Approximation Algorithms and Hardness Results for the Joint Replenishment Problem with Constant Demands

Schulz, Andreas S.; Telha, Claudio

doi:10.1007/978-3-642-23719-5_53

Cited by 14 publications

(10 citation statements)

References 17 publications

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“…Although such a binding contract may decrease the cost of the joint replenishment significantly, it usually limits the flexibility of choosing the joint replenishment cycles. Schulz and Telha (2011) presented a polynomial time approximation scheme (PTAS) for the PJRP case.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the finite time heuristics assume variable demands and run-in time Ω (T ) (Levi et al 2006, Joneja 1990). Schulz and Telha (2011) presented a polynomial-time 9/8-approximation algorithm for the JRP with dynamic policies and finite horizon. As the time horizon T increases, the ratio converges to 9/8.…”

Section: Introductionmentioning

confidence: 99%

“…As the time horizon T increases, the ratio converges to 9/8. Schulz and Telha (2011) also presented an FPTAS for the Strict PJRP case with no fixed base and a finite time horizon.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Continuous Joint Replenishment Problem is Strongly NP-Hard

Tuisov¹,

Yedidsion²

2020

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Continuous Joint Replenishment Problem is Strongly NP-Hard

Tuisov¹,

Yedidsion²

2020

Preprint

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“…Under joint replenishment policy (JRP), Porras and Dekker (2008) provided a complete analysis and presented a new inventory model over JRP when a correction is made for the empty replenishment and Hong and Kim (2009) gave a genetic algorithm for JRP and devised an unbiased estimator to find out the exact cost. In continuation of this, Schulz and Telha (2011) theoretically showed that the JRP with constant demands may have no polynomial-time algorithm. Taleizadeh et al (2015) gave Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor-managed inventory system with deteriorating items.…”

Section: Introductionmentioning

confidence: 99%

Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution

Mishra

2017

J Ind Eng Int

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In this paper we develop an inventory model, to determine the optimal ordering quantities, for a set of two substitutable deteriorating items. In this inventory model the inventory level of both items depleted due to demands and deterioration and when an item is out of stock, its demands are partially fulfilled by the other item and all unsatisfied demand is lost. Each substituted item incurs a cost of substitution and the demands and deterioration is considered to be deterministic and constant. Items are order jointly in each ordering cycle, to take the advantages of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. We provide an extensive numerical and sensitivity analysis to illustrate the effect of different parameter on the model. The key observation on the basis of numerical analysis, there is substantial improvement in the optimal total cost of the inventory model with substitution over without substitution.

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“…Hong and Kim (2009) later developed a genetic algorithm for JRP and devised an unbiased estimator to find out the exact cost. Schulz and Telha (2011) theoretically showed that it might not be possible to devise a polynomial-time algorithm to optimize a JRP with constant demand. Taleizadeh et al (2015) developed a model that jointly optimizes price, replenishment frequency, and replenishment cycle and production rate in a vendor-managed inventory system with deteriorating items.…”

mentioning

confidence: 99%

An EOQ model for multiple products with varying degrees of substitutability

et al. 2019

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In this paper, the authors present an EOQ model with substitutions between products and a dynamic inventory replenishment policy. Their key assumption is that many products in the market are substitutable at different levels, and that, in most cases, a customer who discovers that a desired product is unavailable will choose to consume a product with similar attributes or functionality, rather than not purchase at all. Therefore, given a firm that stocks multiple substitutable products, the authors assume that a stock out of one product has a direct impact on other products' demand. The main purpose of our model is to enable inventory managers to develop ordering policies that ensures that, in the event that a specific product runs out and cannot be replenished due to unforeseen circumstances, the consequent increase in demand for related products will not cause further stock out incidents. To this end, the authors introduce a dependency factor, a variable that indicates the level of dependency, or correlation, between one product and another. The dependencies among the various products offered by the firm are embedded into the EOQ formula and assumptions, enabling managers to update their ordering schedules as needed. This approach has the potential to generate more practical and realistic purchasing and inventory optimization policies. JEL C44 C51 C61 L60

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Approximation Algorithms and Hardness Results for the Joint Replenishment Problem with Constant Demands

Cited by 14 publications

References 17 publications

The Continuous Joint Replenishment Problem is Strongly NP-Hard

The Continuous Joint Replenishment Problem is Strongly NP-Hard

Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution

An EOQ model for multiple products with varying degrees of substitutability

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