TY - JOUR

T1 - The residual time approach for (Q, r) model under perishability, general lead times, and lost sales

AU - Barron, Yonit

AU - Baron, Opher

N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/12

Y1 - 2020/12

N2 - We consider a (Q, r) perishable inventory system with state-dependent compound Poisson demands with a random batch size, general lead times, exponential shelf times, and lost sales. We assume r< Q and analyze the system using an embedded Markov process at the replenishment points. Using the queueing and Markov chain decomposition approach, we characterize the distribution of the residual lead time and derive the stationary distribution of the inventory level. We construct closed-form expressions for the expected total long-run average cost function. The closed form allows us to efficiently obtain, numerically, the optimal Q and r parameters. Numerical study provides several guidelines for the optimal control. For example, we show that approximating the lead time distribution by an exponential one only works when the optimal reorder point of the approximation is very small; in other cases the usage of the exact distribution can lead to substantial cost savings (up to 14%). We further provide intuition insight on the optimal controls and how they depend on different factors, e.g., the lead time variability, and the demand features (arrival rate, size and variability).

AB - We consider a (Q, r) perishable inventory system with state-dependent compound Poisson demands with a random batch size, general lead times, exponential shelf times, and lost sales. We assume r< Q and analyze the system using an embedded Markov process at the replenishment points. Using the queueing and Markov chain decomposition approach, we characterize the distribution of the residual lead time and derive the stationary distribution of the inventory level. We construct closed-form expressions for the expected total long-run average cost function. The closed form allows us to efficiently obtain, numerically, the optimal Q and r parameters. Numerical study provides several guidelines for the optimal control. For example, we show that approximating the lead time distribution by an exponential one only works when the optimal reorder point of the approximation is very small; in other cases the usage of the exact distribution can lead to substantial cost savings (up to 14%). We further provide intuition insight on the optimal controls and how they depend on different factors, e.g., the lead time variability, and the demand features (arrival rate, size and variability).

KW - (Q, r) policy

KW - Lost sales

KW - Perishability

KW - Queueing

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85088834340&partnerID=8YFLogxK

U2 - 10.1007/s00186-020-00717-7

DO - 10.1007/s00186-020-00717-7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85088834340

SN - 1432-2994

VL - 92

SP - 601

EP - 648

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

IS - 3

ER -