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.     

Sharing clearances to improve machine layout

This paper considers a double-row layout problem with shared clearances in the context of semiconductor manufacturing. By sharing some clearances, reductions in both layout area and material handling cost of approximately 7–10% are achieved. Along with minimal clearances for separating adjacent machines, clearances that can be shared by adjacent machines are considered. The shared clearances may be located on either or both sides of machines. A mixed integer linear programming formulation of this problem is established, with the objective to minimise both material flow cost and layout area. A hybrid approach combining multi-objective tabu search and heuristic rules is proposed to solve it. Computational results show that the hybrid approach is very effective for this problem and finds machine layouts with reduced areas and handling costs by exploiting shared clearances.     

基于多功能机器与多能工的动态单元制造系统模型

为了成功地实施动态单元制造系统,同时考虑技术性问题（包括生产单元构建和设计、生产单元之间与生产单元内部的物料移动等）和人员问题（包括员工工资、员工雇佣和解雇等）,综合研究和分析了多功能机器和多操作技能员工的动态单元制造系统的生产单元构建、生产单元之间与生产单元内部物料移动、库存和延迟生产、员工分配和柔性生产路径,创新性地提出一个整合的混合整数规划模型。通过遗传算法对数值试验求解,结果验证了新模型的可行性和有效性。     

A data-driven approach to multi-product production network planning

The clearing function models the non-linear relationship between work-in-process and throughput and has been proposed for production planning in environments with queuing (congestion) effects. One approach in multi-product, multi-stage environments has been to model the clearing function at the bottleneck machine only. However, since the bottleneck shifts as the product release mix changes, this approach has its limitations. The other approach is the Alternative Clearing Function formulation, where the clearing function is first estimated at the resource level using piecewise linear regression from simulation experiments, and then embedded into a linear programme. This paper develops an alternative to the Allocated Clearing Function formulation, wherein system throughput is estimated at discrete work-in-process points. A mixed integer programming formulation is then presented to use these throughput estimates for discrete release choices. The strength of the formulation is illustrated with a numerical example and the new approach is compared with the ACF.     

Optimal cost design of flow lines with reconfigurable machines for batch production

Modular reconfigurable machines offer the possibility to efficiently produce a family of different parts. This paper formalises a cost optimisation problem for flow lines equipped with reconfigurable machines which carry turrets, machining modules and single spindles. The proposed models take into account constraints related to: (i) design of machining modules, turrets, and machines, (ii) part locations, and (iii) precedence relations among operations. The goal is to minimise equipment cost while reaching a given output and satisfying all the constraints. A mixed integer programming model is developed for the considered optimisation problem. The approach is validated through an industrial case study and extensive numerical experiments.     

Designing group layout of unequal-area facilities in a dynamic cellular manufacturing system with variability in number and shape of cells

This paper presents a new mixed-integer non-linear programming model for designing the group layout (GL) of unequal-area facilities in a cellular manufacturing system (CMS) under a dynamic environment. There are some features that make the presented model different from the previous studies. These include: (1) manufacturing cells with variable numbers and shapes, (2) machine depot keeping idle machines, (3) machines of unequal-areas, (4) manufacturing cells with rectangle regular shapes established on the continuous shop floor and (5) integration of cell formation and GL as interrelated decisions involved in the design of a CMS in a dynamic environment. The objective function is to minimises the total costs of intra- and inter-cell material handling, machine overhead, machine relocation, machine processing, purchasing machines and forming cells. Since the problem is NP-hard, an efficient simulated annealing (SA) algorithm is developed to solve the presented model. The performance of this model is illustrated by two numerical examples. It is then tested using several test problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison to the classical genetic algorithm (GA). The obtained results show that the quality of the solutions obtained by SA is better than GA.     

Optimal design of flexible production lines with unreliable machines and infinite buffers

Despite the increasing use of automated manufacturing systems, combining flexible technology, only a few models for designing such systems are available. This paper presents a model for the determination of the profit-maximizing configuration of workstations (both machine types and number) along a flexible production line with unreliable machines and infinite buffers. A mixed integer programming formulation of the problem is introduced and an optimal solution algorithm is developed. For large scale problems a heuristic procedure is presented.     

The integrated machine allocation and layout problem

Cellular manufacturing has received a considerable amount of attention in the research literature as an approach for improving the performance of manufacturing facilities. However, recent studies have shown that cellular layouts are not always superior to the traditional functional machine layout. We propose a model that does not require the machines to be placed in a functional layout or in a cellular arrangement, but allows the material flow requirements to dictate the machine placement. The model is formulated as an aggregation of the quadratic assignment problem and several network flow problems coupled with linear side constraints. A mixed integer program is presented to find the optimal solution for small problems, and heuristics are developed to solve larger problems. Computational results evaluating the quality of the solution methodologies are also presented.     

A production planning model for cellular manufacturing systems with refixturing considerations

In this paper we consider the problem of assigning operations of part types to one or more machines in a cellular manufacturing system. We develop a mixed integer linear model considering trade-off between refixturing and material handling movement. Examples are included to illustrate the applications of the models developed.     

Cell design and multi-period machine loading in cellular reconfigurable manufacturing systems with alternative routing

This paper deals with the design and loading of Cellular Reconfigurable Manufacturing Systems in the presence of alternative routing and multiple time periods. These systems consist of multiple reconfigurable machining cells, each of which has Reconfigurable Machine Tools and Computer Numerical Control (CNC) machines. Each reconfigurable machine has a library of feasible auxiliary machine modules for achieving particular operational capabilities, while each CNC machine has an automatic tool changer and a tool magazine of a limited capacity. The proposed approach consists of two phases: the machine cell design phase which involves the grouping of machines into machine cells, and the cell loading phase that determines the routing mix and the tool and module allocation. In this paper, the cell design problem is modelled as an Integer Linear Programming formulation, considering the multiple process plans of each part type as if they were separate part types. Once the manufacturing cells are formed, a Mixed Integer Linear Programming model is developed for the cell loading problem, considering multi-period demands for the part types, and minimising transportation and holding costs while keeping the machine and cell utilisations in each period, and the system utilisation across periods, approximately balanced. An illustrative problem and experimental results are presented.     

Cell formation and layout designs in a cellular manufacturing environment a case study

This paper presents the application of a recent integrated approach for the design of cellular manufacturing, addressing, concurrently, all three phases of the design namely parts/machines grouping, intra-cell and inter-cell layout designs to a white-goods manufacturing company. It provides a platform to investigate the impact of the cell formation method on intra-cell and inter-cell layout designs, and vice versa, by generating multiple efficient layout designs for different cell partitioning strategies. This approach enables the decision-maker to have wider choices with regard to the different numbers of cells and to assess various criteria such as travelling cost, duplication of machines and space requirement against each alternative.     

Simultaneous optimization of production planning and inventory management of polyurethane foam plant

In this work, the management of a polyurethane foam plant is tackled through a mixed integer linear programming model that simultaneously solves production and inventory planning problems. The production process considers the foaming stage where large polyurethane blocks are produced as well as the curing step where the blocks are dried. The proposed formulation takes into account several tradeoffs involved in the overall production process. The daily production planning is tightly related to production requirements, available space for the curing and stored elements. Moreover, the required time to dry blocks introduces a delay that must be appropriately considered in order to allow an adequate operation of downstream operations. Thus, an integrated approach where all these problems are jointly addressed is proposed using a mathematical programming model. Several study cases provided by a local company are tested to demonstrate the model performance.     

Formulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds

We consider the multi-item uncapacitated lot-sizing problem with inventory bounds, in which a production plan for multiple items has to be determined considering that they share a storage capacity. We present (a) a shortest path formulation and (b) a formulation based on the a priori addition of valid inequalities, which are compared with a facility location formulation available in the literature. Two easy-to-implement mixed integer programming heuristic frameworks are also presented, (a) a rounding scheme and (b) a relax-and-fix approach performed in a time partitioning fashion. Computational experiments are performed to evaluate the different approaches. The numerical results show that the proposed relax-and-fix heuristic outperforms all other approaches. Its solutions are within 4.0% of optimality in less than 10 minutes of running time for all tested instances, with mean gaps in the order of 2.1 and 1.8% for instances with more relaxed and tighter capacities, respectively. The obtained solutions were always better than those obtained by a commercial MIP solver running for one hour using any of the available formulations.     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

多单元制造系统布局设计

从布局设计的角度,提出多单元制造系统的概念,把各种制造系统的布局问题转化为多单元制造系统布局设计问题,包括设备布局和制造单元布局两个方面。对于设备布局问题,给出一种优化建模与虚拟现实技术相结合的求解策略;对于单元布局问题,给出一种集成的布局设计方法。     

Cell formation problem with consideration of both intracellular and intercellular movements

The cellular manufacturing system (CMS) is a well-known strategy which enhances production efficiency while simultaneously cutting down the system-wide operation cost. Most of the researchers have been focused on developing different approaches in order to identify machine-cells and part-families more efficiently. In recent years, researchers have also focused their studies more scrupulously by collectively considering CMS with production volume, operation sequence, alternative routing or even more. However, very few of them have tried to investigate both the allocation sequence of machines within the cells (intra-cell layout) and the sequence of the formed cells (inter-cell layout). Solving this problem is indeed very important in reducing the total intracellular and intercellular part movements which is especially significant with large production volume.

In this paper, a two-phase approach has been proposed to tackle the cell formation problem (CFP) with consideration of both intra-cell and inter-cell part movements. In the first phase, a mathematical model with multi-objective function is formed to obtain the machine cells and part families. Afterwards, in the second phase, another mathematical model with single-objective function is presented which optimizes the total intra-cell and inter-cell part movements. In other words, the scope of problem has been identified as a CFP together with the background objective of intra-cell and inter-cell layout problems (IAECLP). The primary assumption for IAECLP is that only linear layouts will be considered for both intra-cell and inter-cell. In other words, the machine within cells and the formed cells are arranged linearly. This paper studies formation of two mathematical models and used the part-machine incidence matrix with component operational sequence.

The IAECLP is considered as a quadratic assignment problem (QAP). Since QAP and CFP are NP-hard, genetic algorithm (GA) has been employed as solving algorithm. GA is a widespread accepted heuristic search technique that has proven superior performances in complex optimization problems and further it is a popular and well-known methodology. The proposed algorithms for CFP and IAECLP have been implemented in JAVA programming language.     

A practical method for design of hybrid-type production facilities

A comprehensive method for the design of hybrid-type production shops, which comprise both manufacturing cells and individual workcentres, is presented. The method targets the minimization of the material handling effort within the shop and includes four basic steps: (1) identification of candidate manufacturing cells, (2) evaluation and selection of the cells to be implemented, (3) determination of the intra-cell layout, and (4) determination of the shop layout. For the cell formation step the 1CTMM technique has been enhanced to cater for important practical issues. The layout of each significant cell is determined by a simulated annealing (SA)-based algorithm. Once the sizes and shapes of the selected cells are known the shop layout is determined by a similar algorithm. The resulting hybrid shop consists of the selected cells and the remaining machines. The methodology has been implemented in an integrated software system and has been applied to redesign the shop of a large manufacturer of radar antennas.     

An extended distance-based facility layout problem

The distance-based facility layout problem with unequal-area departments has been studied by many researchers for over 30 years. Still, current approaches require certain assumptions that limit the type of solutions obtained. In this paper, we consider manufacturing systems in which replicates of the same machine type may exist in the facility, and propose an extended distance-based facility layout problem that concurrently determines the number and shape of the departments, the assignment of machines to departments, and the allocation of part flow volume to individual machines. A non-linear mixed-integer program that accurately captures the extended facility layout and part flow allocation problem, a decomposition approach that exploits the structure of the formulation using a heuristic solution procedure, as well as computational results that evaluate the proposed approach, are presented.     

Multi-item production routing problem with backordering: a MILP approach

The aim of this paper is to present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem. The PRP-B is considered in the context of a supply chain consisting of a production facility with limited production and storage capacities and geographically dispersed points of sale with limited storage capacities. The PRP-B integrates multiple item lot sizing decisions and vehicle routing decisions to the points of sale, where backordering of end customer demands is allowed at a penalty. Two integrated mixed integer programming models are formulated and a solution procedure consisting of a relax-and-fix heuristic combined with a local search algorithm is proposed. The numerical results show that this hybrid heuristic outperforms a state-of-the-art MIP commercial solver, in terms of solution quality and CPU times.     

带检测环节的制造单元布局优化

针对带检测环节的智能制造单元，考虑其具有随机性因素的特点，本文对其机器布局问题进行研究。首先对该智能制造单元的生产过程及特点进行分析，建立其机器布局优化问题的随机非线性整数规划的数学模型；然后建立该智能制造单元对应的仿真模型，对该优化问题进行求解；最后分析抽检率的变化对最优解造成的影响，并对该智能制造单元的性能指标进行方差分析，研究不同的布局方案和抽检率对系统性能的影响程度。研究成果为企业进行智能制造单元的机器布局提供决策依据。