Stochastic Dual Dynamic integer Programming for a multi-echelon lot-sizing problem with remanufacturing and lost sales

2019 ◽  
Author(s):  
Franco Quezada ◽  
Celine Gicquel ◽  
Safia Kedad-Sidhoum
Keyword(s):  
Integer Programming ◽  
Lot Sizing ◽  
Lost Sales ◽  
Lot Sizing Problem

Heuristics for disassembly lot sizing problem with lost sales

2020 ◽  
Vol 38 (4) ◽  
pp. 449
Author(s):  
Mustapha Hrouga ◽  
Matthieu Godichaud ◽  
Lionel Amodeo
Keyword(s):  
Lot Sizing ◽  
Lost Sales ◽  
Lot Sizing Problem

scholarly journals A Heuristic Approach for Determining Lot Sizes and Schedules Using Power-of-Two Policy

2007 ◽  
Vol 2007 ◽  
pp. 1-18
Author(s):  
Esra Ekinci ◽  
Arslan M. Ornek
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Flow Shop ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Binary Integer Programming ◽  
Multistage Manufacturing ◽  
Lot Sizing Problem ◽  
Lot Sizes

We consider the problem of determining realistic and easy-to-schedule lot sizes in a multiproduct, multistage manufacturing environment. We concentrate on a specific type of production, namely, flow shop type production. The model developed consists of two parts, lot sizing problem and scheduling problem. In lot sizing problem, we employ binary integer programming and determine reorder intervals for each product using power-of-two policy. In the second part, using the results obtained of the lot sizing problem, we employ mixed integer programming to determine schedules for a multiproduct, multistage case with multiple machines in each stage. Finally, we provide a numerical example and compare the results with similar methods found in practice.

scholarly journals Modelling Multi-Period Set-up Times in the Proportional Lot-Sizing Problem

2009 ◽  
Vol 3 (2) ◽  
pp. 15-35 ◽  
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Lot Sizing ◽  
Programming Models ◽  
Mixed Integer ◽  
Lot Sizing Problem ◽  
Set Up

This paper presents new mixed integer programming models for the Proportional Lot-Sizing Problem (PLSP) with set-up times longer than a period. Proposed models explicitly calculate the distribution of times amongst products in periods with a changeover and determine a final period for every set-up operation. Presented results prove that the proposed models are easier to solve using standard MIP methods than already known models.

scholarly journals Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty

2021 ◽  
Author(s):  
Franco Quezada ◽  
Céline Gicquel ◽  
Safia Kedad-Sidhoum
Keyword(s):  
Integer Programming ◽  
Production Planning ◽  
Optimization Problem ◽  
Lot Sizing ◽  
Computational Experiments ◽  
Scenario Tree ◽  
Partial Decomposition ◽  
Large Size ◽  
Lot Sizing Problem ◽  
Planning Problems

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders’ cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems.

Heuristics for disassembly lot sizing problem with lost sales

2020 ◽  
Vol 38 (4) ◽  
pp. 449
Author(s):  
Mustapha Hrouga ◽  
Matthieu Godichaud ◽  
Lionel Amodeo
Keyword(s):  
Lot Sizing ◽  
Lost Sales ◽  
Lot Sizing Problem
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