Modelling and Analysis Using a Switching Stochastic Max-Plus Linear Model

Modelling and Analysis Using a Switching Stochastic Max-Plus Linear Model: Applied on an Automatic Palletiser

Neijenhuis, Robert (TU Delft Mechanical, Maritime and Materials Engineering; TU Delft Delft Center for Systems and Control)

van den Boom, A.J.J. (mentor)
van Eekelen, Joost (mentor)

Delft University of Technology

2017-07-11

Automated Case Picking (ACP) is a concept for warehouse automation made by Vanderlande Industries. A subsystem of the ACP concept is the automatic palletiser that is responsible for handling cases from a tray onto an order carrier. The research questions concern whether the automatic palletiser can be modelled as a Switching Stochastic Max-Plus Linear (SSMPL) model and what conclusions can be drawn on capacity, bottleneck and sensitivity issues.

The physical components of the automatic palletiser that are handling the cases are in succession a conveyor system, a tray lift, a Tray Unloading Robot (TUR), a PickUp Table (PUT), a Palletiser Robot (PR) and a carrier lift. These physical components and several software and vision based components are depending on each other and together determine the behaviour of the system.

The automatic palletiser is treated as a Discrete Event Dynamic System (DEDS) and is linear in the max-plus algebra as it contains synchronizations and no concurrency. Structural changes within the system are solved by describing it as a Switching Max-Plus Linear (SMPL) system. The system switches between modes that describe a certain system structure.

The automatic palletiser is described by an SSMPL model in which stochastic parameters are used to describe the actions that take a variable amount of time. The model is written in a state-space representation which makes it suitable for implementation into MATLAB. Timing variables are based on simulation data performed by Vanderlande. Simulation of the model results in a structural difference with the reference simulation as a result of the stochastic characteristics. Cross-validation shows that the model gives the expected result when the identification and the test data are different.

Analyses on activeness of the robots, cycle times and on critical cycles conclude on the TUR being the system’s bottleneck. It is recommended to research the change in accuracy due to fastening the robot.

Research on Max-Plus Scaling (MPS) functions matrix multiplication makes it possible to easily describe a sequence of max-plus matrix multiplications in terms of MPS functions. This is useful in simulation applications as performed in this thesis. However, due to characteristics of the internal cycle times of the system, the automatic palletiser in the present form does not qualify for implementation of MPS functions.

Max-plus
Switching
SSMPL

http://resolver.tudelft.nl/uuid:5ecb6da9-b8de-432e-b6a1-22aaa827d47f

2022-07-11

Student theses

master thesis

© 2017 Robert Neijenhuis