8 research outputs found
Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"
In a recent paper Gutiérrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general
Improved Algorithms for a Lot-Sizing Problem with Inventory Bounds and Backlogging
This paper considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging
is allowed. For general concave production and inventory costs, we present an O(T2) dynamic
programming algorithm where T is the length of the planning horizon. Furthermore, for
fixed-charge and nonspeculative costs, we provide O(Tlog T) and O(T) algorithms, respectively.
This paper therefore concludes that the time complexity to solve the bounded inventory lot-sizing
problem with backlogging is the same as the complexity to solve the uncapacitated lot-sizing
problem for the commonly used cost structure
Economic Lot-Sizing Problem with Bounded Inventory and Lost-Sales
In this paper we consider an economic lot-sizing problem with bounded inventory and lost-sales. Different structural properties are characterized based on the system parameters such as production and inventory costs, selling prices, and storage capacities. Using these properties and the results on the lot-sizing problems with bounded inventory, we present improved and new algorithms for the problem. Specifically, we provide algorithms for the general lot-sizing problem with bounded inventory and lost-sales, the lot-sizing problem with nonincreasing selling prices and the problem with only lost-sales
An efficient approach for solving the lot-sizing problem with time-varying storage capacities
We address the dynamic lot size problem assuming time-varying storage capacities. The planning horizon is divided into T periods and stockouts are not allowed. Moreover, for each period, we consider a setup cost, a holding unit cost and a production/ordering unit cost, which can vary through the planning horizon. Although this model can be solved using O(T3) algorithms already introduced in the specialized literature, we show that under this cost structure an optimal solution can be obtained in O(T log T) time. In addition, we show that when production/ordering unit costs are assumed to be constant (i.e., the Wagner-Whitin case), there exists an optimal plan satisfying the Zero Inventory Ordering (ZIO) property.
A review of discrete-time optimization models for tactical production planning
This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation
(MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty
Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).DÃaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521
Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"
In a recent paper Gutièrrez et al. [1] show that the lot-sizing problem with inventory bounds can be solved in time. In this note we show that their algorithm does not lead to an optimal solution in general.Inventory Lot-sizing Inventory bounds