A new mathematical programming formulation for the Single-Picker Routing Problem

•We define and consider the Single-Picker Routing Problem in a block layout.•We suggest a new mathematical programming formulation for this problem which takes into account the characteristics of optimal routes in a warehouse.•The size of the resulting formulation is independent of the number of pic...

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Bibliographic Details
Published in:European journal of operational research 2016-08, Vol.253 (1), p.68-84
Main Authors: Scholz, André, Henn, Sebastian, Stuhlmann, Meike, Wäscher, Gerhard
Format: Article
Language:English
Subjects:
Block layout
Customers
Decision analysis
Human
Location analysis
Mathematical models
Mathematical programming
Order picking
Picker Routing
Picking
Route optimization
Studies
Traveling Salesman
Traveling salesman problem
Warehouses
Warehousing
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Summary:•We define and consider the Single-Picker Routing Problem in a block layout.•We suggest a new mathematical programming formulation for this problem which takes into account the characteristics of optimal routes in a warehouse.•The size of the resulting formulation is independent of the number of pick locations.•We compare the proposed formulation to Steiner and standard TSP formulations in terms of number of variables and constraints.•We conduct numerical experiments in order to compare the computing times required for solving the model formulations. The Single-Picker Routing Problem deals with the determination of the sequence according to which article locations have to be visited in a distribution warehouse and the identification of the corresponding paths which have to be traveled by human operators (order pickers) in order to collect a set of items requested by internal or external customers. The Single-Picker Routing Problem (SPRP) represents a special case of the classic Traveling Salesman Problem (TSP) and, therefore, can also be modeled as a TSP. Standard TSP formulations applied to the SPRP, however, neglect that in distribution warehouses article locations are arranged in a specifically structured way. When arranged according to a block layout, articles are located in parallel picking aisles, and order pickers can only change over to another picking aisle at certain positions by means of so-called cross aisles. In this paper, for the first time a mathematical programming formulation is proposed which takes into account this specific property. By means of extensive numerical experiments it is shown that the proposed formulation is superior to standard TSP formulations.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.02.018