Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems

Purpose This paper aims to present a novel bi-objective mathematical model for a production-inventory system under uncertainty. Design/methodology/approach This paper addresses agile and lean manufacturing concepts alongside with green production methods to design an integrated capacitated lot sizing problem (CLSP). From a methodological perspective, the problem is solved in three phases. In the first step, an FM/M/C queuing system is used to minimize the number of customers waited to receive their orders. In the second step, an effective approach is applied to deal with the fuzzy bi-objective model and finally, a hybrid metaheuristic algorithm is used to solve the problem. Findings Some numerical test problems and sensitivity analyzes are conducted to measure the efficiency of the proposed model and the solution method. The results validate the model and the performance of the solution method compared to Gams results in small size test problems and prove the superiority of the hybrid algorithm in comparison with the other well-known metaheuristic algorithms in large size test problems. Originality/value This paper presents a novel bi-objective mathematical model for a CLSP under uncertainty. The proposed model is conducted on a practical case and several sensitivity analysis are conducted to assess the behavior of the model. Using a queue system, this problem aims to reduce the items waited in the queue to receive service. Two objective functions are considered to maximize the profit and minimize the negative environmental effects. In this regard, the second objective function aims to reduce the amount of emitted carbon.

Download Full-text

Decomposition methods for the lot-sizing and cutting-stock problems in paper industries

Applied Mathematical Modelling ◽

10.1016/j.apm.2017.04.010 ◽

2017 ◽

Vol 48 ◽

pp. 250-268 ◽

Cited By ~ 8

Author(s):

Aline A.S. Leao ◽

Marcos M. Furlan ◽

Franklina M.B. Toledo

Keyword(s):

Lot Sizing ◽

Decomposition Methods ◽

Cutting Stock

Download Full-text

Population Based Metaheuristic Algorithm Approach for Analysis of Multi-Item Multi-Period Procurement Lot Sizing Problem

Advances in Operations Research ◽

10.1155/2017/3601217 ◽

2017 ◽

Vol 2017 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Prasanna Kumar ◽

Mervin Herbert ◽

Srikanth Rao

Keyword(s):

Genetic Algorithm ◽

Mathematical Model ◽

Inventory Management ◽

Lot Sizing ◽

Population Based ◽

Optimization Approach ◽

Time Data ◽

Significant Difference ◽

Lot Sizing Problem ◽

Order Quantities

This research study focuses on the optimization of multi-item multi-period procurement lot sizing problem for inventory management. Mathematical model is developed which considers different practical constraints like storage space and budget. The aim is to find optimum order quantities of the product so that total cost of inventory is minimized. The NP-hard mathematical model is solved by adopting a novel ant colony optimization approach. Due to lack of benchmark method specified in the literature to assess the performance of the above approach, another metaheuristic based program of genetic algorithm is also employed to solve the problem. The parameters of genetic algorithm model are calibrated using Taguchi method of experiments. The performance of both algorithms is compared using ANOVA analysis with the real time data collected from a valve manufacturing company. It is verified that two methods have not shown any significant difference as far as objective function value is considered. But genetic algorithm is far better than the ACO method when compared on the basis of CPU execution time.

Download Full-text

COMPARISON OF MIP MODELS FOR THE INTEGRATED LOT-SIZING AND ONE-DIMENSIONAL CUTTING STOCK PROBLEM

Pesquisa Operacional ◽

10.1590/0101-7438.2016.036.01.0167 ◽

2016 ◽

Vol 36 (1) ◽

pp. 167-196 ◽

Cited By ~ 5

Author(s):

Gislaine Mara Melega ◽

Silvio Alexandre de Araujo ◽

Raf Jans

Keyword(s):

Lot Sizing ◽

Cutting Stock Problem ◽

Cutting Stock ◽

One Dimensional ◽

Mip Models

Download Full-text

Solving a combined cutting-stock and lot-sizing problem with a column generating procedure

Computers & Operations Research ◽

10.1016/j.cor.2007.03.005 ◽

2008 ◽

Vol 35 (10) ◽

pp. 3371-3392 ◽

Cited By ~ 24

Author(s):

Sigrid Lise NonÅs ◽

Anders Thorstenson

Keyword(s):

Lot Sizing ◽

Cutting Stock ◽

Lot Sizing Problem

Download Full-text

The Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem: Evaluating the Generalized Mathematical Model

Mathematical Problems in Engineering ◽

10.1155/2015/182781 ◽

2015 ◽

Vol 2015 ◽

pp. 1-18 ◽

Cited By ~ 7

Author(s):

Claudio F. M. Toledo ◽

Alf Kimms ◽

Paulo M. França ◽

Reinaldo Morabito

Keyword(s):

Mathematical Model ◽

Lot Sizing ◽

Raw Materials ◽

Soft Drink ◽

Scheduling Problem ◽

Production Lines ◽

Modeling Methodology ◽

Synchronization Problem ◽

Problem Instances ◽

Lot Sizing And Scheduling

This paper presents the synchronized and integrated two-level lot sizing and scheduling problem (SITLSP). This problem is found in beverage production, foundry, glass industry, and electrofused grains, where the production processes have usually two interdependent levels with sequence-dependent setups in each level. For instance, in the first level of soft drink production, raw materials are stored in tanks flowing to production lines in the second level. The amount and the time the raw materials and products have to be stored and produced should be determined. A synchronization problem occurs because the production in lines and the storage in tanks have to be compatible with each other throughout the time horizon. The SITLSP and its mathematical model are described in detail by this paper. The lack of similar models in the literature has led us to also propose a set of instances for the SITLSP, based on data provided by a soft drink company. Thus, a set of benchmark results for these problem instances are established using an exact method available in an optimization package. Moreover, results for two relaxations proved that the modeling methodology could be useful in real-world applications.

Download Full-text

Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry

TEMA (São Carlos) ◽

10.5540/tema.2016.017.03.0305 ◽

2016 ◽

Vol 17 (3) ◽

pp. 305 ◽

Cited By ~ 6

Author(s):

Sônia Cristina Poltroniere ◽

Silvio Alexandre Araujo ◽

Kelly Cristina Poldi

Keyword(s):

Lower Bounds ◽

Production Scheduling ◽

Optimization Problems ◽

Lot Sizing ◽

Paper Industry ◽

Cutting Stock Problem ◽

Cutting Stock ◽

Lot Sizing Problem ◽

Different Types ◽

Trim Loss

Two important optimization problems occur in the planning and production scheduling in paper 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 in- ventory 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.

Download Full-text