arXiv subjects

Katsunobu Sasanuma

Publications and source records attributed to Katsunobu Sasanuma.

5 recordsLinked to original sources

arXiv2021

An opaque selling scheme to reduce shortage and wastage in perishable inventory systems

Effective management of perishable inventory systems is often strewn with challenges, especially when a strong trade-off relationship exists between shortage and wastage of perishables: A smaller inventory increases the chance to lose sales (leading to higher expected shortage cost), while a larger inventory increases the chance to waste perishables (leading to higher expected wastage cost). The root cause of this strong trade-off relationship is high product demand variability. To mitigate the issue and reduce the cost of operating perishable inventory systems, some grocery stores utilize an opaque selling scheme: selling an anonymous product whose brand or exact specification is shielded from customers at the time of sale. The use of opaque products has now become a popular means to reduce shortage/wastage at grocery stores. However, there has been little discussion of the effectiveness of opaque schemes applied to perishable inventory systems. In this paper, we propose an opaque scheme based on the balancing policy on demand, which tries to average out orders for products. We confirm both analytically and numerically that this opaque scheme effectively reduces product demand variability, thereby reducing both shortage and wastage for perishable inventory systems under a base-stock policy. We also present an analytical formula that reveals insights into the opaque scheme: The ratio between the opaque proportion and the coefficient of variation of product demands plays a key role to determine the effectiveness of our opaque scheme. Furthermore, we provide a rule of thumb to find the threshold opaque scheme parameters needed to achieve the maximum total cost savings for perishable inventory systems. We hope that many retailers selling perishables (e.g., fresh produce and baked goods) find the opaque scheme useful, implement it, and contribute to the reduction of the food wastage.

math.OC↗

arXiv2021

Controlling arrival and service rates to reduce sensitivity of queueing systems with customer abandonment

The Erlang A model--an M/M/s queue with exponential abandonment--is often used to represent a service system with impatient customers. For this system, the popular square-root staffing rule determines the necessary staffing level to achieve the desirable QED (quality-and-efficiency-driven) service regime; however, the rule also implies that properties of large systems are highly sensitive to parameters. We reveal that the origin of this high sensitivity is due to the operation of large systems at a point of singularity in a phase diagram of service regimes. We can avoid this singularity by implementing a congestion-based control (CBC) scheme--a scheme that allows the system to change its arrival and service rates under congestion. We analyze a modified Erlang A model under the CBC scheme using a Markov chain decomposition method, derive non-asymptotic and asymptotic normal representations of performance indicators, and confirm that the CBC scheme makes large systems less sensitive than the original Erlang A model.

math.PR↗

arXiv2021

A Marginal Analysis Framework to Incorporate the Externality Effect of Ordering Perishables

Finding the optimal policy for multi-period perishable inventory systems requires solving computationally-expensive stochastic dynamic programs (DP). To avoid the difficulty of solving DP models, we propose a framework that uses an externality term to capture the long-term impact of ordering decisions on the average cost over an infinite horizon. By approximating the externality term, we yield a tractable approximate optimality condition, which is solved through standard marginal analysis. The resulted policy is near-optimal in long-run average cost and ordering decisions.

math.OC↗

arXiv2021

Markov Chain Decomposition Based On Total Expectation Theorem

A divide-and-conquer approach to analyzing Markov chains (MCs) is not utilized as widely as it could be, despite its potential benefits. One primary reason for this is the fact that most MC decomposition approaches involve a complex and inflexible methodology: decomposed subchains must be disjoint, transition rates of these decomposed subchains must be altered in a way tailored to the particular MC model, and the procedure to aggregate suchains needs to incorporate a nonlinear normalization constraint, complicating the analytical expression of performance measures. In contrast, we propose a versatile yet simple decomposition method for continuous time MCs based on the total expectation theorem. Leveraging the properties of this theorem, our method has great flexibility in the choice of subchains, and the procedure to obtain expected values of interest is simply a linear summation of subchains' properties, which is not affected by the normalization constraint. We prove that to maintain the correct distribution of decomposed subchains one may use our novel termination scheme, a modification of transition rates, that ensures partial flow conservation at boundary states. This termination scheme is applicable to MCs with any structure, since the scheme depends only on the boundary-state distribution, not on the structure of the MCs. To demonstrate the generality and capability of our method, we analytically solve various models, such as a congestion-based staffing queue and a Markov-modulated Mt/Mt/1 queue. As not all systems admit an analytical solution, we complement this analysis with numerical studies of MCs with various sizes using the algorithm based on our method.

math.PR↗

arXiv2020

Approximate Performance Measures for a Single Station Two-Stage Reneging Queue

We study a single station two-stage reneging queue with Poisson arrivals, exponential services, and two levels of exponential reneging behaviors, extending the popular Erlang A model that assumes a constant reneging rate. We derive approximate analytical formulas representing performance measures for our two-stage queue following the Markov chain decomposition approach. Our formulas not only give accurate results spanning the heavy-traffic to the light-traffic regimes, but also provide insight into capacity decisions.

math.PR↗