Multi-scale Planning and Scheduling Under Uncertain and Varying Demand Conditions in the Pharmaceutical Industry

Hierarchically Structured Integrated Multi-scale Approach

Hlynur Stefansson and Prof. Nilay ShahCentre for Process Systems Engineering Imperial College London

Overview

Introduction Project objectives Case study Proposed approach Models Solution procedure Results Conclusions

Introduction

Typical process planning and scheduling approaches Fixed time horizon All data given

Make to order manufacturing Customers require high service levels and flexibility Unpredictable demand Competitive prices

The pharmaceutical industry is a good example of an industry where planning and scheduling of make to order production is a big challenge

Project Objectives

We propose an approach for a continuous and dynamic planning and scheduling process Decisions have to be made before all data are available

Objectives An effective approach A combination of a proactive and reactive planning Accurate and efficient optimisation models and solution procedures Decision support for actual MTO planning and scheduling problems

Case Study – Problem Description

Actavis is one of the five largest generic pharmaceutical companies in the world

Single plant planning and scheduling for a secondary pharmaceutical production plant

Production environment Over 40 product families and 1000

stock keeping units 4 production stages with a large

number of multi-purpose production equipment

Campaign production operating in batch mode

Machines

Time

Granulation

Compression

Coating

Packing

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Coating

Packing

Case Study – Problem Description

Online and dynamic characteristics A campaign plan made for long term planning Each week the plant receives new customer orders with requested

delivery date, feedback given to customers with confirmed delivery dates

Final detailed schedule made before production starts

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Integrated Multi-Scale Algorithm

Multi-scale modelling is emerging as an interesting scientific field in process systems engineering

The idea of multi-scale modelling is straightforward: Compute information at a smaller (finer) scale and pass it to a model at

a larger (coarser) scale by leaving out degrees of freedom as moving from finer to coarser scales

Scale 1

Scale 2

Scale N

Removedegrees of freedom

Adddegrees of freedom

Multi-scale modelling

Integrated Multi-Scale Algorithm

Integrated multi-scale approach based on a hierarchically structured framework

Optimisation models to provide support for the relevant decisions at each level

Levels are diverse regarding aggregation, time horizon and availability of information at the time applied

Level3

Level2

Level1

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Continuous moving time frame

Information availability

Available information UncertaintyAggregation

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Aggregation

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Continuous moving time frame

Information availability

Aggregation

Objectives: Campaign planning to fulfil demand and minimize production cost

Input: Combination of sales forecasts and long-term orders, information regarding products, production process, performance and current status,

Output: Campaign plan, raw material procurement plans

Horizon: 12 months

Frequency: Every 3 months

Formulation: MILP - Discrete time and an iterative proced. to improve robustness

12 months

campaigns with different product groups

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Aggregation

Model for level 1

Model for level 1

Forcast errors analysed and a more robust plan obtained with an iterative MILP + LP procedure

Robustness criteria depends on the

required service level

Plan meets robustness

criteria

LPs solved for alternative

demand samples

Demand forecast adjusted

MILP solved for forecasted demand

No

Yes Campaign plan

Demand forecastStatistically generated

demand samples

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Aggregation

Objectives: Simultaneous campaign planning and order scheduling, minimize delays and production cost

Input: Customer orders, information regarding products, production process, performance and current status

Output: Campaign plan, order allocation and confirmed delivery dates

Horizon: 3 months

Frequency: Every week

Formulation: MILP - Discrete time

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Aggregation

3 months

campaigns with different product groups

specific orders

Model for level 2

Objectives: Detailed production scheduling with exact timing of all setup, production and cleaning tasks, minimize delays and production cost

Input: Confirmed customer orders, information regarding products, production process, performance and current status

Output: Detailed production schedule with exact timing of all tasks

Horizon: 1 month

Frequency: Every day

Formulation: MILP - Continuous time

Level3 – Detailed scheduling

Level2 – Campaign planning and order scheduling

Level1 – Campaign planning

0 1 2 3 4 5 6 7 8 9 10 11 12 time

Aggregation

1 month

production tasks within campaigns

campaigns with different product groups

Model for level 3

Integration of levels

Information is transferred between levels with: Hard constraints Bounds on variables Shaping methods Penalty functions

Feasible solutions can still be obtained when the guidelines are violated although they become less optimal

The MIP models become very large in order to fulfil actual industrial requirements

Standard solution methods are insufficient Decomposition heuristics with pre- and post-processing

procedures

Pre-processing

Optimisation with

decomposition heuristics

Post-processing

Formulation – Solution Procedure

subtracts knowledge from data and makes optimisaiton models tractable

improves the solutions

Computational Results

Level Number oforders

Integervariables

Constraints Max computationaltime [CPU seconds]

1 400 41844 52478 31716

2 180 31726 46986 21060

3 70 8817 25344 1062

Full scale test cases based on data collected in the production plant An example of computational results:

Conclusions

There is a need for designing and applying integrated multi-scale procedures for specific types of planning and scheduling problems in the process industry

Benefits: Solutions of improved quality More efficient planning and scheduling process within acceptable

computational time Improved customer service by faster response driven by optimisation

models

Work remains on the robustness procedure at the top level and further testing of the MIA in the factory

Multi-scale Planning and Scheduling Under Uncertain and Varying Demand Conditions in the Pharmaceutical Industry

Hierarchically Structured Integrated Multi-scale Approach

Hlynur Stefansson and Prof. Nilay ShahCentre for Process Systems Engineering Imperial College London