A closed-form solution for the distribution free continuous review integrated inventory model

Gutgutia, Anuraag; Jha, J.K.

doi:10.1007/s12351-016-0258-5

Cited by 17 publications

(6 citation statements)

References 35 publications

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“…For this reason, the most common approach in practical environments is to find the optimal parameters of the inventory system that guarantee the achievement of a target service level. In addition, this approach is more attractive to practitioners as it is easier for them to interpret the fill rate they strive to offer their customers [ 26 ]. However, to implement the service approach it is first required to have appropriate expression to compute accurately the service level because small errors in the calculation of the service level might have an important impact on the determination of optimal parameters [ 27 ].…”

Section: Resultsmentioning

confidence: 99%

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context

2022

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In the continuous review reorder point, base-stock (s, S) policy, the replenishment order is launched when the inventory position reaches the reorder point, s. It is commonly assumed that the inventory position is exactly equal to the reorder point at the moment the order is launched, when actually it could be lower at that moment. This implies neglecting the possible undershoots at the reorder point, which has a direct impact on the calculation of the expected shortages per replenishment cycle. This article presents a method for an exact calculation of the fill rate (fraction of demand that is immediately satisfied from shelf) which takes explicit account of the existence of undershoots and is applicable to any discrete demand distribution function in a context of lost sales. This method is based on the determination of the stock probability vector at the moment the replenishment order is launched. Furthermore, neglecting the undershoots is shown to lead to an overestimation of the fill rate, particularly when we move farther away from the unitary demand assumption. From a practical point of view, this behaviour involves underestimating the base-stock level, S, when a target fill rate is set for its determination. The method proposed in this paper overcomes these shortcomings.

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Section: Resultsmentioning

confidence: 99%

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context

2022

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“…Following Yano (1985), there is a stream of literature on distribution‐free min–max, continuous‐review integrated inventory modeling approaches (e.g., Gutgutia & Jha, 2018; Moon et al., 2014; Tajbakhsh, 2010). The distribution‐free nature relies on the assumption that the distribution of LTD can be constructed using a mixture model where the LTD mixture of the component distributions of lead time and demand has a finite mean and variance.…”

Section: Literature Reviewmentioning

confidence: 99%

A nonparametric approach for setting safety stock levels

Saldanha

Price

Thomas

2023

Production and Operations Management

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In practice, lead time demand (LTD) can be skewed, multi-modal or highly variable, and these factors compromise the validity of typical approaches used for setting safety stock levels. Motivated by encountering this problem at our industry partner, we develop an approach for setting safety stock levels using the bootstrap, a widely used statistical procedure. Existing bootstrap approaches for inventory management either operate directly on observed LTD or assume deterministic lead times, permitting direct application of the bootstrap approach for univariate quantile estimation. As LTD is a convolution of multiple random demands over a random lead time, a multivariate bootstrap approach is required. As we demonstrate, when lead times are stochastic, our multivariate approach provides improved safety stock estimates. We develop a multivariate central limit theorem for the bootstrap mean and bootstrap quantile-components of the safety stock calculation-highlighting why the generalization of these bootstrap methods is critical for inventory management. These results provide a theoretical underpinning for the bootstrap estimator of safety stock and permit the construction of confidence intervals for safety stock estimates, allowing decision makers to understand the reliability with which the desired service level will be achieved. Building on our theoretical results, and supported by numerical experiments, we provide insights on the behavior of the bootstrap for various LTD distributions, which our results demonstrate are critical when employing the bootstrap method. Implementation of our approach with our industry partner resulted in an inventory investment reduction of $1.17 million combined with an overall increase in service level. Our approach is general and can be implemented without modification in other settings.

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“…Braglia et al (2017) studied the periodic-review joint-replenishment problem considering backorders-lost sales mixtures, controllable major ordering cost and lead times. Gutgutia and Jha (2018) built a continuous review integrated inventory model. Raza (2018) used a revenue-sharing contract to coordinate a supply chain with corporate social responsibility.…”

Section: Literature Reviewmentioning

confidence: 99%

Joint pricing and ordering decisions for a loss-averse retailer with quantity-oriented reference point effect and demand uncertainty: a distribution-free approach

Qiu

Sun

2021

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PurposeThis work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.Design/methodology/approachThe demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.FindingsThe proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.Practical implicationsThe results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.Originality/valueThe demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.

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A closed-form solution for the distribution free continuous review integrated inventory model

Cited by 17 publications

References 35 publications

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context

A nonparametric approach for setting safety stock levels

Joint pricing and ordering decisions for a loss-averse retailer with quantity-oriented reference point effect and demand uncertainty: a distribution-free approach

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