划的目标,采用遗传算法有效求解及优化了该问题。利用Visual Studio2010建立B/S模式的管理信息系统对数学模型进行功能实现,通过COM接口将MATLAB与B/S系统联动实现算法嵌入,完成了对生产计划的求解与管理信息系统的开发。管理信息系统在特定企业运用的结果表明：该模型及管理信息系统符合企业生产计划编制需求,达到了预期目标,具有较好的学术价值和实际意义。     

Incorporating engineering process improvement activities into production planning formulations using a large-scale wafer fab model

In most semiconductor wafer fabrication facilities (wafer fabs), both production and engineering lots share the same expensive equipment. Production lots will be shipped to customers whereas engineering lots are used to support production and process development efforts. While production activities might lead to large revenue, engineering activities result in increased future output. In the present paper, we propose three different production planning formulations. The first formulation assumes a reduced available capacity for production due to engineering activities. Costs for production products are minimised. The second formulation is based on the idea that aggregated demand is available for engineering activities for the entire planning window. Costs for production and engineering products are minimised. Learning effects are incorporated to model the capacity increase due to engineering activities. The third model assumes that demand information for engineering activities is available only for the first period. In addition to learning effects, forgetting effects are modelled to provide an incentive to plan releases of engineering lots in later periods. Costs for production and engineering products and forgetting effects are minimised. The performance of the production planning models is assessed using a simulation model of a large-scale wafer fab including specific dispatching strategies to deal with production and engineering lots. The simulation results demonstrate that the second model slightly outperforms the third one when a rolling horizon approach is taken, while the second model provides significantly higher profit than the first one.     

Material and capacity requirements planning with dynamic lead times

Traditional material requirements planning (MRP) does not consider the finite capacity of machines, and assumes fixed lead times. This paper develops an approach (material and capacity requirements planning; MCRP) to integrate capacity planning into MRP. To obtain a capacity feasible production plan, different measures for capacity adjustment such as alternative routeings, safety stock, lot splitting and lot summarisation, are discussed. Additionally, lead times are no longer assumed to be fixed. They are calculated dynamically with respect to machine capacity utilisation. A detailed example is presented to illustrate how the MCRP approach works successfully.     

A spread-sheet model for efficient production and scheduling of a manufacturing line/cell

In this paper we develop an efficient spread-sheet production planning/scheduling model for a resource-constraint production line or a manufacturing cell that produces several products but one at a time with significant changeover time and changeover cost. There are also management and physical constraints related to the operating hours, production capacity and amount of inventory allowed. The production line/cell supplies several products to customers who pull the products according to their own operating policy (working hours) that may be different from manufacture's operating hours. We also show several real-world applications and highlight the benefits and merits of the model.     

A capacity-oriented hierarchical approach to single-item and small-batch production planning using project-scheduling methods

Most production planning and control (PPC) systems used in practice have an essential weakness in that they do not support hierarchical planning with feedback and do not observe resource constraints at all production levels. Also, PPC systems often do not deal with particular types of production, for example, low-volume production. We propose a capacity-oriented hierarchical approach to single-item and small-batch-production planning for make-to-order production. In particular, the planning stages of capacitated master production scheduling, multi-level lot sizing, temporal and capacity planning, and shop floor scheduling are discussed, where the degree of aggregation of products and resources decreases from stage to stage. It turns out that the optimization problems arising at most stages can be modelled as resourceconstrained project scheduling problems.     

基于 Witness 轿车焊装车间焊接生产线的仿真与优化研究

通过对某汽车焊接生产线工艺流程的研究,运用 Witness 仿真软件建立层次清晰的系统仿真模型。 根据仿真目标,设计了 2 组仿真试验,依据仿真结果进行焊接生产线的瓶颈分析、设备利用率分析以及设备产能匹配分析,为生产调度计划的制定、生产线的规划与布局提供科学的依据。     

Solving the integrated lot-sizing and job-shop scheduling problem

Production planning and scheduling are usually performed in a sequential manner, thus generating unfeasibility conflicts. Moreover, solving these problems in complex manufacturing systems (with several products sharing different resources) is very challenging in production management. This paper addresses the solution of multi-item multi-period multi-resource single-level lot-sizing and scheduling problems in general manufacturing systems with job-shop configurations. The mathematical formulation is a generalisation of the one used for the Capacitated Lot-Sizing Problem, including detailed capacity constraints for a fixed sequence of operations. The solution method combines a Lagrangian heuristic, determining a feasible production plan for a fixed sequence of operations, with a sequence improvement method which iteratively feeds the heuristic. Numerical results demonstrate that this approach is efficient and more appropriate than a standard solver for solving complex problems, regarding solution quality and computational requirements.     

模块化生产在复杂系统制造过程的运用研究

基于复杂系统制造过程对完善生产资料准备、缩短制造周期、增强生产计划控制力、提升高端制造业发展水平的迫切要求,根据模块化理论、制造工艺、项目管理、最优化理论等方法,构建复杂系统制造模块顺序网络图,并建立求解制造周期的整数规划模型,最后举出实例,运用优化求解软件CPLEX得出整个系统制造周期及对应的关键制造路径,运用求解结果制定生产资料准备计划及生产计划,发现模块化技术实行后,生产计划及生产资料准备计划实现最大并行化开展,且生产资料准备先于生产计划开展前完成,整个系统制造周期大大缩短,验证了模型的有效性、准确性和优越性。     

A linear model for production management—optimal solving policies

A linear model for production management considering generic data on stocks, manufacturing processes, resource capacities and costs is presented. Any type of continuous or discrete production process also including assembly and disassembly tasks is taken into account. The model inversion issue is analysed and relevant joint production/inventory management policies are solved by optimising linear and quadratic programs under resource and stock capacity constraints. Beyond the single-period inversion issue that is the focus of the paper, the model is tailored to support multi-period and multi-level planning approaches, the development of which is the subject of separate publications.     

Integrated dynamic single item lot-sizing and quality inspection planning

This paper proposes an integrated model for single item dynamic lot-sizing problem and Quality Inspection Planning (QIP). The objective is to provide a model of production planning that takes into account a targeted level of outgoing quality or an Acceptable quality level (AQL) when the manufacturing system inherently generates a proportion of defectives that increases significantly when the system switches from the in-control state to the out-of-control state. The average outgoing quality of each period of time of the planning horizon is bounded as a function of the inspection capacity. The effects of integrating QIP are analysed and discussed through several experiments representing different quality control system’s parameters, i.e. inspection capacity, inspection cost and AQL. The simulation results show that it is very important to take into account the inspection process into production planning decisions. This study will help the decision-makers to negotiate service levels or react properly to given customer quality requirements based on cost and lead time parameters in addition to their process characteristics in terms of capability and stability.     

Two-period vs. multi-period model for supply chain disruption management

A novel two-period modelling approach is developed for supply chain disruption mitigation and recovery and compared with a multi-period approach. For the two-period model, planning horizon is divided into two aggregate periods: before disruption and after disruption. The corresponding mitigation and recovery decisions are: (1) primary supply and demand portfolios and production before a disruption, and (2) recovery supply, transshipment and demand portfolios and production after the disruption. In the multi-period model, a multi-period planning horizon is applied to account for a detailed timing of supplies and production. The primary and recovery portfolios are determined simultaneously and for both approaches the integrated decision-making, stochastic mixed integer programming models are developed. While the simplified two-period setting may overestimate (for best-case capacity constraints) or underestimate (for worst-case capacity constraints) the available production capacity, it can be easily applied in practice for a fast, rough-cut evaluation of disruption mitigation and recovery policy. The findings indicate that for both two- and multi-period setting, the developed multi-portfolio approach leads to computationally efficient mixed integer programming models with an embedded network flow structure resulting in a very strong linear programming relaxation.     

Modelling of multi-period multi-product production planning considering production routes

The multi-period multi-product (MPMP) production planning problems, generally, deal with matching production levels of individual products with fluctuated demands over planning horizon. The conventional MPMP optimisation models suffer from insufficient utilisation of available capacity of machines. This fallacy is due to inappropriate formulation of machine capacity and material handling constraints. In this study, a novel mathematical model is proposed to simultaneously optimise production quantities and provide information about managerial decisions such as subcontracting, carrying inventory/backordering, and also hiring/layoff personnel. The problem is then formulated as a mixed integer linear programming (MILP) model by applying appropriate linearisation of non-linear components. The objective is to minimise production costs comprising of production, storage, shortage, subcontracting costs and costs associated with hiring/dismissing labourers. Superiority of the proposed model over existing ones, has been initially evaluated by solving the case presented by Byrne and Bakir [Byrne, M.D. and Bakir, M.A., 1999. Production planning using a hybrid simulation-analytical approach. International Journal of Production Economics, 59 (1), 305–311], and then evaluated by comparing the results obtained from solving both the proposed and the conventional MPMP production planning models using a 100-randomly-generated-test-problem.     

Modeling and optimizing of strategic and tactical production planning in the automotive industry under uncertainty

This work considers the strategic flexibility and capacity planning under uncertain demands in production networks of automobile manufacturers. We present a deterministic and a stochastic model, which extend existing approaches, especially by an anticipation scheme for tactical workforce planning. This scheme is compared to an extended formulation of the deterministic model, which incorporates workforce planning via detailed shift models. The stochastic model is efficiently solved by an accelerated decomposition approach. The solution approach is integrated into a decision support system, which calculates minimum-cost product allocations and capacity plans. Our numerical results show that, in spite of the considerably increased complexity, our approach can efficiently handle hundreds of scenarios. Finally, we present an industrial case study.     

区间数多产品多计划期生产计划问题的目标规划求解方法

针对多目标、多产品、多计划期和需求、生产费用、生产能力等参数不确定的综合生产计划问题进行了研究。引入区间数描述生产计划问题中存在的不确定性,建立了以生产成本最小和设备利用率最大为优化目标的目标规划模型。为求解模型,运用区间规划理论和基于区间序关系的可能度定义,实现了区间目标规划模型的清晰等价转换,并采用Lingo软件完成模型求解。该方法解决了传统不确定优化方法在获取概率分布和模糊隶属度函数较为困难的不足,能根据决策者的偏好以交互方式分析出不同置信水平对目标的影响,为决策者在不确定环境下进行生产计划决策提供理论依据。最后,通过算例说明方法的有效性和灵活性。     

Lagrangean relaxation approach to joint optimization for production planning and scheduling of synchronous assembly lines

This paper focuses on simultaneous optimisation of production planning and scheduling problem over a time period for synchronous assembly lines. Differing from traditional top-down approaches, a mixed integer programming model which jointly considers production planning and detailed scheduling constraints is formulated, and a Lagrangian relaxation method is developed for the proposed model, whereby the integrated problem is decomposed into planning, batch sequencing, tardiness and earliness sub-problems. The scheduling sub-problem is modelled as a time-dependent travelling salesman problem, which is solved using a dynasearch algorithm. A proposition of Lagrangian multipliers is established to accelerate the convergence speed of the proposed algorithm. The average direction strategy is employed to solve the Lagrangian dual problem. Test results demonstrate that the proposed model and algorithm are effective and efficient.     

Effect of limited capacity on optimal planning parameters for a multi-item production system with setup times and advance demand information

An analytical production/inventory model to optimise the planning parameters lot-size, safety stock and planned lead time is developed for a stochastic single-stage production system with multiple items and limited capacity. Based on queuing analysis, the influence of item specific lot-sizes on the production lead time distribution is modelled. Applying stochastic advance demand information, the expected values for finished-goods-inventory, backorders and service level are explicitly stated. Numerical optimisation is applied to solve the respective cost minimisation problem and a solution heuristic is developed to support this approach. A numerical study provides managerial insights concerning capacity limitation effects on the optimal planning parameters. Higher shop loads, i.e. tighter capacity constraints, are found to significantly increase optimal lot-size and optimal safety stock. Safety stock and planned lead time are substitutes, an increase of both leads to higher FGI and lower backorders, however, the specific trade-off depends on the demand information quality. A sensitivity analysis investigating other (non-) financial system parameters is conducted as well. The main contribution of this paper is that the interaction of different planning parameters, i.e. lot-size, safety stock and planned lead time, for different items is simultaneously studied for a capacity constrained production/inventory system.     

Hybrid (re)manufacturing: manufacturing and operational implications

Remanufacturing presents an option to recover value from used products. However, hybrid (re)manufacturing (i.e. simultaneous manufacturing and remanufacturing) is a challenge, owing to non-uniform availability and heterogeneous quality of returns. In this paper, we examine how heterogeneous quality and non-uniform quantity of returns influence the optimal production rates and inventory levels in a hybrid (re)manufacturing system that incurs costs to readjust manufacturing and remanufacturing capacities on a temporary basis. Specifically, we propose a mixed integer linear programming (MILP) based approach to obtain the optimal production plan for a specified planning horizon. We apply the proposed model to the (representative) operational data of an office equipment manufacturer to evaluate the impacts of quality of returns, quality-based segregation of returns, and capacity readjustment costs. The study provides insights into the effects of trade-offs among different operational costs in a hybrid (re)manufacturing system.     

和声搜索算法优化快速消费品生产配送协调调度

研究具有生产准备环节的快速消费品生产配送问题,考虑工厂和配送中心的库存限制,工厂产能限制和劳动力限制,建立一个多周期、多工厂、多产品、多配送中心、多客户的混合整数线性规划模型,旨在最小化准备成本、生产成本、库存成本和配送成本。通过设计一种遗传和声搜索算法对模型进行求解。最后给出一个算例说明所提模型和算法的可行性和有效性。     

Robust production planning and control for multi-stage systems with flexible final assembly lines

Production planning of final assembly systems is a challenging task, as the often fluctuating order volumes require flexible solutions. Besides, the calculated plans need to be robust against the process-level disturbances and stochastic nature of some parameters like manual processing times or machine availability. In the paper, a simulation-based optimisation method is proposed that utilises lower level shop floor data to calculate robust production plans for final assembly lines of a flexible, multi-stage production system. In order to minimise the idle times when executing the plans, the capacity control that specifies the proper operator–task assignments is also determined. The analysed multi-stage system is operated with a pull strategy, which means that the production at the final assembly lines generates demands for the preceding stages providing the assembled components. In order to guarantee the feasibility of the plans calculated for the final assembly lines, a decomposition approach is proposed to optimise the production plan of preceding stages. By this way, the robust production can be ensured resulting in reduced losses and overall production costs even though the system is exposed to changes and disturbances.