Algoritmo genético para solucionar el problema de dimensionamiento y programación de lotes con costos de alistamiento dependientes de la secuencia

The main purpose of this paper is to develop a hybrid genetic algorithmin order to determine the lot sizes and their production scheduling in asingle machine manufacturing system for multi-item orders, the objectivefunction minimizes the sum of holding costs, tardy costs and setup costs.The problem considers a set of orders to be processed each one with itsown due date. Each order must be delivered complete. In the schedulingare considered sequence dependent setup times. The proposed hybridgenetic algorithm has embedded a heuristic that is used to calculate itsfitness function. The heuristic method presents a modification on theoptimal timming algorithm in which are involved sequence dependentset up times. A design of experiments is developed in order to assess thealgorithm performance, which is also tested using random-generateddata and results are compared with those generated by an exact method.The results show that the algorithm achieves a good performance in bothsolution quality and time especially for large instances.El objetivo de este artículo es desarrollar un algoritmo genético el cualpermita determinar los tamaños de lote de producción y su programaciónen un sistema de manufactura de una máquina para órdenesmultiproducto, cuya función objetivo minimiza la suma de los costosde inventario por terminaciones tardías y de alistamiento. El problemacontempla un conjunto de órdenes a ser procesadas con sus respectivasfechas de entrega. Cada orden debe ser entregada en su totalidad. Dentrode la programación de los trabajos se consideran tiempos de alistamientodependientes de la secuencia. En la metaheurística implementada se utilizade manera embebida un método heurístico para el cálculo de la funciónde adaptación. El método heurístico presentado es una variación delOptimal Timming Algorithm el cual involucra los tiempos de alistamientodependientes de la secuencia. Se desarrolla un diseño de experimentospara probar el desempeño del algoritmo utilizando instancias generadasde forma aleatoria y comparando sus soluciones contra las encontradaspor un método exacto. Los resultados muestran que el algoritmo lograun buen desempeño tanto en tiempo de ejecución como en calidad de lasolución especialmente en instancias grandes.

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time