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 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 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

Sign in / Sign up

Export Citation Format

Share Document