Technical Note
A note on the Optimal Periodic Pattern (OPP) algorithm for the system in which buyers periodically order from a vendor

https://doi.org/10.1016/j.cie.2017.10.031Get rights and content

Highlights

  • We revisit research contributed by Afzalabadi et al. (2016).

  • For the algorithm two counterexamples with appropriate comments are presented.

  • We provide conditions for optimal ordering policy in the periodic demand case.

Abstract

In this study, we revisit research contributed by Afzalabadi et al. (2016), where a lot size problem for discrete periodic demand case was considered. Our note indicates incorrectness of the main thesis that the OPP algorithm finds the optimal solution in a finite number of steps. Numerical counterexamples with appropriate comments are presented. We also provide a reformulation of the model and proper conditions for optimality.

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 (A,h) and vendor’s τ-periodical demand sequence D=(D0,D1,) we

References (2)

Cited by (1)

  • Heuristics for a periodic-review policy in a two-echelon inventory problem with seasonal demand

    2019, Computers and Industrial Engineering
    Citation 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.

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