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.

Tactical Production and Lot Size Planning with Lifetime Constraints: A Comparison of Model Formulations

2017 ◽  
Vol 34 (05) ◽  
pp. 1750019 ◽  
Author(s):  
Andrea Raiconi ◽  
Julia Pahl ◽  
Monica Gentili ◽  
Stefan Voß ◽  
Raffaele Cerulli
Keyword(s):  
Finite Number ◽  
Lot Sizing ◽  
Classical Problem ◽  
Lot Size ◽  
Experimental Phase ◽  
Classical Version ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
Lot Sizes ◽  
Production Resources

In this work, we face a variant of the capacitated lot sizing problem. This is a classical problem addressing the issue of aggregating lot sizes for a finite number of discrete periodic demands that need to be satisfied, thus setting up production resources and eventually creating inventories, while minimizing the overall cost. In the proposed variant we take into account lifetime constraints, which model products with maximum fixed shelflives due to several possible reasons, including regulations or technical obsolescence. We propose four formulations, derived from the literature on the classical version of the problem and adapted to the proposed variant. An extensive experimental phase on two datasets from the literature is used to test and compare the performance of the proposed formulations.

MINIMALISASI BIAYA SIMPAN DAN BIAYA SETUP PADA MULTIPLE PRODUK: SIMULASI DENGAN CAPACITATED LOT SIZING PROBLEM

2019 ◽  
Vol 4 (2) ◽  
pp. 205-214
Author(s):  
Erika Fatma
Keyword(s):  
Production Cost ◽  
Lot Sizing ◽  
Setup Time ◽  
Production Costs ◽  
Total Production ◽  
Product Cycle ◽  
Lot Size ◽  
Setup Costs ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing

Lot sizing problem in production planning aims to optimize production costs (processing, setup and holding cost) by fulfilling demand and resources capacity costraint. The Capacitated Lot sizing Problem (CLSP) model aims to balance the setup costs and inventory costs to obtain optimal total costs. The object of this study was a plastic component manufacturing company. This study use CLSP model, considering process costs, holding costs and setup costs, by calculating product cycle and setup time. The constraint of this model is the production time capacity and the storage capacity of the finished product. CLSP can reduce the total production cost by 4.05% and can reduce setup time by 46.75%.  Keyword: Lot size, CLSP, Total production cost.

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.

Production Planning Considering Transfer Lot Size

2010 ◽  
Vol 44-47 ◽  
pp. 552-556
Author(s):  
Zhi Cong Zhang ◽  
Kai Shun Hu ◽  
Hui Yu Huang ◽  
Shuai Li
Keyword(s):  
Production Planning ◽  
Performance Measures ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Production Plan ◽  
Lot Size ◽  
Planning And Scheduling ◽  
Production Planning And Scheduling ◽  
Lot Sizing Problem ◽  
Plan Change

Traditional methods conduct production planning and scheduling separately and solve transfer lot sizing problem between these two steps. Unfortunately, this may result in infeasibility in planning and scheduling. We take into account transfer lot size in production planning to obtain the consistency and to eliminate the gap between planning and real production. We present the detailed Transfer Lot-Based Model with mixed integer programming. Experiments show that performance measures of a production plan change remarkably with increasing of transfer lot size.

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 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.

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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