A Problem of Supermarket Order Picking
Eliana Costa e Silva1 and Isabel Cristina Lopes2
1CIICESI/ESTGF - Polytechnic Institute of Porto and ALGORITMI2LEMA/CIEFGEI/ESEIG - Polytechnic Institute of Porto
Santiago de CompostelaJune 29 - July 3, 2015
A Problem of Supermarket Order Picking
Problem description:
Currently there is an increasing demand in providing supermarket clients withonline shopping services.
One of the tasks that is fundamental in this type of service is order picking.
Order picking consists in taking and gathering a list of items from storagelocations in order to satisfy independent customers’ orders.
The critical issue in today’s business environment is to simultaneouslyreduce the cost and increase the speed of order picking.
Source: http://www.fact-finder.com/blog/2013/12/17/online-grocery-market-huge-potential-part/
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Some examples:
Spain:
I ulabox - https://www.ulabox.com/I tudespensa -
http://www.tudespensa.com/I Carrefour -http://www.carrefour.es/
Portugal:
I Continente -http://www.continente.pt
I Jumbo - http://www.jumbo.pt
Sweden:
I MatHem - https://www.mathem.se/
UK:
I Tesco - http://www.tesco.com/I mySupermarket - https:
//www.mysupermarket.co.uk/
Germany:
I Lebensmittel -http://www.lebensmittel.de/
Source: http://www.tudespensa.com/
Source: http://www.lebensmittel.de/
Source: http://www.tesco.com/
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How does it work?Most large supermarkets also have online grocery stores.
An online customer makes an order on the company’s website.
The company has employees that go through the shop picking the productsfrom the shelves and put them in boxes.
The groceries are delivered the next day at the customer’s home.
Source: http://www.thisismoney.co.uk/money/article-2044152/High-hopes-Waitrose-web-supermarket-opens-dark-store.html
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 4 / 13
Order picking
Order picking is the process of retrieving products from storage in responseto a specific customer request.
Each operator steers the trolley on the shop floor to select items to multiplecustomers, therefore may have to walk a considerable distance.
It is generally recognized as one of the most significant activities in awarehouse (Koster et al, 2007).
It accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) ofthe total warehouse operating costs.
Critical issues: reduce the cost and increase the speed of order picking.
DOCK
SHOP
HRP DEPOT
WAREHOUSE
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 5 / 13
Order picking
The most common picking scenarios (Koster, 2007) are:I Discrete picking: the order selector picks for one customer order at a time,
moving around the warehouse until that order is completed, and then startingon the next customer order.
I Batch picking: multiple customer orders (the batch) are pickedsimultaneously by an order picker.
Discrete picking - pickers collected items for a single customer at a time -usually minimizes the probability of swapping products between differentorders.
Changing the location of the products is usually not allowed, because it isdictated by marketing strategies.
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 6 / 13
Picking process
The picker steers a trolley on theshop floor.
Usually the trolley is a vehicle with4 or 6 independent boxes with equalcapacity.
The picker follows a route throughthe aisles of the shop, takes theproducts from the shelves, and putsthe items of each client in aseparated box.
When a box is full, the picker opensa new box and proceeds picking theitems into this one, for the samecustomer.
When all the six boxes are full thepicker returns to the depot.
Source: http://grocerytrader.co.uk/?p=11301
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Problem statementGiven a set of orders of different customers to be collected at the shop, how tominimize the traveling distance needed to pick all the items, satisfying the weightand volume capacity constraints of the trolley, and imposing that in each boxthere are items of only one customer.
The problem can be viewed as a variant of the Capacitated Vehicle RoutingProblem (CVRP) (Toth, 2002), where:
The depot d and each aisle vi belong to the set of vertices V ;
Each circuit (route) visits the depot vertex d exactly once;
Each vertex is visited at least once in the total of the circuits, and at mostonce in each circuit;
Each vertex needs to be visited while there are items to collect;
The total weight and the total volume of the items picked in a circuit do notexceed the vehicle and boxes capacities;
The items are separated according to clients as they are being picked and putin the boxes of the trolley, respecting the assignment of boxes to clients.
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 8 / 13
Directed weighted graphG = (VI , A, ρ)
Total ordering on the set of aisles:u < v ⇔ ux < vx ∨ (ux = vx ∧ uy > vy)where (ux, uy) and (vx, vy) are thecoordinates of the center of the aisles.
The set of arcs A contains all arcs (u, v):u < v together with arcs in both directionslinking the depot d to all aisles:
A = {(u, v) ∈ (VI\{d})2 | u < v}
∪{(u, v) ∈ V 2I | u = d ∨ v = d}.
ρ : A→ R is the weight of arc (u, v) ∈ A:the minimum traveling distance throughoutthe aisles of the store, to get from vertex u,located at the center of an aisle, to vertex v(not the usual euclidean distance).
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 9 / 13
Directed weighted graphG = (VI , A, ρ)
Total ordering on the set of aisles:u < v ⇔ ux < vx ∨ (ux = vx ∧ uy > vy)where (ux, uy) and (vx, vy) are thecoordinates of the center of the aisles.
The set of arcs A contains all arcs (u, v):u < v together with arcs in both directionslinking the depot d to all aisles:
A = {(u, v) ∈ (VI\{d})2 | u < v}
∪{(u, v) ∈ V 2I | u = d ∨ v = d}.
ρ : A→ R is the weight of arc (u, v) ∈ A:the minimum traveling distance throughoutthe aisles of the store, to get from vertex u,located at the center of an aisle, to vertex v(not the usual euclidean distance).
E. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 10 / 13
A Problem of Supermarket Order Picking
Aim of this project:
Find a mathematical model.
Explore different numerical solutions.
Possible Steps
Exploratory analysis of the data set
Creating test instances (subsets of the original data set)
Developing a Mathematical Model
Computing traveling distances between aisles
Obtaining numerical results for the test instances
Mathematical background:
Programming (preferably, in Matlab),
Mathematical Programming (Integer Linear Programming),
Optimization solvers, Modeling language (preferably, AMPL)
Graph theoryE. Costa e Silva, I.C. Lopes (Portugal) Supermarket Order Picking 11 / 13
Bibliography
E. Frazelle, World-Class Warehousing and Material Handling, McGraw-Hill,New York (2001).
V. Kamarainen, J. Smaros, T. Jaakola, and J. Holmstrom, Cost-effectivenessin the e-grocery business, International Journal of Retail & DistributionManagement 29 (1) (2001).
R. De Koster, T. Le-Duc, and K. J. Roodbergen, Design and control ofwarehouse order picking: a literature review, European Journal of OperationalResearch 182 (2) (2007) 481-501.
J. Tompkins, J. White, Y. Bozer, and J. Tanchoco, Facilities planning, Wiley,New Jersey (2003).
P. Toth, and D. Vigo, The Vehicle Routing Problem, Monographs on DiscreteMathematics and Applications, Society for Industrial and AppliedMathematics (2002).
J. P. Van den Berg, A literature survey on planning and control ofwarehousing systems, IIE Transactions 31 (8) (1999) 751-762.
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Source: http://www.theguardian.com/business/shortcuts/2014/jan/07/inside-supermarkets-dark-stores-online-shopping
Eliana Costa e Silva [email protected] Cristina Lopes [email protected]
Portugal
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