scholarly journals Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

2021 ◽  
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Programming Model ◽  
Lot Sizing ◽  
A Priori ◽  
Planning Horizon ◽  
Computational Effort ◽  
Setup Times ◽  
Mixed Integer ◽  
New Model ◽  
Cycle Times ◽  
Work In Process

Abstract The planning horizon of small bucket models is often divided into many fictitious micro-periods, with non-zero demand only in the last micro-period of each real (macro-)period. On the one hand, such models ensure schedules with short cycle times and low work-in-process inventory in multilevel systems; on the other, they make setup times that are longer than a single period more likely. This paper presents a new mixed-integer programming model for the case with setup operations that overlap multiple periods. The new model assumes that the capacity is constant in the whole planning horizon and explicitly determines the entire schedule of each changeover. Moreover, a two-level MIP heuristic is presented that uses model-specific cuts to fix a priori some minor decisions. The results of the computational experiments show that the new model and MIP heuristic require a substantially smaller computational effort from a standard MIP solver than the known models.MSC Classification: 90B30 , 90C11

Environmentally sustainable stochastic procurement model

2018 ◽  
Vol 29 (3) ◽  
pp. 472-498 ◽  
Author(s):  
Harpreet Kaur ◽  
Surya Prakash Singh
Keyword(s):  
Carbon Emissions ◽  
Environmental Sustainability ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Business Environment ◽  
Manufacturing Firms ◽  
Mixed Integer ◽  
Content Type ◽  
Environmentally Sustainable ◽  
Procurement Planning

Purpose Procurement planning has always been a huge and challenging activity for business firms, especially in manufacturing. With government legislations about global concern over carbon emissions, the manufacturing firms are enforced to regulate and reduce the emissions caused throughout the supply chain. It is observed that procurement and logistics activities in manufacturing firms contribute heavily toward carbon emissions. Moreover, highly dynamic and uncertain business environment with uncertainty in parameters such as demand, supplier and carrier capacity adds to the complexity in procurement planning. The paper aims to discuss these issues. Design/methodology/approach This paper is a novel attempt to model environmentally sustainable stochastic procurement (ESSP) problem as a mixed-integer non-linear program. The ESSP optimizes the procurement plan of the firm including lot-sizing, supplier and carrier selection by addressing uncertainty and environmental sustainability. The model applies chance-constrained-based approach to address the uncertain parameters. Findings The proposed ESSP model is solved optimally for 30 data sets to validate the proposed ESSP and is further demonstrated using three illustrations solved optimally in LINGO 10. Originality/value The ESSP model simultaneously minimizes total procurement cost and carbon emissions over the entire planning horizon considering uncertain demand, supplier and carrier capacity.

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 Multi-Period Network Design Problem in Regional Hazardous Waste Management Systems

2019 ◽  
Vol 16 (11) ◽  
pp. 2042 ◽  
Author(s):  
Jun Zhao ◽  
Lixiang Huang
Keyword(s):  
Network Design ◽  
Design Problem ◽  
Programming Model ◽  
Planning Horizon ◽  
Network Design Problem ◽  
Mixed Integer ◽  
Hazardous Wastes ◽  
Total Risk ◽  
Total Cost ◽  
Treatment And Disposal

The management of hazardous wastes in regions is required to design a multi-echelon network with multiple facilities including recycling, treatment and disposal centers servicing the transportation, recycling, treatment and disposal procedures of hazardous wastes and waste residues. The multi-period network design problem within is to determine the location of waste facilities and allocation/transportation of wastes/residues in each period during the planning horizon, such that the total cost and total risk in the location and transportation procedures are minimized. With consideration of the life cycle capacity of disposal centers, we formulate the problem as a bi-objective mixed integer linear programming model in which a unified modeling strategy is designed to describe the closing of existing waste facilities and the opening of new waste facilities. By exploiting the characteristics of the proposed model, an augmented ε -constraint algorithm is developed to solve the model and find highly qualified representative non-dominated solutions. Finally, computational results of a realistic case demonstrate that our algorithm can identify obviously distinct and uniformly distributed representative non-dominated solutions within reasonable time, revealing the trade-off between the total cost and total risk objectives efficiently. Meanwhile, the multi-period network design optimization is superior to the single-period optimization in terms of the objective quality.

Optimization Methods for Lot-Sizing Problem in an Automated Foundry

2013 ◽  
Vol 58 (3) ◽  
pp. 863-866 ◽  
Author(s):  
J. Duda ◽  
A. Stawowy
Keyword(s):  
Production Planning ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Planning Problem ◽  
Lot Size ◽  
Mip Model ◽  
Production Planning Problem ◽  
Problem Instances

Abstract In the paper we studied a production planning problem in a mid-size foundry that provides tailor-made cast products in small lots for a large number of clients. Assuming that a production bottleneck is the furnace, a mixed-integer programming (MIP) model is proposed to determine the lot size of the items and the required alloys to be produced during each period of the finite planning horizon that is subdivided into smaller periods. As using an advanced commercial MIP solvers may be impractical for more complex and large problem instances, we proposed and compared a few computational intelligence heuristics i.e. tabu search, genetic algorithm and differential evolution. The examination showed that heuristic approaches can provide a good compromise between speed and quality of solutions and can be used in real-world production planning.

A Genetic Algorithm Approach for Multi-Product Multi-Machine CONWIP Production System

2011 ◽  
Vol 110-116 ◽  
pp. 3624-3630
Author(s):  
Saeede Ajorlou ◽  
Issac Shams ◽  
Mirbahador G. Aryanezhad
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Programming Model ◽  
Search Algorithms ◽  
Mixed Integer ◽  
Simplified Model ◽  
Mathematical Programming Model ◽  
Production Lines ◽  
Work In Process ◽  
Genetic Algorithm Approach

In this paper, a new mathematical programming model is developed to address common issues relating to single-stage CONstant-Work-In-Process based production lines. A Ge-netic Algorithm (GA) approach is then proposed to directly solve the model in order to simultaneously determines the optimal job sequence and WIP level. Unlike many existing approaches, which are based on deterministic search algorithms such as nonlinear programming and mixed integer programming, our proposed method does not rely on a linearized or simplified model of the system. results from a comprehensive numerical example indicate computational efficiency and validation of our method.

COMBINING PROCESS SELECTION AND LOT SIZING MODELS FOR PRODUCTION SCHEDULING OF ELECTROFUSED GRAINS

2009 ◽  
Vol 26 (03) ◽  
pp. 421-443 ◽  
Author(s):  
JOSÉ ROBERTO DALE LUCHE ◽  
REINALDO MORABITO ◽  
VITÓRIA PUREZA
Keyword(s):  
Customer Service ◽  
Production Scheduling ◽  
Programming Model ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Due Dates ◽  
Process Selection ◽  
Simple Task ◽  
Model Combining ◽  
Constructive Heuristic

This work presents an optimization model to support decisions in the production planning and control of the electrofused grain industry. A case study was carried out in a Brazilian company with the aim of helping to increase productivity and improve customer service concerning meeting deadlines. A mixed integer linear programming model combining known models of process selection and single-stage lot sizing were applied to the production scheduling of electrofused grains. Optimizing this scheduling is not a simple task mainly because of the scale of the equipment setup times, the diversity of the products and the deadlines of the order due dates. A constructive heuristic is also proposed as an alternative solution method, particularly for large-sized instances. The results show that the model and the heuristic can produce better solutions than the ones currently used by the company.

scholarly journals Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times

2021 ◽  
Vol 11 (23) ◽  
pp. 11210
Author(s):  
Mohammed Alnahhal ◽  
Diane Ahrens ◽  
Bashir Salah
Keyword(s):  
Lot Sizing ◽  
Planning Horizon ◽  
Service Level ◽  
Mixed Integer ◽  
Lot Size ◽  
Dynamic Planning ◽  
Holding Costs ◽  
Delivery Times ◽  
Mip Model ◽  
Total Inventory

This study investigates replenishment planning in the case of discrete delivery time, where demand is seasonal. The study is motivated by a case study of a soft drinks company in Germany, where data concerning demand are obtained for a whole year. The investigation focused on one type of apple juice that experiences a peak in demand during the summer. The lot-sizing problem reduces the ordering and the total inventory holding costs using a mixed-integer programming (MIP) model. Both the lot size and cycle time are variable over the planning horizon. To obtain results faster, a dynamic programming (DP) model was developed, and run using R software. The model was run every week to update the plan according to the current inventory size. The DP model was run on a personal computer 35 times to represent dynamic planning. The CPU time was only a few seconds. Results showed that initial planning is difficult to follow, especially after week 30, and the service level was only 92%. Dynamic planning reached a higher service level of 100%. This study is the first to investigate discrete delivery times, opening the door for further investigations in the future in other industries.

scholarly journals Production Planning Problem of a Two-Level Supply Chain with Production-Time-Dependent Products

2021 ◽  
Vol 11 (20) ◽  
pp. 9687
Author(s):  
Jun-Hee Han ◽  
Ju-Yong Lee ◽  
Bongjoo Jeong
Keyword(s):  
Supply Chain ◽  
Production Planning ◽  
Programming Model ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Planning Problem ◽  
Manufacturing Plant ◽  
Production Lines ◽  
Multiple Production ◽  
Production Planning Problem

This study considers a production planning problem with a two-level supply chain consisting of multiple suppliers and a manufacturing plant. Each supplier that consists of multiple production lines can produce several types of semi-finished products, and the manufacturing plant produces the finished products using the semi-finished products from the suppliers to meet dynamic demands. In the suppliers, different types of semi-finished products can be produced in the same batch, and products in the same batch can only be started simultaneously (at the same time) even if they complete at different times. The purpose of this study is to determine the selection of suppliers and their production lines for the production of semi-finished products for each period of a given planning horizon, and the objective is to minimize total costs associated with the supply chain during the whole planning horizon. To solve this problem, we suggest a mixed integer programming model and a heuristic algorithm. To verify performance of the algorithm, a series of tests are conducted on a number of instances, and the results are presented.

scholarly journals Modelling and Solving Assembly Line Worker Assignment and Balancing Problem with Sequence-Dependent Setup Times

2021 ◽  
Author(s):  
Hamid YILMAZ
Keyword(s):  
Assembly Line ◽  
Programming Model ◽  
Setup Times ◽  
Mixed Integer ◽  
Benchmark Problems ◽  
Worker Assignment ◽  
Sequence Dependent ◽  
Sequence Dependent Setup ◽  
Dependent Setup Times ◽  
Sequence Dependent Setup Times

Abstract Assembly lines appear with various differentiations in order to better include the disabled in the labor market and to increase production efficiency. In this way, the optimal workforce assignment problem that emerges heterogeneously is called assembly line worker assignment and balancing problem (ALWABP). This paper addresses the ALWABP where the simple version is enriched by considering sequence-dependent setup times between tasks. A mixed integer linear programming model is presented and a simulated annealing algorithm is developed such as an NP-hard problem. In order to test the proposed solutions, 640 benchmark problems in the literature were combined and used. The solutions obtained through using the proposed algorithm are compared with the mixed integer programming model on the small-size test problems. Experimental results show that the proposed algorithm is more effective and robust for a large set of benchmark problems.

Sign in / Sign up

Export Citation Format

Share Document