© Dr Evgeny Selensky, 2001

1. Routing Scheduling OSSP VRP JSSP Energetic Reasoning Disjunctive Scheduling Edge Finding Local Search Path Constraint Mutual Reformulation of Shop Scheduling and Vehicle Routing Dr Evgeny Selensky University of Glasgow evgeny@dcs.gla.ac.uk 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 Problems • Vehicle 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 © Dr Evgeny Selensky, 2001

2. Outline of Study Reformulated Problems • 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 • Use default encoding of VRP • Reformulate VRP as OSSP and solve it with Scheduler • Use default encoding of JSSP • Reformulate JSSP as VRP and solve it with Dispatcher • Compare results * http://www.ms.ic.ac.uk/jeb/pub/jobshop1.txt Tours on the plane for R103 JSSP VRP VRP OSSP Scheduling Technique Routing Technique Experiments • 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 * M. Solomon, 1987 © Dr Evgeny Selensky, 2001

3. 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; VRP JSSP More urban and specialised More rural and open 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 © Dr Evgeny Selensky, 2001