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C H A P T E R S 1 0 & 1 1

R O U T I N G T O R E D U C E T R A V E L

A N D

W O R K F L O W A N D B A L A N C E

Warehouse and Distribution

Science

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C H A P T E R 1 0

Routing

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Learning Objectives

Understand the complexities of implementing pickrouting

Explain why straight line and serpentine paths areusually good

Understand the relationship between product placementand travel time in picking & some rules of thumb about

best placement of popular skus

Understand why developing optimal pick routings is a

difficult problem to solve and not included in most WMS Implement by hand a simplified version of Ratliff and

Rosenthals algorithm for a small pick problem

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Shortest Route Problem

What is the shortestroute or path from agiven node in anetwork to all othernodes? Mapquest

Deliveries

Warehouse picking

Critical path in projectmanagement

More

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Traveling Salesman Problem

http://www.tsp.gatech.edu/games/tspOnePlayer.html

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Complexity of the TSP

In the theory of computational complexity, thedecision version of the TSP belongs to the class ofNP-complete problems.

Thus, it is likely that the worst case running time forany algorithm for the TSP increases exponentiallywith the number of cities.

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TSP at UCF for ILL

UCF Main campus Objectiveobtain route

with minimum traveldistance to visit all

departments to deliverinter-library load (ILL)material

Start and End at Library Nodes - Department

buildings (X, Y)locations

Assume One Vehicle

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TSP Model

Objective: To minimize the total travel distance of theroute

Minimize dij * Xij

Constraints:

1. Vehicle should leave each node (including library)

Xij = 1 j

2. Vehicle should visit each node and return to the depot (library)

Xij = 1 i

3. Subtour elimination: Vehicle should make only one complete tour.Xij |S| - 1 S N

1

N

i

1

N

j

1

N

i

1

N

j

i S j S

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Results of the Traveling Salesman Tour

2

87

2021

1894

91

90

45

80

53

1214

75

5

54

95

Math &

Physics

Engg 1 & 2

HPA2

HPA1

Bio. Sci.

BA 1

BA 2

Colbourn Hall

CAS

Education

Library

Creol

HP Hall

BHC

Communications

Chemistry CSB

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What if have two vehicles?

2. Two routes instead of one Cluster first, route second

CLUSTER 2CLUSTER 1

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Two Optimal Routesw Capacity Constraint

2

87

2021

1894

91

90

45

80

53

1214

75

5

54

95

ROUTE 1ROUTE 2

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So what about TSP for a warehouse?

Rectilinear Aisles

Need to know distancebetween each pair of

locations Not supported by

WMS

What if the picker

doesnt followsuggested route?

Think iPad

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Heuristics

Global path imposes a sequence that will berespected by all travel

Known as Probabilistic Traveling Salesman Problem PTSP

Want a pick path that is short (efficient) and simpleto understand

Serpentine pick path

Branch and Pick

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Serpentine Example

Popular skus Wider aisles

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Branch and Pick Example

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Branch and Pick Alternatives

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Branch and Pick Alternatives

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Routing Heuristic

Simplified version of optimal-finding algorithm byRatliff and Rosenthal

Use Dynamic Programming

Assumptions: Each aisle can be visited only once;

To get to the next aisle, the picker can travers the entire aisleor retreat back to the end where they entered;

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Example Problem for Routing Heuristic

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Shortest Path Problem with 9 Nodes

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1st Sub-problem: Aisle 1 to 2

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2nd Sub-problem: Aisle 2 to 3

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2nd Sub-problem: Aisle 2 to 3

16

16

26

20

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2nd Sub-problem: Aisle 2 to 3

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3rd Sub-problem: Aisle 3 to 4

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3rd Sub-problem: Aisle 3 to 4

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4th Sub-problem: Aisle 4 to End

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Shortest Path

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For any problem, thecross arcs will be thesame

The end arcs willchange depending onthe locations to visit

Another Problem

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Can you find the shortest path for this?

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How much is optimization worth?

Do we need to optimize routes when there are veryfew items (1-3) in a pick order?

Why?

Do we need to optimize routes when there are verymany items (i.e. you need to visit almost every aislemultiple times) in a pick order?

Why?

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Where is Optimal Routing most Beneficial?

Warehouses with many items, which are slowmoving

Warehouses with orders of moderate size

Examples Hardware distribution centers

Building supply warehouses

Aftermarket auto parts to dealerships

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C H A P T E R 1 1

Workflow & Balance

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Learning Objectives

Identify the steps to implementing a bucket brigadeto balance workload

Identify the advantages of bucket brigades over other

workload balancing policies

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Self Organized Teams

Requires no central planning or higher authority.

It is adaptive, i.e. spontaneously adjusts to changesin the environment

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Bucket Brigades in Action

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Sample Flow Line

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Faster workerSlower worker

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Figure 11.3Line self-balances atf(x).

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EventualPartition of

Work ContentSlowest worker isgreen; fastest worker isred.

Fastest worker doesmore of the work.

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Some Advantages of Bucket Brigades

Pure pull system, so WIP is controlled

Does not require accurate time studies

Support teams and grouping work cells

Simple and easy for each worker to know what to do Workers can usually put themselves in order of

slowest to fastest

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Replacing Zones with Bucket Brigades

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Distribution of Average Pick Rate

BeforeAfter Bucket Brigades

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Bucket Brigades are most appropriate when

All work is based on a single skill, e.g. sewing,making sandwiches

Workers can easily move among stations and take

over work in process Demand for product varies significantly