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The structure of the genetic algorithm of lot-sizing and scheduling problem formulated as capacitated lot sizing problem

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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.
1. INTRODUCTION
The objective of the set of lot-sizing and scheduling problems is to determine minimal costs as their solution. These costs are connected to inventoriable costs (high inventory level, high costs) and costs of lot organising (small-size lots, frequent starts, high costs). In existing formulations of the problems of this type a solution is being searched in the space between these contradictory goals.
A list of selected works where lot-sizing and scheduling problem is presented is to be found, amongst others, in following works: (Karimi et al., 2003) [5], (Quadt, Kuhn, 2008) [9].
The mathematical model for Capacitated Lot Sizing Problem (CLSP) is considered to be the very first and fundamental formulation of lot-sizing and scheduling problem. The most frequent situation of CLPS utilisation is a problem with long planning horizons. In such a problem changeover costs and changeover time are charged in any case when a machine’s status is ready-to-manufacture. The set of parameters and variables of the CLSP formulation is to be found in Table 1.
A PLCM for CLSP may be formulated according to mathematical description presented in
Table 2.
2. GENETIC ALGORITHM
In the paper (Książek, 2011) [7] results of a computational experiment are presented; the experiment consisted of solving a particular problem for the same set of data at first with an implemented genetic algorithm and then solving the PLCM formulation of the problem with GLPK solver (GNU Linear Programming Kit). The genetic algorithm was implemented circuit the language JAVA SE 6. On the other hand, GLPK is a free programme kit for solving integer-programming models.
AGH University of Science and Technology, Faculty of Management, Department of Operation Research and (...)

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