Theory and Methodology Formulating and solving production planning problems (original) (raw)
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Formulating and solving production planning problems
European Journal of Operational Research, 1999
Production planning problems frequently involve the assignment of jobs or operations to machines. The simplest model of this problem is the well known assignment problem (AP). However, due to simplifying assumptions this model does not provide implementable solutions for many actual production planning problems. Extensions of the simple assignment model known as the generalized assignment problem (GAP) and the multi-resource generalized assignment problem (MRGAP) have been developed to overcome this diculty. This paper presents an extension of the (MRGAP) to allow splitting individual batches across multiple machines, while considering the eect of setup times and setup costs. The extension is important for many actual production planning problems, including ones in the injection molding industry and in the metal cutting industry. We formulate models which are logical extensions of previous models which ignored batch splitting for the problem we address. We then give dierent formulations and suggest adaptations of a genetic algorithm (GA) and simulated annealing (SA). A systematic evaluation of these algorithms, as well as a Lagrangian relaxation (LR) approach, is presented.
EA for solving combined machine layout and job assignment problems
Machine layout and material flow between machines are crucial considerations for improving productivity in any manufacturing environment. The machine layout and the operations assignment problems are both known to be NP hard problems. In this paper, we consider a combined machine layout and job assignment problem and introduce an evolutionary algorithm to solve this combined problem. The usefulness of our approach is demonstrated through numerical examples.
Improved Algorithms for Machine Allocation in Manufacturing Systems
Operations Research, 1994
In this paper we present two algorithms for a machine allocation problem occurring in manufacturing systems. For the two algorithms presented we prove worst-case performance ratios of 2 and 3/2, respectively. The machine allocation problem we consider is a general convex resource allocation problem, which makes the algorithms applicable to a variety of resource allocation problems. Numerical results are presented for two real-life manufacturing systems.
Operation assignment and capacity allocation problem in automated manufacturing systems
Computers & Industrial Engineering, 2009
We address an operation assignment and capacity allocation problem that arises in semiconductor industries and flexible manufacturing systems. We assume the automated machines have scarce time and tool magazine capacities and the tools are available in limited quantities. The aim is to select a subset of operations with maximum total weight. We show that the problem is NP-hard in the strong sense, develop two heuristics and a Tabu Search procedure. The results of our computational tests have revealed that our Tabu Search procedure produces near optimal solutions very quickly.
A Decision Support Tool for Resource Allocation in Batch Manufacturing
2005 IEEE International Conference on Systems, Man and Cybernetics, 2005
A decision support tool for production planning is discussed in this paper to perform the job of machine grouping and labour allocation within a machining line. The production plans within the industrial partner have been historically inefficient because the relationship between the cycle times, the machine group size, and the operator's utilisation hasn't been properly understood. Starting with a simulation model, a rule-base has been generated to predict the operator's utilisation for a range of production settings. The resource allocation problem is then solved by breaking the problem into a series of smaller sized tasks. The objective is to minimise the number of operators and the difference between the maximum and minimum cycle times of machines within each group. The results from this decision support tool will be presented for the particular case study.
A two-stage solution approach for plastic injection machines scheduling problem
Journal of Industrial & Management Optimization, 2017
One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.
Applied Sciences
This research focuses on small- and medium-sized businesses that provide machining or other process services but do not produce their own products. Their daily manufacturing schedule varies according to client needs. Small- and medium-sized businesses strive to operate in these circumstances by extending their customer base and creating adequate production planning targets. Their resources are limited, including the technical and technological components of their equipment, tools, people resources, time, and capacities. As a result, planning operations with the present resources of small- and medium-sized businesses in the midst of the global economic crisis is a widespread issue that must be addressed. This study seeks to offer a novel mathematical optimization model based on a genetic algorithm to address job shop scheduling and capacity planning difficulties in small- and medium-sized businesses, therefore improving performance management and production planning procedures. On th...
Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2006
Production planning of a flexible manufacturing system (FMS) is plagued by two interrelated problems, i.e. part type selection and operation allocation on machines. The combination of these problems is termed the machine-loading problem, which is a well-known complex puzzle and treated as a strongly NP-hard problem. In this research, a machine-loading problem has been modelled, taking into consideration several technological constraints related to the flexibility of machines, availability of machining time, tool slots, etc., while aiming to satisfy the objectives of minimizing the system unbalance, maximizing throughput, and achieving very good overall FMS utilization. The solution of such problems, even for moderate numbers of part types and machines, is marked by excessive computation complexities and therefore advanced random search and optimization techniques are needed to resolve them. In this paper, a new kind of genetic algorithm, termed a genetic algorithm with chromosome di...
Application of Genetic Algorithm into Multicriteria Batch Manufacturing Scheduling
Strojniški vestnik – Journal of Mechanical Engineering, 2011
Technical innovations in the area of manufacturing logistics are introduced partially and thus fail to realize their full potential. In order to optimise the efficiency of turning manufacturing processes, the production planning and scheduling, cutting tools and material flow process, manufacturing capacities have been analysed. All data from production operations, quantities and the, duration of operations are now kept in the ERP system. It provided the necessary condition for the establishment of a robust planning model, which includes stock control of material and cutting tools. An update was required for the whole lifecycle of products and means of work. The article presents information and an algorithm for a dynamic scheduling model, based on a genetic algorithm. The orders on the machines are scheduled on the basis of a genetic algorithm, according to the target function criteria. The algorithm provides a satisfactory, almost ideal solution, which is good enough for implementation in practice. With the GA the machine utilization increased, throughput time was reduced and costs and delivery delays improved. The presented model of GA also allows further optimisation of manufacturing plans and the machines layout.
IIE Transactions, 2003
The increasing demand for on-time delivery of products and low production cost is forcing manufacturers to seek effective schedules to coordinate machines and operators so as to reduce costs associated with labor, setup, inventory, and unhappy customers. This paper presents the modeling and resolution of a job shop scheduling system for J. M. Products Inc., whose manufacturing is characterized by the need to simultaneously consider machines and operators, machines requiring significant setup times, operators of different capabilities, and lots dividable into transfer lots. These characteristics are typical for many manufacturers, difficult to handle, and have not been adequately addressed in the literature. In our study, an integer optimization formulation with a separable structure is developed where both machines and operators are modeled as resources with finite capacities. Setups are explicitly considered following our previous work with additional penalties on excessive setups. By analyzing transfer lot dynamics, transfer lots are modeled by using linear inequalities. The objective is to maximize on-time delivery of products, reduce inventory, and reduce the number of setups. By relaxing resource capacity constraints and portions of precedence constraints, the problem is decomposed into smaller subproblems that are effectively solved by using a novel dynamic programming procedure. The multipliers are updated using the recently developed surrogate subgradient method. A heuristic is then used to obtain a feasible schedule based on subproblem solutions. Numerical testing shows that the method generates high quality schedules in a timely fashion.