© Dr Evgeny Selensky, 2001

Motivation• Hard industrially important problems • Identify problem features making one technique better than the other• Use domain knowledge, develop better heuristics and propagation to improve

search

Dr Evgeny SelenskyUniversity of Glasgow

evgeny@dcs.gla.ac.uk

Local SearchPath Constraint

Energetic ReasoningDisjunctive Scheduling

Edge Finding

Routing

VRP

Scheduling

OSSP

JSSP

ProblemsVehicle Routing Problem (VRP):

Given: M identical vehicles initially located at the base, N customers with demands for goods.Find tours of minimal travel from base to all customers respecting capacity constraints on vehicles and time windows on customers.

Shop Scheduling Problem:

Given: M machines on factory floor, N jobs (sets of operations to be processed by a specified machine). Each operation has a given duration. Each machine can process without interruption only one operation at a time and each job can be processed on one machine at a time (capacity or disjunctive constraints). Schedule all operations such that the latest job is finished in minimal time (minimise makespan).

Job Shop Scheduling Problem (JSSP): • a job is a predefined chain of operations Open Shop Scheduling Problem (OSSP): • order of operations is immaterial

Tools

• Scheduler and Dispatcher

Outline of Study

1. Use default encoding of VRP2. Reformulate VRP as OSSP and solve it with Scheduler3.Use default encoding of JSSP4.Reformulate JSSP as VRP and solve it with Dispatcher5.Compare results

Two extreme cases:• VRP with zero distances, known vehicle assignments and predefined orders of visits (jobs); minimise the latest return time• OSSP with non-zero setup times (distances between customers), alternative machines (vehicles) and time windows; minimise the sum of setups

Reformulated Problems

• Platform: Microsoft Windows NT/Intel Pentium III 933 MHz, 1Gb RAM• VRP as OSSP: Limited Discrepancy Search, Time Limit 3 hours• Default VRP: Guided Local Search, Time Limit 3 hours• JSSP as VRP: Guided Local Search, Time Limit 60 or 180 seconds• Default JSSP: Complete Binary Search, Time Limit 60 or 180 seconds

Experiments

Tours on the plane for R103

Scheduling Technique Routing Technique

© Dr Evgeny Selensky, 2001

* M. Solomon, 1987

VRP OSSP

Benchmark* Scheduling Technique Routing TechniqueVehicles/Travel Vehicles/Travel

R103 22/2445 14/1216.59R104 20/2664 11/995.04R107 20/2523 11/1080.43RC103 18/2646 12/1329.21RC104 18/2418 11/1174.87RC107 17/2551 13/1262.33

JSSP VRP

* http://www.ms.ic.ac.uk/jeb/pub/jobshop1.txt

Benchmark* Scheduling Technique Routing TechniqueMakespan Makespan

Thompson6x6 55* 114Lawrence10x5 57* 126Adams10x10 666* 2306Lawrence15x10 1121 5854Lawrence15x15 1287 8589

© Dr Evgeny Selensky, 2001

JSSPVRP

More urban and specialised

More rural and open

Future Research

• Improve representations of pure JSSP and VRP by facilitating edge finder temporal reasoning and breaking symmetries• Enhance search by using texture measurements and slack based heuristics• Move from the extremes by enriching problems with realistic side constraints:

• Try mixing technologies, e.g., get first solution with the scheduling technique and improve it with the routing technique. Is it better?

• VRP: use instances with smaller distances and introduce classes of vehicles;• JSSP: use instances with progressively greater interchangeability of machines and larger setup costs;

Information

• Problem Reformulation and Search (PRAS) is an EPSRC funded project

• Project number: GR/M90641

• Industrial collaborator: , France

• Duration: 3 years, 2000-2003

• Web: http://www.dcs.gla.ac.uk/pras