Analytical models for cycle time and throughput evaluation of multi-shuttle deep-lane AVS/RS

Abstract

The increased need for just-in-time delivery of finite goods has pulled the development of novel automation solutions to manage warehouse activities. Among the available technologies, autonomous vehicle storage and retrieval systems (AVS/RS) rely on light vehicles able to travel independently and to perform different tasks at the same time, thus exhibiting enhanced flexibility and increased throughput level. Nonetheless, techniques to evaluate the performance of such systems still exhibit some gaps and are mainly focused on simple configurations. This paper aims to extend the state of the art by introducing novel analytical models capable to assess the performance of a tier-to-tier, multi-shuttle AVS/RS feeding a deep-lane rack. The proposed approach enables to evaluate the expected cycle time and throughput by (i) enabling the possibility to consider the real criteria adopted to store and retrieve items, and (ii) taking into account the ability of the vehicles to simultaneously perform different tasks. The model is validated against simulations performed on different rack layouts, on AVS/RS with different fleet compositions, for different types of cycle. The developed model aims to support both the design and the deployment phases of AVS/RS by enabling quick and accurate performance estimation in a wide variety of scenarios.

Appendix A: Description of the simulation model

This section contains a high-level description of the simulation model used for validation of the developed approach.

1.1 A.1 Initialization model

A first model has been developed to generate 10 datasets to be used in the different repetitions of each configuration to be simulated: such datasets contain the rack content to be loaded at the beginning of the simulation and a list of ULs to be stored and retrieved.define rackCapacity = N_x⋆N_y⋆N_zfor i = 1:numberOfRepetitions

generate the empty rack structure

set storageCriterion: Closest

Channel

set retrievalCriterion: Random

for j = 1:rackCapacity

generate the jth UL

provide the jth UL with a

random UL type

define the jth UL position in

the rack

accordingly to the

storageCriterion

update rack content

end

for j = 1:fillRate⋆rackCapacity

require retrieval of a UL with

a random type

select the UL to be retrieved

accordingly to

the retrievalCriterion

make the rack position free and

update rack content

end

for j = 1:numberOfInvolvedULs

generate a new UL to be stored

generate a new UL to be

retrieved

provide the two ULs with a

random UL type

end save ith rack content

save ith list of storage and

retrieval ULs end

1.2 A.2 Simulation model

Here, the model that simulates UL storage and retrieval is presented: the results of the former model are used here as an input; the output mainly consists in the evaluation of the average cycle time and an array (which size is equal to rack capacity) listing the number of storage/retrieval activities occurred in each rack position: this is the basis to evaluate the probability distributions a, b, c.load rack configuration and initial contentload the list of storage and retrieval ULsload simulation configuration: storageCriterion,

retrievalCriterion, N_S, L, S, P, U define numberOfCycles = 20000/U define arrayOfInteractions = zeros(size: rackCapacity) for i = 1:numberOfCycles

identify the U items in the list

involved in

the actual cycle

decide the rack positions of ULs to

be stored

accordingly to the

storageCriterion

decide the rack positions of ULs to

be retrieved

accordingly to the

retrievalCriterion

start timeCounter

run vehicles movements to

store/retrieve the U

items, accordingly to cycle

specifications and

to the defined rack positions

end timeCounter

set cycleDuration(i) = timeCounter

increase by one unit the

appropriate value of

arrayOfInteractions end evaluate a, b, c based on arrayOfInteractions evaluate avgCicleDurationSimulation = mean(...

cycleDuration(1:numberofCycles)