KPI-based Schedule Optimisation M.L. van Eck

Work-related Stress Costs over €25 billion a year in the EU. (EU-OSHA) 10% of work-related illness caused by stress 28% workers reported to be affected by stress 80% of managers are concerned about stress in the workplace SLIDE 1

Reducing Stress SLIDE 2

Schedule Optimisation SLIDE 3 KPI Calculation Model Scheduling Approach If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraint Model Task List

Scheduling SLIDE 4 Many scheduling techniques exist Constraint programming Network models Stochastic optimization … Challenges: Interacting resources Flexible processes Concurrency Predicting resource performance Problem formulation

Schedule Optimisation SLIDE 5 KPI Calculation Model Scheduling Approach If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List

Scheduling Approach 1.Automatically construct an executable model (solution space) Activities Resources Constraints KPIs Time 2.Compute an optimal schedule using the executable model SLIDE 6

Schedule Optimisation SLIDE 7 KPI Calculation Model If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List 1. Build Executable Model 2. Find Optimal Schedule

Constraints Collection of “business rules” 1. Confirm Delivery before Receive Shipment & Pay Invoice 2. If orderSize > 10 then Receive Shipment before Pay Invoice 3. … Modelled as (Coloured) Petri Nets with multi-label transitions SLIDE

Schedule Optimisation SLIDE 9 KPI Calculation Model If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List 1. Build Executable Model 2. Find Optimal Schedule

KPI Calculation Model SLIDE 10

Schedule Optimisation SLIDE 11 KPI Calculation Model If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List 1. Build Executable Model 2. Find Optimal Schedule

Executable Model SLIDE 12 Coloured Petri Net (timed) Building the executable model 1.Create an initial net from the task list 2.Compute the multi-label synchronous product with all constraints 3.Add resources & model explicit delaying 4.Add KPI tracking Generate valid schedule by reaching final marking

Executable Model SLIDE 13

Schedule Optimisation SLIDE 14 KPI Calculation Model If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List 1. Build Executable Model 2. Find Optimal Schedule

Calculating Optimal Schedules SLIDE 15 Calculate the state space of the executable model Cost of each state is modelled in marking All final states are valid schedules Problem: Slow  Partial order reductions (Stubborn sets) don’t seem to help

Schedule Optimisation SLIDE 16 KPI Calculation Model If orderSize > 10 then Receive Shipment before Pay Invoice Handle Orders (x5 orders, 10 hours) Confirm Delivery Receive Shipment Pay Invoice Resources Anna John AnnaJohn Schedule Constraints Task List 1. Build Executable Model 2. Find Optimal Schedule

Future Work SLIDE 17 Finding optimal schedules Settle for non-optimal schedules Translate executable model into e.g. constraint program Calculate state space using LoLA Constraint mining Compute a set of schedules Classify into “good” and “bad” Learn additional constraints to guarantee better schedules

SLIDE 18 Questions?

Running Example SLIDE 19 Anna & John Order Handling Process Office Warehouse

Combining Petri Nets Standard synchronous product SLIDE 20 D

Multi-label Synchronous Product SLIDE 21 All labels need to be matched * = any value

Multi-label Synchronous Product SLIDE 22

Multi-label Synchronous Product SLIDE 23

Challenges & Future Work Calculating the statespace is slow Many parallel activities Coloured tokens to model order IDs, resource use, time, costs, etc. Implement multidimensional cost functions E.g. maximise throughput time & minimise stress (Pareto front) Non-linear cost functions are no problem User-friendly restrictions model specification SLIDE 24