Constraint Programming in Operations Management Filippo Focacci ILOG

Constraint Programming in Operations Management Filippo Focacci – ILOG S. A.

Agenda • Constraint-Based Scheduling • Concepts • Constraints • Plant Power. Ops: an industrial application of CP • Introduction • Architecture • Hybrid approach for Integrating planning and scheduling • Integrate business rules in optimization • Demo 2

Constraint-Based Scheduling Introduction • Constraint-Based Scheduling = Scheduling + Constraint Programming • Scheduling problems arise in situations where • A set of activities has to be processed • By a limited number of resources • In a limited amount of time 3

Constraint-Based Scheduling Activities • Non-Preemptive (Interval) Activities Activity A t Start time: s(A) End time: e(A) Processing time: p(A) = e(A) - s(A) 4

Constraint-Based Scheduling Activities • Breakable Activities • Preemption at fixed dates (break calendar) Activity A p 1. . . pi t M T W T F S SM T W T Processing time: p(A) = pi = e(A)-s(A) - breaks(A) 5

Constraint-Based Scheduling Resources • Unary • One person, machine, etc. • Discrete • A group of people with the same capabilities • Energy • A limited number of human-days each week • Reservoir • A stock of raw materials or intermediate products • State • An oven with different possible temperatures 6

Constraint-Based Scheduling Constraints • Temporal constraints • Fixed or variable durations • Precedence constraints • Minimal and maximal delays • Resource constraints • Fixed capacity • Variable capacity (time versus capacity tradeoffs) • Variable capacity over time 7

Constraint-Based Scheduling Constraints • Calendar Constraints • Time intervals during which a resource is not fully available • e. g. , maintenance periods, vacations, forbidden states (at night) • Transition Times • Minimal time required between two activities when in a certain order • e. g. , tool setup between two tasks on the same machine, state change (oven temperature or color used in a painting shop), cleaning, etc. 8

Constraint-Based Scheduling Objective Functions • Examples: • Makespan (max end time) • Sum/max tardiness or earliness • Weighted # of activities • Peak resource usage • Transition times/costs • Weighted # of resources • All possible combinations of the above 9

Constraint-Based Scheduling Resource Constraint Propagation • Several types of global constraints • All make sure the capacity of the resource is not exceeded at any point • Differ in the strength of the propagation they induce: q Explicit timetables Disjunctive constraint q Edge-finding Energetic reasoning q Balance constraint 10

Constraint-Based Scheduling Resource Constraint Propagation • In general, more propagation = more effort • The best propagation algorithm depends • On the application • On the resources within a given application (number of activities, resource criticality, …) 11

Constraint-Based Scheduling Timetables • Identify activities A for which eet(A) > lst(A) • Between lst(A) and eet(A) we know A will be executed 12

Constraint-Based Scheduling Timetables q Q Aggregated necessary demand QMAX t 13

Constraint-Based Scheduling Edge-Finding B p=4 6 C p=5 7 16 15 A A p=2 C p=5 15 7 4 6 16 16 4 7 14

Constraint-Based Scheduling Edge-Finding: Unary Resources • Basic Concept • Prove that an activity A executes before (or after) a set of other activities W. • Jackson's Preemptive Schedule [Pinson 88] [Carlier & Pinson 90/94] • O(n 2) O(n*log(n)) • Iterative algorithm [Nuijten 94] [Martin 96] • O(n 2) with no specific data structure • Task intervals [Caseau & Laburthe 94] • O(n 3) • Incremental 15

Plant Power. Ops Problem Description • Manufacturing planning and scheduling requirements • Continuous production • Determine how to adjust to demand by varying output • Production with co-products and by-products • Determine how to adapt to demand by adjusting the product mix • Campaign and batch production • Determine how to meet demand by determining the length of campaigns, while avoiding costly setups • Industry specific complex constraints • Complex setups, trimming, business policies • Planning and scheduling horizons • Short term – hours to days – re-scheduling and connection with MES • Medium term – days to weeks – integrated planning and scheduling • Long term – weeks to months – planning, what-if analysis 16

Plant Power. Ops Architecture Graphical Planning Board Maintenance & Configuration GUI Planning Plant Floor Engine Parameters Metadata Business Models Middleware • Optimization Development Framework (ODF) from ILOG and SAP • Optimization Extension Kit (OEK) from ILOG and Oracle ODF Reader Planning/IT IT Optimization Algorithms Data Model CSV Reader ODF Writer CSV Writer 17

Plant Power. Ops GUI: Organization Solution Area Problem View Scenario Management Data and Weights Rule Explorer Console 18

Plant Power. Ops Key features • Integrate planning and scheduling • Hybrid CP / MIP • Use business rules to configure and maintain the optimization • Modify the model parameters and data • Add constraints 19

ILOG Plant Power. Ops Integrate Planning and Scheduling Planning engine Data model Planning solution Lot-sizing engine Scheduling Engine Lot-sizing solution Scheduling solution 20

Prepare the Production Schedule Define a rule-based scenario • Activate or deactivate rules and alerts for the current planning or rescheduling scenario 21

Add/Modify Business Policies Define policy rules upon events • Modify the safety stock policy during machine breakdown 22