Stochastic Modelling of Parallel Process Flows in Intra-logistics Systems

Posted: 20 Aug 2018 Last revised: 2 Jul 2019

See all articles by Govind Lal Kumawat

Govind Lal Kumawat

Indian Institute of Management (IIM), Ahmedabad

Debjit Roy

Indian Institute of Management (IIM), Ahmedabad

M. B. M. de Koster

Erasmus University Rotterdam (EUR) - Department of Technology and Operations Management

Ivo Adan

Eindhoven University of Technology (TUE) - Department of Mathematics and Computing Science

Date Written: July 19, 2018

Abstract

Many intra-logistics systems, such as automated container terminals, distribution warehouses, and crossdocks observe parallel process flows, which involve simultaneous (parallel) operations of multiple independent resources while processing a job. Due to the unknown service time of the job, stochastic modeling of the parallel process flows is quite complex. For modeling simplicity, researchers tend to assume sequential operations of the resources. This paper proposes a novel modeling approach using two-phase servers to model the simultaneous operations of resources. We develop a closed queuing network model to estimate the performance measures of a system which observes parallel process flows. To solve the resulting queuing network model, we construct two solution methods: an extended approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods using numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation dis-aggregation approach consistently performs best. We illustrate the proposed parallel modeling approach for two intra-logistic systems: an automated container terminal with automated guided vehicles and a robotic compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and a maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in underestimation of the throughput capacity up to 9%.

Keywords: Logistics, Queuing, Parallel processes

Suggested Citation

Kumawat, Govind Lal and Roy, Debjit and de Koster, M.B.M. René and Adan, Ivo, Stochastic Modelling of Parallel Process Flows in Intra-logistics Systems (July 19, 2018). Available at SSRN: https://ssrn.com/abstract=3216327 or http://dx.doi.org/10.2139/ssrn.3216327

Govind Lal Kumawat (Contact Author)

Indian Institute of Management (IIM), Ahmedabad ( email )

Vastrapur
Ahmedabad, Gujarat 380 015
India

Debjit Roy

Indian Institute of Management (IIM), Ahmedabad ( email )

Vastrapur
Ahmedabad, Gujarat 380 015
India

M.B.M. René De Koster

Erasmus University Rotterdam (EUR) - Department of Technology and Operations Management ( email )

RSM Erasmus University
PO Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1719 (Phone)
+31 10 408 9014 (Fax)

HOME PAGE: http://www.rsm.nl/rdekoster

Ivo Adan

Eindhoven University of Technology (TUE) - Department of Mathematics and Computing Science ( email )

5600 MB Eindhoven
Netherlands
31 40 247 2932 (Phone)
31 40 246 5995 (Fax)

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