A genetic algorithm for lot sizing and scheduling under capacity constraints and allowing backorders (original) (raw)
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A hybrid genetic algorithm to solve a lot-sizing and scheduling problem
2002
Abstract This paper reports a lot-sizing and scheduling problem, which minimizes inventory and backlog costs of multiple products on M parallel machines with sequence-dependent set-up times over T periods. Problem solutions are represented as product subsets (ordered or unordered) for each machine m at each period t. The optimal lot sizes are then determined applying a linear program.
A genetic algorithm for solving economic lot size scheduling problem
Computers & Industrial Engineering, 2002
The purpose of this research is to determine an optimal batch size for a product, and purchasing policy of associated raw materials. The mathematical model for this problem is a constrained nonlinear integer program. Considering the complexity of solving such model, we investigate the use of genetic algorithms (GAs) for solving this model. We develop genetic algorithm code with three different penalty functions usually used for constraint optimizations. The model is also solved using an existing commercial optimization package to compare the solution. The detail computational experiences are presented.
In this paper the structure of the genetic algorithm utilised for solving an integer programming model of lot-sizing and scheduling problem is introduced. The genetic algorithm presented in the paper was employed for solving a lot-sizing and scheduling problem formulated as Capacitated Lot Sizing Problem. The method of chromosome encoding, utilised crossover operators and mutation operators employed in this genetic algorithm are presented and explained, moreover, implemented modifications are indicated.
In this paper we present a novel genetic algorithm-based approach to tackle a lot-sizing and scheduling problem. Mathematical models, commonly used to represent these problems, have the planning horizon divided in periods and sub-periods. Adjusting the right number of sub-periods becomes a hard task, since higher values create flexible environments and smaller values reduce the problem size and problem complexity. The key idea of our method is to take some advantages about adjusting the number of sub-periods. In this way, a genetic algorithm which allows for the use of individuals with different size was developed. This feature was performed to maintain the flexibility, as well as, reducing the computational load. Preliminary results show the benefits obtained when variable number of sub-periods is used, nevertheless, the tightness of the lower bounds becomes more promising when the number of products increases. More studies are necessary to determine an ideal lower bound rule.
Lot-Sizing and Scheduling Optimization Using Genetic Algorithm
2019
Simultaneous lot-sizing and scheduling problem is the problem to decide what products to be produced on which machine and in which order, as well as the quantity of each product. Problems of this type are hard to solve. Therefore, they were studied for years, and a considerable number of papers is published to solve different lotsizing and scheduling problems, specifically real-case problems. This work proposes a Real-Coded Genetic Algorithm (RCGA) with a new chromosome representation to solve a non-identical parallel machine capacitated lot-sizing and scheduling problem with sequence dependent setup times and costs, machine cost and backlogging. Such a problem can be found in real world production line at furniture manufacturer in Sweden. Backlogging is an important concept in this problem, and it is often ignored in the literature. This study implements three different types of crossover; one of them has been chosen based on numerical experiments. Four mutation operators have been combined together to allow the genetic algorithm to scan the search area and maintain genetic diversity. Other steps like initializing of the population and a reinitializing process have been designed carefully to achieve the best performance and to prevent the algorithm from trapped into the local optimum. The proposed algorithm is implemented and coded in MATLAB and tested for a set of standard medium to large-size problems taken from the literature. A variety of problems were solved to measure the impact of different characteristics of problems such as the number of periods, machines, and products on the quality of the solution provided by the proposed RCGA. To evaluate the performance of the proposed algorithm, the average deviation from the lower bound and runtime for the proposed RCGA are compared with three other algorithms from the literature. The results show that, in addition to its high computational speed, the proposed RCGA outperforms the other algorithms for non-identical parallel machine problems, while it is outperformed by the other algorithms for problems with the more identical parallel machine. The results show that the different characteristics of problem instances, like increasing setup cost, and size of the problem influence the quality of the solutions provided by the proposed RCGA negatively.
A Genetic Algorithm for Solving Single Level Lot- Sizing Problems
2007
The single level lot-sizing problem arises whenever a manufacturing company wishes to translate an aggregate plan for production of an end item into a detailed planning of its production. Although the cost driven problem is widely studied in the literature, only laborious dynamic programming approaches are known to guarantee global minimum. Thus, stochastically-based heuristics that have the mechanism to escape from local minimum are needed. In this paper a genetic algorithm for solving single level lot-sizing problems is proposed and the results of applying the algorithm to example problems are discussed. In our implementation, a lot-sizing population-generating heuristic is used to feed chromosomes to a genetic algorithm with operators specially designed for lot-sizing problems. The combination of the population-generating heuristic with genetic algorithm results in a faster convergence in finding the optimal lot-sizing scheme due to the guaranteed feasibility of the initial population.
Hybrid genetic algorithm for the economic lot-scheduling problem
International Journal of Production Research, 2002
The economic lot-scheduling problem (ELSP) is an important production scheduling problem that has been intensively studied over 40 years. Numerous heuristic algorithms have been developed since the problem is NP-hard. Dobson's heuristic has been regarded as the best in its performance. The present paper provides a hybrid genetic algorithm based on the time-varying lot sizes approach in the ELSP literature. Numerical experiments show that the hybrid genetic algorithm outperforms Dobson's heuristic.
A review of applications of genetic algorithms in lot sizing
Lot sizing problems are production planning problems with the objective of determining the periods where production should take place and the quantities to be produced in order to satisfy demand while minimizing production , setup and inventory costs. Most lot sizing problems are combinatorial and hard to solve. In recent years, to deal with the complexity and find optimal or near-optimal results in reasonable computational time, a growing number of researchers have employed meta-heuristic approaches to lot sizing problems. One of the most popular meta-heuristics is genetic algorithms which have been applied to different optimization problems with good results. The focus of this paper is on the recent published literature employing genetic algorithms to solve lot sizing problems. The aim of the review is twofold. First it provides an overview of recent advances in the field in order to highlight the many ways GAs can be applied to various lot sizing models. Second, it presents ideas for future research by identifying gaps in the current literature. In reviewing the relevant literature the focus has been on the main features of the lot sizing problems and the specifications of genetic algorithms suggested in solving these problems.
Heuristic genetic algorithms for general capacitated lot-sizing problems
Computers & Mathematics with Applications, 2002
lot-sizing problems address the issue of determining the production lot-sizes of various items appearing in consecutive production stages over a given finite planning horizon. In general capacitated lot-sizing problems, the product structure can be a general acyclic network, the capacity constraints can be very sophisticated, and all the known parameters can be time-varying. This paper proposes heuristic genetic algorithms for these problems by designing a domain-specific encoding scheme for the lot-sizes and by providing a heuristic shifting procedure as the decoding schedule. The main contribution of these genetic algorithms is the presentation technique that encodes only the binary variables for the setup patterns but derives other decision variables by making use of the problem-specific knowledge. Some results from the computational experiments are also given.
A genetic algorithm for lot sizing optimization with a capacity loading criterion
2007
The lot sizing problems are one of the basic optimization problems, which have to be solved during production planning. Only a few nature-inspired algorithms have been proposed for solving such problems. In this study the authors propose a genetic algorithm for a discrete lot sizing problem with so called small buckets and the criterion of capacity utilization. The results are compared with CPLEX MIP solver and other heuristics. The genetic algorithm proposed here gives solutions, which are 0.4 to 2.9 percent away from the theoretical lower bound.