Optimization of an integrated lot sizing and cutting stock problem in the paper industry

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOTwo important optimization problems occur in the planning and production scheduling inpaper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon. These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and inventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed.Two important optimization problems occur in the planning and production scheduling inpaper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon. These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and inventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed.173305320CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO2010/10133-02013/07375-

A New Decision Model for Reducing Trim Loss and Inventory in the Paper Industry

In the paper industry, numerous studies have explored means of optimizing order allocation and cutting trim loss. However, enterprises may not adopt the resulting solutions because some widths of the inventory exceed or are less than those required for acceptable scheduling. To ensure that the results better suit the actual requirements, we present a new decision model based on the adjustment of scheduling and limitation of inventory quantity to differentiate trim loss and inventory distribution data. Differential analysis is used to reduce data filtering and the information is valuable for decision making. A numerical example is presented to illustrate the applicability of the proposed method. The results show that our proposed method outperforms the manual method regarding scheduling quantity and trim loss

A hybrid algorithm for the integrated production planning in the pulp and paper industry

Tese de mestrado integrado. Engenharia Industrial e Gestão. Faculdade de Engenharia. Universidade do Porto. 201

An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches

We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported

O problema de corte de estoque unidimensional multiperíodo

The Multiperiod Cutting Stock Problem arises embedded in the production planning and programming in many industries which have a cutting process as an important stage. Ordered items have different due date over a finite planning horizon. A large scale integer linear optimization model is proposed. The model makes possible to anticipate or not the production of items. Unused objects in inventory in a period become available to the next period, added to new inventory, which are acquired or produced by the own company. The mathematical model's objective considers the waste in the cutting process, and costs for holding objects and final items. The simplex method with column generation was specialized to solve the linear relaxation. Some preliminary computational experiments showed that the multiperiod model could obtain effective gains when compared with the lot-for-lot solution, which is typically used in practice. However, in real world problems, the fractional solution is useless. So, additionally, two rounding procedures are developed to determine integer solutions for multiperiod cutting stock problems. Such procedures are based on a rolling horizon scheme, which roughly means, find an integer solution only for the first period, since this is the solution to be, in fact, carried out. Finally, we conclude that the proposed model for multiperiod cutting stock problems allows flexibility on analyzing a solution to be put in practice. The multiperiod cutting problem can be a tool that provides the decision maker a wide view of the problem and it may help him/her on making decisions.O problema de corte de estoque multiperíodo surge imerso no planejamento e programação da produção em empresas que têm um estágio de produção caracterizado pelo corte de peças. As demandas dos itens ocorrem em períodos diversos de um horizonte de planejamento finito, sendo possível antecipar ou não a produção de itens. Os objetos não utilizados em um período ficam disponíveis no próximo, juntamente com possíveis novos objetos adquiridos ou produzidos pela própria empresa. Um modelo de otimização linear inteira de grande porte é proposto, cujo objetivo pondera as perdas nos cortes, os custos de estocagem de objetos e itens. O método simplex com geração de colunas foi especializado para resolver a relaxação linear. Experiências computacionais preliminares mostram que ganhos efetivos podem ser obtidos, quando comparado com a solução lote-por-lote, tipicamente utilizada na prática. No entanto, em problemas práticos, uma solução fracionária não é aplicável. Então, foram desenvolvidas duas abordagens para o arredondamento da solução para o problema de corte de estoque multiperíodo. Tais procedimentos são baseados em horizonte rolante, que basicamente, consiste em tentar encontrar uma solução inteira apenas para o primeiro período, já que esta será uma solução implementada na prática; para os demais períodos pode haver mudança na demanda, por exemplo, a chegada de novos pedidos ou o cancelamento de pedidos. Finalmente, concluímos que o modelo proposto para o problema de corte de estoque multiperíodo permite flexibilidade na análise da solução a ser posta em prática. O modelo multiperíodo pode ser uma ferramenta que fornece ao tomador de decisões uma ampla visão do problema e pode auxiliá-lo na tomada de decisão.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Federal de São Paulo (UNIFESP) Departamento de Ciência e TecnologiaUniversidade de São Paulo Inst. de Ciências Matemáticas e de ComputaçãoUNIFESP, Depto. de Ciência e TecnologiaSciEL

Оптимізація процесів планування розкрою полотна на виробництві картону та паперу

Формалізовано задачу оптимізації процесів планування розкрою на виробництві картону та паперу: запропановано критерії оптимізації, складено цільову функцію та визначено математичні обмеження на змінні з урахуванням обмежень реального виробництва. Для вирішення задачі оптимізації був використан Симплекс метод разом з новим підходом до створення карт розкрою що дозволив отримати кращий план відповідно до обраних критеріїв. Проведені дослідження показали, що використання такого підходу до планування дозволяє збільшити прибуток виробництва за рахунок більш точного представлення замовлення та збалансованного використання супутньої продукції у розрахунках задачи розкрою.Improving the production efficiency is one of the main management tasks for the pulp and paper industry. This can be achieved through the use of automated planning systems, designed to take into account the features and limitations of particular production. Such systems allow, on the basis of orders received from consumers, a voluminous production schedule to be made to take into account the needs for raw materials, the productivity of paper or cardboard machines, and the optimal cutting of the canvas on longitudinal cutting machines. Linear programming method for solving optimization problems. Computer simulation using optimized packages to compare the results with the options used in production. Cutting planning processes were optimized on the basis of standard orders for rolled products of an enterprise in the Kyiv region. The problem of optimizing the cutting planning process and criteria for increasing the production efficiency is formalized. The target function is to increase the profit of production by minimizing material losses in planning the cutting of the master rill and minimizing the storage of related products in production warehouses. To solve the optimization problem, it is proposed to use our own method of calculating the optimal cutting patterns for the manufacture of finished products on a longitudinal cutting machine. The MS Office SOLVER package was used for the calculations. Different cutting options were compared via the target function. Important criteria for this inspection are the fulfillment of the entire order, the availability and storage of related products outside the order, and the minimization of time for the reconfiguration of machines. Longitudinal cutting machines of this production can be adjusted only manually, and it takes a long time. Also, technological restrictions on the allowable width of the edge are an important requirement for cutting patterns. All patterns that do not meet these restrictions cannot be compared. There are three options for comparison. An option is made according to the proposed method and with an optimization package using the Simplex method and a number of technological limitations inherent in this production. An option is selected by the production planner manually taking into account previous experience. And the variant of cutting orders is made by the production management system, which accompanies the process of planning and transfer of tasks for longitudinal cutting machines. The function takes the maximum value in the option offered by the production scheduler. But this option is not optimal, because a person adds rolls to the satellite to improve the cutting map to fulfill all orders. This in turn leads to overfulfillment of orders and production of additional products in a warehouse where they can be stored for years until the expiration date. The option offered by the automotive system does not require the use of accompanying rolls but unfortunately does not meet the requirements for optimal cutting of the material. Automatic cutting leaves a large edge that is already within the maximum allowable limitations of the machines and, moreover, does not lead to the execution of the entire order. This violates the basic requirement for production such as full execution of the order. Therefore, this option cannot be used either. The optimal cut for profit maximization is the option obtained using the roll planning technique. This technique allows the average weight of the roll to be obtained through the use of production history. The estimated weight is used to convert the order from tons to the number of pieces. Cutting patterns for the production of the order in this way are presented and, taking into account the technological limitations of production, can be calculated on the basis of the Simplex method in optimization packages. Such cutting patterns have no satellites and allow the fulfilment of all orders. The roll planning technique reduces the number of clippings and avoids overproduction. The analysed cutting plans show that the use of satellites reduces the profitability of the enterprise and does not always minimize material costs

Advances in Modelling of the Integrated Production Logistics in Sugarcane Harvest

The sugar-energy sector is extremely important to the Brazilian economy, with several other production chains derived from it, generating some of the main products linked to food and energy sources. This study proposes an integration model for sugarcane harvesting logistics processes, focusing on optimisation of industrial plant production capacity. Dynamic modelling has been applied to study a broad range of the productive phases of the sugar-energy chain. This paper proposes indicators to evaluate the degree of efficiency of the production logistics processes. Preliminary results showed that phase times in the production logistics processes can be significantly reduced in the harvest phase. When analysed as a coordination-oriented flow having chained activities, the production logistics processes optimise the speeds and travel times during the harvest phase. The developed model uses data set of the production and logistics processes phases of a sugarcane industry. A future study will focus on more detailed and complex stakeholder behaviours based on the model proposed