332 research outputs found
A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout
The Single-Picker Routing Problem deals with the determination of sequences according to which items have to be picked in a distribution warehouse and the identification of the corresponding paths which have to be travelled by human operators (order pickers). The Single-Picker Routing Problem represents a special case of the classic Traveling Salesman Problem (TSP) and, therefore, can also be modeled as a TSP. However, the picking area of a warehouse typically possesses a block layout, i.e. the items are located in parallel picking aisles, and the 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. Based on extensive numerical experiments, it is shown that the proposed formulation is superior to standard TSP formulations
Improved formulations of the joint order batching and picker routing problem
Order picking is the process of retrieving ordered products from storage
locations in warehouses. In picker-to-parts order picking systems, two or more
customer orders may be grouped and assigned to a single picker. Then routing
decision regarding the visiting sequence of items during a picking tour must be
made. (J.Won and S.Olafsson 2005) found that solving the integrated problem of
batching and routing enables warehouse managers to organize order picking
operations more efficiently compared with solving the two problems separately
and sequentially. We therefore investigate the mathematical programming
formulation of this integrated problem. We present several improved
formulations for the problem based on the findings of (Valle, Beasley, and da
Cunha 2017), that can significantly improve computational results. More
specifically, we reconstruct the connectivity constraints and generate new
cutting planes in our branch-and-cut framework. We also discuss some problem
properties by studying the structure of the graphical representation, and we
present two types of additional constraints. We also consider the no-reversal
case of this problem. We present efficient formulations by building different
auxiliary graphs. Finally, we present computational results for publicly
available test problems for single-block and multiple-block warehouse
configurationsComment: 37 pages, 11 figures, 7 table
Exact algorithms for the order picking problem
Order picking is the problem of collecting a set of products in a warehouse
in a minimum amount of time. It is currently a major bottleneck in supply-chain
because of its cost in time and labor force. This article presents two exact
and effective algorithms for this problem. Firstly, a sparse formulation in
mixed-integer programming is strengthened by preprocessing and valid
inequalities. Secondly, a dynamic programming approach generalizing known
algorithms for two or three cross-aisles is proposed and evaluated
experimentally. Performances of these algorithms are reported and compared with
the Traveling Salesman Problem (TSP) solver Concorde
Metaheuristics for the Order Batching Problem in Manual Order Picking Systems
In manual order picking systems, order pickers walk or drive through a distribution warehouse in order to collect items which are requested by (internal or external) customers. In order to perform these operations effciently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours is minimized which are necessary to collect all items. The authors introduce two metaheuristic approaches for the solution of this problem; the rst one is based on Iterated Local Search, the second one on Ant Colony Optimization. In a series of extensive numerical experiments, the newly developed approaches are benchmarked against classic solution methods. It is demonstrated that the proposed methods are not only superior to existing methods, but provide solutions which may allow for operating distribution warehouses signicantly more effcient.Warehouse Management, Order Picking, Order Batching, Iterated Local Search, Ant Colony Optimization
Lower and upper bounds for the joint batching, routing and sequencing problem
Warehouses are nowadays the scene of complex logistic problems integrating
different decision layers. This paper addresses the Joint Order Batching,
Picker Routing and Sequencing Problem with Deadlines (JOBPRSP-D) in rectangular
warehouses. To tackle the problem an exponential linear programming formulation
is proposed. It is solved with a column generation heuristic able to provide
valid lower and upper bounds on the optimal value. We start by showing that the
JOBPRSP-D is related to the bin packing problem rather than the scheduling
problem. We take advantage of this aspect to derive a number of valid
inequalities that enhance the resolution of the master problem. The proposed
algorithm is evaluated on publicly available data-sets. It is able to optimally
solve instances with up to 18 orders in few minutes. It is also able to prove
optimality or to provide high-quality lower bounds on larger instances with 100
orders. To the best of our knowledge this is the first paper that provides
optimality guarantee on large size instances for the JOBPRSP-D, thus the
results can be used to assert the quality of heuristics proposed for the same
problem
- …