scholarly journals Extended Model Formulation of the Proportional Lot-Sizing and Scheduling Problem with Lost Demand Costs

2011 ◽  
Vol 5 (1) ◽  
pp. 49-56
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Lot Sizing ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Extended Model ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Model Formulation ◽  
Mip Models ◽  
Planning Problems ◽  
Lot Sizing And Scheduling

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such extended model formulation.

scholarly journals Practical Tips for Modelling Lot-Sizing and Scheduling Problems

2009 ◽  
Vol 3 (2) ◽  
pp. 37-48
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Lot Sizing ◽  
Valid Inequalities ◽  
A Priori ◽  
Computational Effort ◽  
Scheduling Problems ◽  
Good Balance ◽  
Validation Of Models ◽  
Short Time ◽  
Lot Sizing And Scheduling

This paper presents some important alternatives for modelling Lot-Sizing and Scheduling Problems. First, the accuracy of models can improved by using short time buckets, which allow more detailed planning but lead to higher computational effort. Next, valid inequalities make the models tighter but increase their size. Sometimes it is possible to find a good balance between the size and tightness of a model by limiting a priori the number of valid inequalities. Finally, a special normalization of the variables simplifies the presentation of results and validation of models.

scholarly journals Study on column generation for the lot-sizing and scheduling problem with sequencedependent setup time

2018 ◽  
Vol 189 ◽  
pp. 06002
Author(s):  
Dandan Zhang ◽  
Canrong Zhang
Keyword(s):  
Lot Sizing ◽  
Setup Time ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Optimal Solutions ◽  
Sequence Dependent ◽  
Sequence Dependent Setup Time ◽  
Capacitated Lot Sizing ◽  
Sequence Dependent Setup ◽  
Lot Sizing And Scheduling

The capacitated lot-sizing and scheduling problem with sequence-dependent setup time and carryover setup state is a challenge problem in the semiconductor assembly and test manufacturing. For the problem, a new mixed integer programming model is proposed, followed by exploring its relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions. On account of the sequence-dependent setup time and the carryover of setup states, a per-machine Danzig Wolfe decomposition is proposed. We then build a statistical estimation model to describe correlation between the optimal solutions and two lower bounds including the linear relaxation solutions, and the pricing sub-problem solutions of Danzig Wolfe decomposition, which gives insight on the optimal values about information regarding whether or not the setup variables in the optimal solution take the value of 1, and the information is further used in the branch and select procedure. Numerical experiments are conducted to test the performance of the algorithm.

General lot-sizing and scheduling for perishable food products

2020 ◽  
Vol 54 (3) ◽  
pp. 913-931 ◽  
Author(s):  
Zohreh Alipour ◽  
Fariborz Jolai ◽  
Ehsan Monabbati ◽  
Nima Zaerpour
Keyword(s):  
Lot Sizing ◽  
Food Products ◽  
Production Costs ◽  
Mixed Integer ◽  
Computational Time ◽  
Scheduling Problem ◽  
Solution Quality ◽  
Perishable Product ◽  
Tactical Decision ◽  
Lot Sizing And Scheduling

General lot-sizing and scheduling is a well-studied problem in the literature, but for perishable or time-sensitive products is less investigated. Also, most of studies on perishable product supply chains focus on strategic and tactical decision levels rather than operational decision level and integrated operational and tactical decision levels. We focus on a general lot-sizing and scheduling problem faced by perishable food products. The lifespan and shelf life are two important key features of perishable products that are considered in the problem. This problem can be described as a multi-product, multi-parallel line, multi-period general lot-sizing and scheduling problem with sequence dependent change over time. The objective function is sum of production costs, inventory holding costs, waste costs, and lifespan related cost function. We apply two mixed-integer programming based heuristics to solve generated instances. The heuristics are compared in terms of solution quality and computational time. Also, the sensitivity analysis is presented to analyze the effects of parameters’ changes.

scholarly journals Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

2021 ◽  
Author(s):  
Willy Alves de Oliveira Soler ◽  
Maristela Oliveira Santos ◽  
Maria do Socorro Nogueira Rangel
Keyword(s):  
Lot Sizing ◽  
Computational Study ◽  
Mixed Integer ◽  
Optimization Models ◽  
Scheduling Problem ◽  
Production Lines ◽  
Commodity Flow ◽  
Scarce Resources ◽  
Computational Performance ◽  
Lot Sizing And Scheduling

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

scholarly journals Mathematical modeling to optimize production planning and scheduling in a small foundry with multiple alternating furnaces

2021 ◽  
Vol 16 (04) ◽  
pp. 82-114
Author(s):  
Michael Ferreira Bertulucci ◽  
Giovanna Abreu Alves ◽  
Victor Claudio Bento de Camargo
Keyword(s):  
Mathematical Modeling ◽  
Lot Sizing ◽  
Load Capacity ◽  
Mixed Integer ◽  
Suitable Model ◽  
Extended Model ◽  
Lot Size ◽  
Planning And Scheduling ◽  
Actual Application ◽  
Lot Sizing And Scheduling

Purpose - This study presents an extension to a model in the literature for lot-sizing and scheduling in a small foundry with multiple alternate furnaces. The purpose of the model is to minimize delays and inventory costs. In addition, it determines the best use of the load capacity in the furnaces. Theoretical framework – Lot-sizing in foundries in the marketplace is a subject of academic interest due to its applicability and mathematical and computational complexity. Many papers address the production problem in foundries with a single furnace, however, few papers address the possibility of multiple furnaces. Design/methodology/approach - Mathematical modeling was used to represent the lot-sizing and scheduling problem in a small foundry. Data from the company's order books were collected and model validation questionnaires were applied. Findings - The extended model was able to generate good production plans at different planning horizons, with better performance than the current methods obtained by the company. Originality/value - the extension of the model contributes to the literature by addressing the existence of multiple non-simultaneous furnaces, a feature that has not been greatly explored. A comparison with other models is performed to indicate the most suitable model for actual application. Keywords: Alloys scheduling. Foundry. Lot size. Mixed integer programming.

scholarly journals A Novel MILP Model for the Production, Lot Sizing, and Scheduling of Automotive Plastic Components on Parallel Flexible Injection Machines with Setup Common Operators

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Beatriz Andres ◽  
Eduardo Guzman ◽  
Raul Poler
Keyword(s):  
Supply Chain ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Computational Time ◽  
Scheduling Problem ◽  
Automotive Supply Chain ◽  
Milp Model ◽  
Plastic Components ◽  
Automotive Supply ◽  
Lot Sizing And Scheduling

In this article, a mixed integer linear program (MILP) model is proposed for the production, lot sizing, and scheduling of automotive plastic components to minimize the setup, inventory, stockout, and backorder costs, by taking into account injection molds as the main index to schedule on parallel flexible injection machines. The proposed MILP considers the minimum and maximum inventory capacities and penalizes stockout. A relevant characteristic of the modeled problem is the dependence between mold setups to produce plastic components. The lot sizing and scheduling problem solution results in the assignment of molds to machines during a specific time period and in the calculation of the number of components to be produced, which is often called lot size, following a sequence-dependent setup time. Depending on the machine on which the mold is setup, the number of units to be produced will be distinct because machines differ from one another. The stock coverage, defined in demand days, is also included in the MILP to avoid backorders, which is highly penalized in the automotive supply chain. Added to this, the proposed model is extended by considering setup common operators to respond to and fulfill the constraints that appear in automotive plastic enterprises. In this regard, the MILP presented solves a lot-sizing and scheduling problem, emerged in a second-tier supplier of a real automotive supply chain. Finally, this article validates the MILP by performing experiments with different sized instances, including small, medium, and large. The large-sized dataset is characterized by replicating the amount of data used in the real enterprise, which is the object of this study. The goodness of the model is evaluated with the computational time and the deviation of the obtained results as regards to the optimal solution.

scholarly journals Alternative Mathematical Models and Solution Approaches for Lot-Sizing and Scheduling Problems in the Brewery Industry: Analyzing Two Different Situations

2017 ◽  
Vol 2017 ◽  
pp. 1-18
Author(s):  
Tamara A. Baldo ◽  
Reinaldo Morabito ◽  
Maristela O. Santos ◽  
Luis Guimarães
Keyword(s):  
Lot Sizing ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Heuristic Solution ◽  
Planning And Scheduling ◽  
Technology Investment ◽  
Production Planning And Scheduling ◽  
Mip Models ◽  
Solution Methods ◽  
Result Analysis

This research proposes new approaches to deal with the production planning and scheduling problem in brewery facilities. Two real situations found in factories are addressed, which differ by considering (or not) the setup operations in tanks that provide liquid for bottling lines. Depending on the technology involved in the production process, the number of tank swaps is relevant (Case A) or it can be neglected (Case B). For both scenarios, new MIP (Mixed Integer Programming) formulations and heuristic solution methods based on these formulations are proposed. In order to evaluate the approach for Case A, we compare the results of a previous study with the results obtained in this paper. For the solution methods and the result analysis of Case B, we propose adaptations of Case A approaches yielding an alternative MIP formulation to represent it. Therefore, the main contributions of this article are twofold: (i) to propose alternative MIP models and solution methods for the problem in Case A, providing better results than previously reported, and (ii) to propose new MIP models and solution methods for Case B, analyzing and comparing the results and benefits for Case B considering the technology investment required.

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