# Optimal picking of large orders in carousel systems

Research output: Book/ReportReportProfessional

### Abstract

A carousel is an automated storage and retrieval system which consists of a circular disk with a large number of shelves and drawers along its circumference. The disk can rotate either direction past a picker who has a list of items that have to be collected from $n$ different drawers. In this paper, we assume that locations of the $n$ items are independent and have a continous non-uniform distribution over the carousel circumference. For this model, we determine a limiting behavior of the shortest rotation time needed to collect one large order. In particular, our limiting result indicates that if an order is large, then it is optimal to allocate {\it less} frequently asked items {\it close} to the picker's starting position. This is in contrast with picking of small orders where the optimal allocation rule is clearly the opposite. We also discuss travel times and allocation issues for optimal picking of sequential orders.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 16 Published - 2004

### Publication series

Name Memorandum Faculty of Mathematical Sciences University of Twente, Department of Applied Mathematics 1736 0169-2690

• MSC-62E15
• MSC-90B80
• MSC-90B06
• IR-65920
• MSC-60J20
• EWI-3556
• METIS-218606
• MSC-60F05

### Cite this

Litvak, N. (2004). Optimal picking of large orders in carousel systems. (Memorandum Faculty of Mathematical Sciences; No. 1736). Enschede: University of Twente, Department of Applied Mathematics.
Litvak, Nelli. / Optimal picking of large orders in carousel systems. Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum Faculty of Mathematical Sciences; 1736).
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title = "Optimal picking of large orders in carousel systems",
abstract = "A carousel is an automated storage and retrieval system which consists of a circular disk with a large number of shelves and drawers along its circumference. The disk can rotate either direction past a picker who has a list of items that have to be collected from $n$ different drawers. In this paper, we assume that locations of the $n$ items are independent and have a continous non-uniform distribution over the carousel circumference. For this model, we determine a limiting behavior of the shortest rotation time needed to collect one large order. In particular, our limiting result indicates that if an order is large, then it is optimal to allocate {\it less} frequently asked items {\it close} to the picker's starting position. This is in contrast with picking of small orders where the optimal allocation rule is clearly the opposite. We also discuss travel times and allocation issues for optimal picking of sequential orders.",
keywords = "MSC-62E15, MSC-90B80, MSC-90B06, IR-65920, MSC-60J20, EWI-3556, METIS-218606, MSC-60F05",
author = "Nelli Litvak",
note = "Imported from MEMORANDA",
year = "2004",
language = "Undefined",
series = "Memorandum Faculty of Mathematical Sciences",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1736",

}

Litvak, N 2004, Optimal picking of large orders in carousel systems. Memorandum Faculty of Mathematical Sciences, no. 1736, University of Twente, Department of Applied Mathematics, Enschede.
Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum Faculty of Mathematical Sciences; No. 1736).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Optimal picking of large orders in carousel systems

AU - Litvak, Nelli

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - A carousel is an automated storage and retrieval system which consists of a circular disk with a large number of shelves and drawers along its circumference. The disk can rotate either direction past a picker who has a list of items that have to be collected from $n$ different drawers. In this paper, we assume that locations of the $n$ items are independent and have a continous non-uniform distribution over the carousel circumference. For this model, we determine a limiting behavior of the shortest rotation time needed to collect one large order. In particular, our limiting result indicates that if an order is large, then it is optimal to allocate {\it less} frequently asked items {\it close} to the picker's starting position. This is in contrast with picking of small orders where the optimal allocation rule is clearly the opposite. We also discuss travel times and allocation issues for optimal picking of sequential orders.

AB - A carousel is an automated storage and retrieval system which consists of a circular disk with a large number of shelves and drawers along its circumference. The disk can rotate either direction past a picker who has a list of items that have to be collected from $n$ different drawers. In this paper, we assume that locations of the $n$ items are independent and have a continous non-uniform distribution over the carousel circumference. For this model, we determine a limiting behavior of the shortest rotation time needed to collect one large order. In particular, our limiting result indicates that if an order is large, then it is optimal to allocate {\it less} frequently asked items {\it close} to the picker's starting position. This is in contrast with picking of small orders where the optimal allocation rule is clearly the opposite. We also discuss travel times and allocation issues for optimal picking of sequential orders.

KW - MSC-62E15

KW - MSC-90B80

KW - MSC-90B06

KW - IR-65920

KW - MSC-60J20

KW - EWI-3556

KW - METIS-218606

KW - MSC-60F05

M3 - Report

T3 - Memorandum Faculty of Mathematical Sciences

BT - Optimal picking of large orders in carousel systems

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Litvak N. Optimal picking of large orders in carousel systems. Enschede: University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum Faculty of Mathematical Sciences; 1736).