Technical NoteA note on the Optimal Periodic Pattern (OPP) algorithm for the system in which buyers periodically order from a vendor
Section snippets
Introduction and preliminaries
Although the shortest path problems can be solved very efficiently, a large number of similar heuristics have been developed for more specific models. In the note we are going to discuss Afzalabadi et al. (2016) model, where the authors investigate inventory control decisions in a two echelon supply chain consisting of one vendor and N retailers. For the sake of clarity and to make the analysis tractable, we first briefly review their work.
The network presentation
It is convenient to use a network framework for optimization problems in the model presented above. A network means a directed graph or multigraph with a cost function on its arcs. The sum of values on arcs determines costs on paths. We call a path cycle if it starts and terminates in the same node. In this framework an optimal ordering pattern is determined by a cheapest path in the network.
For given cost parameters of the model and vendor’s -periodical demand sequence we
References (2)
- et al.
Vendor’s optimal inventory policy with dynamic and discrete demands in an infinite time horizon
Computers and Industrial Engineering
(2016) Strong turnpike policies in the single-item capacitated lot-sizing problem with periodical dynamic parameter
Naval Research Logistics
(1997)
Cited by (1)
Heuristics for a periodic-review policy in a two-echelon inventory problem with seasonal demand
2019, Computers and Industrial EngineeringCitation Excerpt :Many researchers have studied a multi-echelon system with a deterministic demand, called the multi-echelon dynamic lot sizing problem. Examples of techniques used to solve this problem are mixed-integer programming models, Lagrangian relaxation and a decomposition strategy (Afzalabadi, Haji, & Haji, 2016; Bookbinder & Tan, 1988; Bylka & Krupa, 2018; Diaby & Martel, 1993; Tarim & Smith, 2008; Zangwill, 1969). Various methods have been used to deal with non-stationary demand in both trend and seasonal patterns, which were based on the same concept of dividing non-stationary demand into many phases of stationary demand.