The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard

Cohen-Hillel, Tamar; Yedidsion, Liron

doi:10.1287/moor.2017.0904

Cited by 15 publications

(9 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this proof, we take advantage of the instance of the DPJRP used in Cohen-Hillel and Yedidsion (2018) with slight changes in the instance parameters and without the integrality constraint that defines the DPJRP. We show that the instance we construct for the CPJRP is as hard as the 3SAT instance from which Cohen-Hillel and Yedidsion (2018) constructed their instance, and thus, Strongly N P-hard.…”

Section: N P-hardness Proofmentioning

confidence: 96%

“…The N P-Hardness proof of the CPJRP is based on the N P-Hardness proof of the DPJRP in Cohen-Hillel and Yedidsion (2018). In this proof, we take advantage of the instance of the DPJRP used in Cohen-Hillel and Yedidsion (2018) with slight changes in the instance parameters and without the integrality constraint that defines the DPJRP.…”

Section: N P-hardness Proofmentioning

confidence: 99%

“…Before we continue with the N P-hardness proof, we would like to show a schematic sketch of the proof in Cohen-Hillel and Yedidsion (2018), as in this paper we meticulously show that each step in this proof holds in the continuous environment for the instance we built.…”

Section: N P-hardness Proofmentioning

confidence: 99%

“…In this section, we explain the steps taken in Cohen-Hillel and Yedidsion (2018). For each step we explain the adjustments required for a continuous environment.…”

Section: Proof Sketchmentioning

confidence: 99%

See 3 more Smart Citations

The Continuous Joint Replenishment Problem is Strongly NP-Hard

Tuisov¹,

Yedidsion²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The Continuous Periodic Joint Replenishment Problem (CPJRP) has been one of the core and most studied problems in supply chain management for the last half a century. Nonetheless, despite the vast effort put into studying the problem, its complexity has eluded researchers for years. Although the CPJRP has one of the tighter constant approximation ratio of 1.02, a polynomial optimal solution to it was never found.Recently, the discrete version of this problem was finally proved to be N P-hard. In this paper, we extend this result and finaly prove that the CPJRP problem is also strongly N P-hard.

show abstract

Section: N P-hardness Proofmentioning

confidence: 96%

Section: N P-hardness Proofmentioning

confidence: 99%

Section: N P-hardness Proofmentioning

confidence: 99%

“…In this section, we explain the steps taken in Cohen-Hillel and Yedidsion (2018). For each step we explain the adjustments required for a continuous environment.…”

Section: Proof Sketchmentioning

confidence: 99%

See 2 more Smart Citations

The Continuous Joint Replenishment Problem is Strongly NP-Hard

Tuisov¹,

Yedidsion²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…(1997). Cohen‐Hillel and Yedidsion (2018) also proved that the periodic joint replenishment problem is strongly NP‐hard. Therefore, heuristics are mainly used to handle such problems.…”

Section: Introductionmentioning

confidence: 99%

Efficient methods for stochastic joint replenishment and delivery problem

Wang

Wei

2020

Int Trans Operational Res

View full text Add to dashboard Cite

In this paper, we consider the joint replenishment and delivery scheduling of the one‐warehouse, n$n$‐retailer system with stochastic demand. In this distribution system, items are first jointly replenished and therefore can share a major ordering cost. Then a coordinated delivery scheduling is adopted to arrange the delivery plan. The problem is formulated as a mixed integer nonlinear program. Subsequently, we introduce two algorithms to handle this complex problem: a Lipschitz optimization method and a modified RAND heuristic. Numerical experiments show that the proposed methods are quite efficient. Sensitivity analysis also shows some interesting findings in terms of management.

show abstract