Warehousing in the Global Supply Chain pp 211-231 | Cite as

# Designing Unit Load Automated Storage and Retrieval Systems

## Abstract

The successful performance of the unit load automated storage and retrieval systems is dependent upon the appropriate design and optimization process. In this chapter a model of designing unit load automated storage and retrieval system for the single- and multi-aisle systems is presented. Because of the required conditions that the unit load automated storage and retrieval systems should be technically highly efficient and that it should be designed on reasonable expenses, the objective function represents minimum total cost. The objective function combines elements of layout, time-dependant part, the initial investment and the operational costs. Due to the nonlinear, multi-variable and discrete shape of the objective function, the method of genetic algorithms has been used for the optimization process of decision variables. The presented model proves to be a useful and flexible tool for choosing a particular type of the single- or multi-aisle system in designing unit load automated storage and retrieval systems. Computational analysis of the design model indicates the model suitability for addressing industry-size problems.

## Keywords

Economical Design Unit Load Average Travel Time Storage Compartment Handling Equipment## Nomenclature

- AS/RS
Automated storage and retrieval system

- S/R machine
Storage and retrieval machine

- SR
Storage rack

- I/O
Input/output location

- TUL
Transport unit load

- SC
Single command cycle

- DC
Dual command cycle

- 3D
Three dimensional

- PP
Palette position

- GA
Genetics algorithms

- SIT
Square-In-Time

- TC
Total cost

*R*Number of picking aisles (variable)

*Y*Number of SR (variable);

*Y*= 2*R**S*Number of S/R machines (variable)

*N*_{x}Number of storage compartments in horizontal direction (variable)

*N*_{y}Number of storage compartments in vertical direction (variable)

*Q*(TUL)Storage capacity

*Pf*(TUL/h)Throughput capacity

*Min*TC (EUR)Minimum total cost

*P*_{z}(m^{2})Surface of the land for warehouse

*D*_{z}(/)Share for the warehouse building

*C*_{1}(EUR/m^{2})Cost of buying the land

*C*_{2}(EUR/m^{2})Cost of laying the foundation of warehouse per square meter of foundation

*C*_{3}(EUR/m^{2})Cost of building the walls of warehouse per square meter of walls

*C*_{4}(EUR/m^{2})Cost of building the roof of warehouse per square meter of roof

*C*_{5}(EUR/m)Cost of buying upright frames per meter

*C*_{6}(EUR/m)Cost of buying rack beams per meter

*C*_{7}(EUR/piece)Cost of buying buffers per piece

*C*_{8}(EUR/PP)Cost of assembly per pallet position

*C*_{9}(EUR/PP)Cost of fire safety per pallet position

*C*_{10}(EUR/m^{3})Cost of air conditioning per cubic meter

*C*_{11}(EUR/piece)Cost of buying single-aisle S/R machine

*C*_{12}(EUR/m)Cost of the picking aisle per meter

*C*_{13}(EUR/piece)Cost of buying multi-aisle S/R machine which includes aisle transferring machine

*C*_{14}(EUR/m)Cost of the cross aisle per meter

*H*_{WAR}(m)Height of the warehouse

*H*_{min}(m)Minimum height of the warehouse

*H*_{max}(m)Maximum height of the warehouse

*L*_{TZ}(m)Length of the transport zone

*L*_{RS}(m)Length of the storage rack

*H*_{RS}(m)Height of the storage rack

*L*_{WAR}(m)Length of the warehouse

*L*_{min}(m)Minimum length of the warehouse

*L*_{max}(m)Maximum length of the warehouse

*W*_{WAR}(m)Width of the warehouse

*W*_{min}(m)Minimum width of the warehouse

*W*_{max}(m)Maximum width of the warehouse

*W*_{RD}(m)Width of the S/R machine

*H*_{RD}(m)Lift height of the S/R machine

*g*(m)Length of the palette/TUL

*h*(m)Height of the palette/TUL

*w*(m)Width of the palette/TUL

*n*(/)Number of TUL in the storage compartment

*b*_{1}(m)Safety addition to the width of the storage compartment

*b*_{2}(m)Safety addition to the height of the storage compartment

*b*_{3}(m)Width of the storage compartment

*b*_{4}(m)Width of the upright frame

*b*_{5}(m)Thickness of the upright frame

*b*_{6}(m)Height of rack beams

*b*_{7}(m)Elevation of the first level storage compartment from the floor

*b*_{8}(m)Safety spacing between racks that are placed close to each other

*b*_{9}(m)Safety addition to the height of the warehouse

*b*_{10}(m)Addition to the width of the palette at input buffer

*b*_{20}(m)Addition to the end of the warehouse

*L*_{v}(m)Length of the rack beam

*v*_{x}(m/s)Maximum velocity of the S/R machine in the horizontal direction

*v*_{y}(m/s)Maximum velocity of the hoisted carriage in the vertical direction

*v*_{i}(m/s)Maximum velocity of the transferring vehicle in the cross warehouse aisle

*a*_{x}(m/s^{2})Acceleration/deceleration of the S/R machine in the horizontal direction

*a*_{y}(m/s^{2})Acceleration/deceleration of the hoisted carriage in the vertical direction

*a*_{i}(m/s^{2})Acceleration/deceleration of the transferring vehicle in the cross warehouse aisle

*T*(SC) (s)Expected single command travel time

*n*_{SC}(/)Number of single command cycles

*T*(DC) (s)Expected dual command travel time

*n*_{DC}(/)Number of dual command cycles

*T*_{shift}(s)Time of one shift

*η*(%)Efficiency of the S/R machine

*T*_{01}(s)Pickup time

*T*_{02}(s)Deposit time

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