Single Item Lot Sizing Models with Bounded Inventory and Remanufacturing

2010 ◽  
Vol 102-104 ◽  
pp. 791-795
Author(s):  
Neng Min Wang ◽  
Zheng Wen He ◽  
Qiu Shuang Zhang ◽  
Lin Yan Sun
Keyword(s):  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Production Capacity ◽  
Planning Horizon ◽  
Programming Algorithm ◽  
Single Item ◽  
Time Dynamic ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing ◽  
Finite Planning Horizon

Dynamic lot sizing problem for systems with bounded inventory and remanufacturing was addressed. The demand and return amounts are deterministic over the finite planning horizon. Demands can be satisfied by manufactured new items, but also by remanufactured returned items. In production planning, there can be situations where the ability to meet customer demands is constrained by inventory capacity rather than production capacity. Two different limited inventory capacities are considered; there is either bounded serviceables inventory or bounded returns inventory. For the two inventory case, we present exact, polynomial time dynamic programming algorithm based on the idea of Teunter R, et al. (2006).

Study on the Bounded Inventory Model with Returning Items and Disposals

2010 ◽  
Vol 102-104 ◽  
pp. 920-925
Author(s):  
Neng Min Wang ◽  
Zheng Wen He ◽  
Lin Yan Sun
Keyword(s):  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Planning Horizon ◽  
Cost Functions ◽  
Programming Algorithm ◽  
Inventory Level ◽  
Lot Sizing Problem ◽  
Production Inventory ◽  
Dynamic Lot Sizing ◽  
Inventory Holding

This paper addresses a dynamic lot sizing problem with mixed returning items and disposals and bounded inventory. The returning items mean that returns are in good enough condition to re-enter the inventory supply stream. The producing, the holding, backlogging and disposals cost functions are concave cost functions. Furthermore, backlogging level and inventory level at each period is limited. The goal is to minimize the total cost of production, inventory holding/backlogging and disposal. A dynamic programming algorithm with complexity O(T3) is developed to solve this model, where T is the length of the planning horizon.

scholarly journals Lot-sizing problem with several production centers

2005 ◽  
Vol 25 (3) ◽  
pp. 479-492 ◽  
Author(s):  
Franklina Maria Bragion de Toledo ◽  
André Luís Shiguemoto
Keyword(s):  
Dynamic Programming ◽  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Production Capacity ◽  
Efficient Implementation ◽  
Programming Algorithm ◽  
Future Research ◽  
Production Environment ◽  
Lot Sizing Problem ◽  
Forward Dynamic Programming

In this paper, a case study is carried out concerning the lot-sizing problem involving a single item production planning in several production centers that do not present capacity constraints. Demand can be met with backlogging or not. This problem results from simplifying practical problems, such as the material requirement planning (MRP) system and also lot-sizing problems with multiple items and limited production capacity. First we propose an efficient implementation of a forward dynamic programming algorithm for problems with one single production center. Although this does not reduce its complexity, it has shown to be rather effective, according to computational tests. Next, we studied the problem with a production environment composed of several production centers. For this problem two algorithms are implemented, the first one is an extension of the dynamic programming algorithm for one production center and the second one is an efficient implementation of the first algorithm. Their efficiency are shown by computational testing of the algorithms and proposals for future research are presented.

scholarly journals Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 689
Author(s):  
José M. Gutiérrez ◽  
Beatriz Abdul-Jalbar ◽  
Joaquín Sicilia ◽  
Inmaculada Rodríguez-Martín
Keyword(s):  
Dynamic Programming ◽  
Storage Capacity ◽  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Planning Horizon ◽  
Cost Structure ◽  
Programming Algorithm ◽  
Lot Sizing Problem ◽  
Geometric Technique ◽  
Searching Method

Efficient algorithms for the economic lot-sizing problem with storage capacity are proposed. On the one hand, for the cost structure consisting of general linear holding and ordering costs and fixed setup costs, an dynamic programming algorithm is introduced, where is the number of time periods. The new approach induces an accurate partition of the planning horizon, discarding most of the infeasible solutions. Moreover, although there are several algorithms based on dynamic programming in the literature also running in quadratic time, even considering more general cost structures and assumptions, the new solution uses a geometric technique to speed up the algorithm for a class of subproblems generated by dynamic programming, which can now be solved in linearithmic time. To be precise, the computational results show that the average occurrence percentage of this class of subproblems ranges between 13% and 45%, depending on both the total number of periods and the percentage of storage capacity availability. Furthermore, this percentage significantly increases from 13% to 35% as the capacity availability decreases. This reveals that the usage of the geometric technique is predominant under restrictive storage capacities. Specifically, when the percentage of capacity availability is below 50%, the average running times are on average 100 times faster than those when this percentage is above 50%. On the other hand, an on-line array searching method in Monge arrays can be used when the costs are non-speculative costs.

scholarly journals Economic lot-sizing problem with remanufacturing option: complexity and algorithms

2021 ◽  
Author(s):  
Ashwin Arulselvan ◽  
Kerem Akartunalı ◽  
Wilco van den Heuvel
Keyword(s):  
Polynomial Time ◽  
Lot Sizing ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Item ◽  
Inventory Costs ◽  
Time Period ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing ◽  
The Cost

AbstractIn a single item dynamic lot-sizing problem, we are given a time horizon and demand for a single item in every time period. The problem seeks a solution that determines how much to produce and carry at each time period, so that we will incur the least amount of production and inventory cost. When the remanufacturing option is included, the input comprises of number of returned products at each time period that can be potentially remanufactured to satisfy the demands, where remanufacturing and inventory costs are applicable. For this problem, we first show that it cannot have a fully polynomial time approximation scheme. We then provide a polynomial time algorithm, when we make certain realistic assumptions on the cost structure.

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