scholarly journals Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 785
Author(s):  
Jangha Kang
Keyword(s):  
Lot Sizing ◽  
Building Blocks ◽  
Mixed Integer ◽  
Efficient Production ◽  
Arbitrary Length ◽  
Sequence Dependent ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
Sequence Dependent Setup ◽  
Setup Variables

Since setup operations have significant impacts on production environments, the capacitated lot-sizing problem considering arbitrary length of setup times helps to develop flexible and efficient production plans. This study discusses a capacitated lot-sizing problem with sequence-dependent setup, setup carryover and setup crossover. A new mixed integer programming formulation is proposed. The formulation is based on three building blocks: the facility location extended formulation; the setup variables with indices for the starting and the completion time periods; and exponential number of generalized subtour elimination constraints (GSECs). A separation routine is adopted to generate the violated GSECs. Computational experiments show that the proposed formulation outperforms models from the literature.

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.

scholarly journals A multistage stochastic lot-sizing problem with cancellation and postponement under uncertain demands

2021 ◽  
Author(s):  
Carlos E Testuri ◽  
Héctor Cancela ◽  
Víctor M. Albornoz
Keyword(s):  
Information Structure ◽  
Lot Sizing ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Uncertain Demand ◽  
Programming Approach ◽  
Lead Times ◽  
Multi Stage ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing

A multistage stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed.  The problem determines the procurement of a product under uncertain demand at minimal expected cost during a time horizon.  The supply of the product is made through the purchase of optional distinguishable orders of fixed size with delivery time.  Due to the unveiling of uncertainty over time it is possible to make cancellation and postponement corrective decisions on order procurement.  These decisions involve costs and times of implementation.  A model of the problem is formulated as an extension of a discrete capacitated lot-sizing problem under uncertain demand and lead times through a multi-stage stochastic mixed-integer linear programming approach.  Valid inequalities are generated, based on a conventional inequalities approach, to tighten the model formulation.  Experiments are performed for several problem instances with different uncertainty information structure.  Their results allow to conclude that the incorporation of a subset of the generated inequalities favor the model solution.

scholarly journals A fix-and-optimize heuristic for the capacitated multi-item stochastic lot-sizing problem

2020 ◽  
Vol 11 (1) ◽  
pp. 41-51
Author(s):  
M. Edib Gurkan ◽  
Huseyin Tunc
Keyword(s):  
Lot Sizing ◽  
Numerical Study ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Solution Approach ◽  
Decomposition Scheme ◽  
Lot Sizing Problem ◽  
Single Production ◽  
Capacitated Lot Sizing ◽  
Cost Efficient

This study addresses the stochastic multi-item capacitated lot-sizing problem. Here, it is assumed that all items are produced on a single production resource and unmet demands are backlogged. The literature shows that the deterministic version of this problem is NP-Hard. We consider the case where period demands are time-varying random variables. The objective is to determine the minimum expected cost production plan so as to meet stochastic period demands over the planning horizon. We extend the mixed integer programming formulation introduced in the literature to capture the problem under consideration. Further, we propose a fix-and-optimize heuristic building on an item-period oriented decomposition scheme. We then conduct a numerical study to evaluate the performance of the proposed heuristic as compared to the heuristic introduced by Tempelmeier and Hilger [16]. The results clearly show that the proposed fix-and-optimize heuristic arises as both cost-efficient and time-efficient solution approach as compared to the benchmark heuristic.

scholarly journals A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 878 ◽  
Author(s):  
Yajaira Cardona-Valdés ◽  
Samuel Nucamendi-Guillén ◽  
Rodrigo E. Peimbert-García ◽  
Gustavo Macedo-Barragán ◽  
Eduardo Díaz-Medina
Keyword(s):  
Lot Sizing ◽  
Mixed Integer ◽  
Lot Size ◽  
Penalty Cost ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
Batch Ordering ◽  
New Formulation ◽  
Production Resources

This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

A comparison of mixed integer programming formulations of the capacitated lot-sizing problem

2017 ◽  
Vol 56 (23) ◽  
pp. 7064-7084 ◽  
Author(s):  
Hakan F. Karagul ◽  
Donald P. Warsing ◽  
Thom J. Hodgson ◽  
Maaz S. Kapadia ◽  
Reha Uzsoy
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing
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