Production, Manufacturing, Transportation and LogisticsStochastic modeling of parallel process flows in intra-logistics systems: Applications in container terminals and compact storage systems
Introduction
Stochastic models are widely used to evaluate the performance of intra-logistics systems, such as automated container terminals (Gupta, Roy, De Koster, Parhi, 2017, Hoshino, Ota, Shinozaki, Hashimoto, 2007, Mishra, Roy, Van Ommeren, 2017), distribution warehouses (Heragu, Cai, Krishnamurthy, Malmborg, 2011, Lerher, Ekren, Dukic, Rosi, 2015, Marchet, Melacini, Perotti, Tappia, 2012), and cross-docks (Bartholdi III & Gue, 2000). In many intra-logistics systems, the processing of a job involves parallel process steps where different resources can work independently to process the job. This is the case when the processing of a job can be partly executed without the job being physically present (e.g., setup of a resource while the job is arriving at the resource). Upon completion of the simultaneous operations (parallel process flows), the resources may or may not need to synchronize for completing the remaining process steps. A hard-coupling or synchronization between resources is essential if there is no intermediate storage buffer, and one resource needs to hand over the job to the subsequent resource for further processing. On the other hand, synchronization of resources is not required if one resource hands over the unfinished job to a buffer from where the second resource can pick the job for further processing.
An example of simultaneous operations without an intermediate buffer can be found in automated container terminals with automated guided vehicles (AGVs) (Roy, Gupta, & De Koster, 2015). Here, unloading operations of a container from a vessel can be divided into two phases: (1) fetching the container by a quay crane and (2) dropping it on an AGV. The movement of an empty AGV from the stackside (or dwell point) to the quayside and the retrieval of the container by a quay crane can be executed simultaneously. Next, the AGV and the quay crane must synchronize to load the container on the AGV. This phase requires hard-coupling of the AGV and the quay crane.
Similarly, in a shuttle-based compact storage system (Tappia, Roy, De Koster, & Melacini, 2017), a storage or retrieval transaction within a tier involves working of two independent resources: a shuttle and a transfer car. When a shuttle retrieves a load from its current storage lane, it picks-up the load and travels to the cross-aisle. Simultaneously, the transfer car travels in the cross-aisle to the storage lane from its dwell point. Once both arrive at the cross-aisle location, the transfer car picks-up the shuttle and carries it to the outbound buffer. This process requires hard-coupling of the shuttle and the transfer car.
In practice, simultaneous operations of independent resources while serving a job have performance benefits over their sequential operations (Hu et al., 2005). However, stochastic modeling of the simultaneous operations is quite difficult. Since different resources can execute part of a job simultaneously, the effective service requirement of the job is hard to estimate. To overcome this difficulty and to make the analysis simpler, existing studies typically use ‘sequential’ modeling approach, which assumes sequential operations of different resources that can work at least partly simultaneous. For example, Yang, Choi, and Ha (2004), Roy and De Koster (2014), Dhingra, Roy, and De Koster (2017), Roy et al. (2015), and Gupta et al. (2017) assume sequential operations of quay/stack cranes and AGVs while modeling the seaside operations at an automated container terminals with AGVs. They assume that the quay crane’s container retrieval process can only start after an empty AGV arrives at the quayside. Similarly, Tappia et al. (2017) assume sequential operations between the transfer car and the shuttles in their stochastic model of the compact storage system.
In this paper, we develop a ‘parallel’ modeling approach that is efficient in modeling simultaneous operations of independent resources. Specifically, our approach is applicable to model simultaneous operations where resources must be synchronized (hard-coupled) upon completion of their simultaneous operations. Such operations can be found in many environments, e.g., in intra-logistics systems. Simultaneous operations can be modeled using simulation. Developing simulation models is relatively easy, but time consuming. In addition, they are computationally expensive when the system performance is obtained with a large number of scenarios. We propose an analytical closed queuing network with two-phase servers to realistically model the simultaneous operations of resources and to estimate the performance measures of the system. To analyze the resulting queuing network, we develop two solution methods: an approximate mean value analysis and a network aggregation dis-aggregation based approach. We validate the solution methods using numerical experiments and derive several insights on their accuracy. Results indicate that the solution methods are quite accurate in estimating the performance measures, but the network aggregation dis-aggregation based approach is the better one.
We demonstrate the advantages of the parallel modeling approach over the sequential modeling approach using two applications: an automated container terminal with AGVs (Fig. 1(a)) and a shuttle-based compact storage system (described in Section 5). Fig. 1(b) and (c) shows the sequential modeling approach and the parallel modeling approach for the unloading operations at an automated container terminal with AGVs, respectively. We model the simultaneous operations of quay/stack cranes and AGVs and estimate the performance measures. Similarly, in the compact storage system, we model the simultaneous operations of shuttles and the transfer car in the storage tier and estimate the performance measures (see Section 5).
The rest of the paper is organized as follows. In Section 2, we present the literature review. The modeling approach and solution methods are described in Section 3. In Sections 4 and 5, we develop stochastic models for the seaside operations at an automated container terminal with AGVs and for a shuttle-based compact storage system, respectively. We conclude the paper in Section 6.
Section snippets
Literature review
In reviewing the stochastic modeling literature, we primarily focus on the systems which observe simultaneous operations of different resources. Specifically, studies on intra-logistics systems are more relevant to this paper. Developing stochastic models for intra-logistics systems is a well-established area of research. Vis and De Koster (2003) present a comprehensive literature review of container terminal operations covering a variety of decision problems related to resource planning,
Modeling approach and solution methods
In this section, we develop an analytical two-phase server based closed queuing network for modeling the parallel process flows in intra-logistics systems. We propose two solution methods to analyze the resulting queuing network and compare their accuracy based on the numerical results.
Modeling of parallel process flows in an automated container terminal
In this section, we present an application of the proposed modeling approach in automated container terminals and show its benefits in comparison to the existing sequential modeling approach.
Modeling of parallel process flows in a compact storage system
In this section, we present another application of our modeling approach in a shuttle-based compact storage system. We show the performance gap between our approach and the existing approach when both approaches are applied to the same system.
Conclusions
This paper presents a stochastic modeling approach for parallel process flows, which involves simultaneous operations of multiple resources while processing a job. These processes are commonly found in several intra-logistics systems, such as container terminals, distribution warehouses, and cross-docks. Specifically, we model the simultaneous operations in which hard-coupling of resources is essential to hand over the unfinished jobs. To model such operations, we propose a two-phase server
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