Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

Adaptive genetic algorithm based on fuzzy reasoning for the multilevel capacitated lot-sizing problem with energy consumption in synchronizer production

The multilevel capacitated lot-sizing problem (MLCLSP) is a vital theoretical problem of production planning in discrete manufacturing. An improved algorithm based on the genetic algorithm (GA) is proposed to solve the MLCLSP. Based on the solution results, the distribution of energy consumption in a synchronous production case is analyzed. In the related literature, the GA has become a much-discussed topic in solving these kinds of problems. Although the standard GA can make up for the defects of the traditional algorithm, it will lead to the problems of unstable solution results and easy local convergence. For these reasons, this research presents an adaptive genetic algorithm based on fuzzy theory (fuzzy-GA) to solve the MLCLSP. Firstly, the solving process of the MLCLSP with the fuzzy-GA is described in detail, where algorithms for key technologies such as the capacity constraint algorithm and the algorithm of solving fitness value are developed. Secondly, the auto-encoding of decision variables for MLCLSPs is studied; within this, the decision variables of whether to produce or not are encoded into a hierarchical structure based on the bill of material; combined with external demand, the decision variables of lot-sizing are constructed. Thirdly, the adaptive optimization process of parameters of the GA for the MLCLSP based on fuzzy theory is expounded, in which membership function, fuzzy rule, and defuzzification of the MLCLSP is mainly presented. Experimental studies using the processed dataset collected from a synchronizer manufacturer have demonstrated the merits of the proposed approach, in which the energy consumption distribution of the optimized production plan is given. The optimal lot-sizing is closer to the average value of the optimal value compared with the standard GA, which indicates that the proposed fuzzy-GA approach has better convergence and stability

Industrial insights into lot sizing and schedulingmodeling

© 2015 Brazilian Operations Research Society. Lot sizing and scheduling by mixed integer programming has been a hot research topic inthe last 20 years. Researchers have been trying to develop stronger formulations, as well as to incorporatereal-world requirements from different applications. This paper illustrates some of these requirements anddemonstrates how small- and big-bucket models have been adapted and extended. Motivation comes fromdifferent industries, especially from process and fast-moving consumer goods industries

Green food supply chain design considering risk and post-harvest losses: a case study

The global food insecurity, malnourishment and rising world hunger are the major hindrances in accomplishing the zero hunger sustainable development goal by 2030. Due to the continuous increment of wheat production in the past few decades, India received the second rank in the global wheat production after China. However, storage capacity has not been expanded with similar extent. The administrative bodies in India are constructing several capacitated silos in major geographically widespread producing and consuming states to curtail this gap. This paper presents a multi-period single objective mathematical model to support their decision-making process. The model minimizes the silo establishment, transportation, food grain loss, inventory holding, carbon emission, and risk penalty costs. The proposed model is solved using the variant of the particle swarm optimization combined with global, local and near neighbor social structures along with traditional PSO. The solutions obtained through two metaheuristic algorithms are compared with the optimal solutions. The impact of supply, demand and capacity of silos on the model solution is investigated through sensitivity analysis. Finally, some actionable theoretical and managerial implications are discussed after analysing the obtained results

Optimizing the Total Production and Maintenance Cost of an Integrated Multi-Product Process and Maintenance Planning (IPPMP) Model

Today, a competitive manufacturing environment imposes further production cost reduction on modern companies. Seeking proper recommendations in production and maintenance planning are the two essential cornerstones of effective production organizations. In the current research, we have considered the problem of integrated multi-product process and maintenance planning on a capacitated machine that is susceptible to random breakdown. Maintenance processes comprise general perfect repair (non-cyclical) as preventive maintenance (PM) in the early stages and minimal repair as corrective maintenance for the occurrence of machine breakdown. Furthermore, a rational presumption is reflected in the problem statement in which the time and cost of PM are pertinent to the interval between the prior perfect repair and current PM. The purpose served by this paper is to minimize the cost of production accompanying PM, and the expected corrective repair, consequently, a mixed-integer linear programming (MILP) model has been constructed to pave the way. The model investigated under two circumstances of the machine age effect and its absence. The outcome depicted that the presence of the machine age effect led to an accurate and lessen total cost calculation.Comment: This paper has been accepted by IEEE ISSE2020 6th IEEE International Symposium on Systems Engineerin

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

Algoritmo heurístico basado en listas tabú para la planificación de la producción en sistemas multinivel con listas de materiales alternativas y entornos de coproducción

Maestría en IngenieríaEn esta investigación se presenta el desarrollo un algoritmo heurístico basado en los principios de búsqueda tabú para la solución del problema de lotificación multinivel con restricciones de capacidad, listas de materiales alternativas y entornos de coproducción, basado en la estructura del modelo de Planificación de Materiales y Operaciones Genéricas GMOP propuesto en el año 2013. El algoritmo propuesto utiliza el mecanismo de memoria a corto plazo (Lista Tabú) para la selección de Strokes alternativos para la fabricación de cada producto. La validación del algoritmo se realizó analizando la calidad y los tiempos de obtención de las soluciones. El algoritmo demostró potencial al alcanzar porcentajes de diferencia entre el 10% y 17% con respecto a las soluciones óptimas en los problemas de mayor tamaño y un equilibrio entre calidad y tiempos de solución problemas relativamente pequeños.This research shows the development process of a heuristic algorithm based on the principles of taboo search for the solution of the capacitated multilevel lot sizing problem with alternate bill of materials and co-production environments, based on the structure of the Generic Materials and Operations Planning model (GMOP). The proposed algorithm uses the short-term memory mechanism (Taboo List) for the selection of alternate strokes to produce each product. The validation of the algorithm was carried out analyzing the quality and the solution times. The algorithm demonstrated potential by reaching difference percentages around 10% and 17% compared with optimal solutions in large problems and a balance between quality and solution times when is used in relatively small problems