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Exploring Quantum Inspired optimization for the Vehicle Routing Problem (VRP)

Astrid Katrine Kyhl, Troels Steenstrup, Casper Guldager

May 2023

Photo from IBM Research

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Contents�

01

Substantial saving optimization potential

02

Quantum Inspired Optimization as potential solution

03

Outcomes and discussion

04

Q&A

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01�Substantial saving potential from technician intraday re-optimization

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Our ambition is to cut technician milage by 25% resulting in improved operating costs and reduced CO2-emission.

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The Problem

~850 Technician Vehilcles

~80000 Km driven daily

~1000 Avg. Jobs/Faults daily

Constraints

Technicians Start and End point

~150 Unique Skills

SLA’s

Overtime

Equipment/Warehouse Visits

Daily Capacity / Absence planning

Lunch time

Multi-Faults

Multi Technicians Required

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We Address the Inefficiency 3 Fold

2. Increase the fraction of auto dispatch from ~30% to 90-100% - Problem is too large for the human brain to beat a large scale optimization engine

(QIO Potential)

1. AI-driven planning day-to-day and long-term by better forecasting of faults and job times

(Ongoing with Classic computers)

3. Utilize intraday re-optimization to address perturbations to original plan most efficiently

(QIO Potential)

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Document Classification: KPMG Confidential

© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Document Classification: KPMG Confidential

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© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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QIO Potential

Scenario Builder

Fast Intra-Day Re-Optimization

  • Fleet & Skill Composition
  • Skill Broadness & Utilisation
  • Optimal Technician Distribution
  • SLA bundling
  • Testing constraints & business process impact

  • 0-touch dispatch
  • Reactive Real-time optimisation
  • Increased transparency and insights
  • Flexible parameter settings

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02�Quantum Inspired Optimization as potential solution

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Three possible roads to quantum optimization:

Gate Based

Quantum Computing

Quantum

Annealing

Quantum Inspired

Optimization

QUBO

QUBO

QUBO

QAOA

Special purpose�quantum hardware

Classical hardware & classical solvers

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Quantum Inspired leverages the power of classical hardware and quantum algorithms to

Flexible – and easily adjustable – models

Solves larger and more complex problems

Identifies solutions of better quality

Finds solutions quicker

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Applications of quantum-inspired optimization problems can yield solutions anywhere from

1-10% more accurate solutions anywhere from �2-3 times as fast

according to Troels Steenstrup, technology head of KPMG’s Global Quantum Hub.”

© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Solving VRP by combining the strengths of quantum and classical

Create an approximate QUBO assignment problem and solve using simulated annealing on QIO hardware.

Create final routes using classical OR based on these assignments.

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03�Outcome and discussion

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Quantum Inspired resulted in measurable KPI improvements

  • Technicians

Replace with: 99% (2 hours to 1 minute)

  • Milage

  • Run time

17 %

Technicians

58 %

Milage

99 %

Run time

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Document Classification: KPMG Confidential

© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Document Classification: KPMG Confidential

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© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Q&A

04

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Document Classification: KPMG Confidential

© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Document Classification: KPMG Confidential

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Contact Information

Astrid Katrine Kyhl

astk@tdcnet.dk

Troels Steenstrup Jensen

trsjensen@kpmg.com

Casper Guldager

caguldager@kpmg.com

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Document Classification: KPMG Confidential

© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.

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Document Classification: KPMG Confidential

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© 2023 KPMG P/S, a Danish limited liability partnership and a member firm of the KPMG global organisation of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. All rights reserved.