TY - JOUR

T1 - Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

AU - Otten, Sonja

AU - Krenzler, Ruslan

AU - Xie, Lin

AU - Daduna, Hans

AU - Kruse, Karsten

N1 - Ruslan Krenzler and Sonja Otten are funded by the industrial project “Robotic Mobile Fulfillment System”, which is financially supported by Ecopti GmbH (Paderborn, Germany) and Beijing Hanning Tech Co., Ltd. (Beijing, China).

PY - 2022/6

Y1 - 2022/6

N2 - We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

AB - We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

KW - Backordering

KW - Lost customers

KW - Product form approximation

KW - Robotic mobile fulfilment system

KW - Semi-open queueing network

KW - Warehousing

KW - Business informatics

KW - Informatics

UR - http://www.scopus.com/inward/record.url?scp=85121363563&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/c5d4af19-7d06-33f2-b263-48543de5c238/

U2 - 10.1007/s00291-021-00662-9

DO - 10.1007/s00291-021-00662-9

M3 - Journal articles

AN - SCOPUS:85121363563

VL - 44

SP - 603

EP - 648

JO - OR Spectrum

JF - OR Spectrum

SN - 0171-6468

IS - 2

ER -