On the Boundary of Planning and Scheduling: A Study Roman Barták Charles University, Prague

© Roman Barták, Problem area complex production environments –plastic, petrochemical, chemical, pharmaceutical industries several different resources –producers, movers, stores batch/serial processing with time windows transition patterns (set-up times) by-products, co-products (re-cycling) non-ordered production (for store) alternatives –processing routes, production formulas, raw material

© Roman Barták, Problem area - example & objectives complex production environment Task –preparing a schedule for a given time period (not minimising the makespan) –objective maximising the profit (minimising the cost) silo sacks warehouse processor B1 processor B2 silo processor A purchase order

© Roman Barták, Constraint Programming (CP) Declarative problem solving –stating constraints about the problem variables a set of variables X={x 1,…,x n } variables’ domains D i (usually finite set of possible values) a set of constraints (constraint is a relation among several unknowns) –finding a solution satisfying all (most) the constraints systematic search with consistency techniques & constraint propagation stochastic and heuristic methods (local search)

© Roman Barták, CP - Advantages & Limitations Advantages –declarative modelling transparent representation of real-life problems easy introduction of heuristics –co-operative solving integration of solving methods from different areas (OR, AI …) –semantic foundation amazingly clean and elegant languages Weaknesses –NP-hard problems & tractability –unpredictable behaviour –model instability

© Roman Barták, Planning and Scheduling - Traditional View Planning –finding a sequence of activities transferring the initial world into a required state –AI & CP –uses scheduler’s constraints (otherwise too tighten or too relaxed plans) Scheduling –allocating the activities to available resources over time respecting the constraints –OR & CP –all activities are know in advance PLANNERSCHEDULER Plan = a list of activities Schedule = allocated activities

© Roman Barták, Planning and Scheduling in Industry not strictly distinguished –different discrimination criteria (time horizon & resolution) marketing planning –what and when should be produced –not planning in AI terminology production planning –generation of activities –allocation to departments production scheduling –exact allocation of activities to machines over time –sometimes new activities introduced Marketing plan Production plan Schedule

© Roman Barták, Separate Planning and Scheduling Co-operation between planner and scheduler –too tighten plans (impossible to schedule) –too free plans (less profitable schedule) backtrack from the scheduler to the planner Activity generation –what if appearance of the activity depends on the allocation of other activities? alternatives transition patterns (set-ups) processing of by-products non-ordered production

© Roman Barták, Mixing Planning and Scheduling A scheduler with planning capabilities generating activities during scheduling MARKETING PLANNING Marketing Plan = what should be produced (custom orders plus expected stock) Schedule - what activities are necessary to satisfy the marketing plan - how the activities are allocated to the resources over time PRODUCTION SCHEDULER ACTIVITY GENERATOR ACTIVITY ALLOCATOR ActivityValues for parameters

© Roman Barták, Conceptual models Expressiveness –What could be modelled? (problem area) –What is easy/hard to express? (constraints)

© Roman Barták, Constraint classification in scheduling resource constraints –resource limits in given time point –capacity, compatibility transition constraints –activity transitions in single resource –set-ups dependency constraints –dependencies between different resources –supplier-consumer relation

© Roman Barták, Time-line model a discrete time line with time slices description of situation at each time point/slice planning and scheduling - no difference –a variable for activity in the description of time point/slice comments –covers all the typical problems in complex production environments –all the variables are known in advance too many variables in large-scale industrial problems Production (item1)Change-overProduction (item 2)Production (item 3) Storing (item 1)emptyStoring (items 1&B) No productionProduction (item4)Production (item5) time resources empty Time slice

© Roman Barták, Order-centric model a chain of activities per order (task) description of the activity –start, end (duration), resource enhancement –activities in the production chain are generated during scheduling starting from the order (alternatives, set-ups) –sharing activities between production chains (by-products) time resources storing extruding storing extruding polymerizing

© Roman Barták, How to model? (in order-centric model) alternatives –pre-processing (chosen by the planner) –alternative activities in slots set-ups –set-up slot is either empty or contains the set-up activity (depending on the allocation of the next activity) by-products (re-cycling) –sharing activities between the production chains non-ordered production –pre-processing (non-ordered production is planned in advance - before the scheduling)

© Roman Barták, Resource-centric model a sequence of activities per resource “what the resource can process” rather than “how to satisfy the order” description of the activity –start, end (duration), quantities, state, suppliers, consumers representation –a list of virtual activities –transition constraints between successive activities Production (item1)Change-overProduction (item 2)Production (item 3) Storing (item 1)emptyStoring (items 1&B) No productionProduction (item4)Production (item5) time resources empty No orderOrder1No order

© Roman Barták, Comparison of models

© Roman Barták, What’s next? ad-hoc implementation –dynamic constraints –propagation (early detection of inconsistencies) –labelling (incremental) –heuristics (choice of alternatives) theoretical foundation –structural constraint satisfaction (A. Nareyek) parallelism –agent based scheduling