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 Shah
Centre for Process Systems Engineering
Imperial College London
Overview
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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

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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
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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
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
Machines
Granulation
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Time
Time
Integrated Multi-Scale Algorithm
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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
Multi-scale modelling
Scale 1
Scale 2
Add
degrees of
freedom
Remove
degrees of
freedom
Scale N
Integrated Multi-Scale Algorithm
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Integrated multi-scale approach based on a hierarchically
structured framework
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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
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Aggregation
Available information
Uncertainty
Continuous moving time frame
Level1 – Campaign planning
Level2 – Campaign planning and order scheduling
Level3 – Detailed scheduling
0
1
2
3
4
5
66
77
Information availability
88
99
10
10
11
11
12
12
time
time
Model for level 1
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Objectives: Campaign planning to fulfil demand and minimize
production cost
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Input: Combination of sales forecasts and long-term orders, information
regarding products, production process, performance and current status,
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Output: Campaign plan, raw material procurement plans
Horizon: 12 months
campaigns with different product groups
Frequency: Every 3 months
Formulation: MILP - Discrete time and
an iterative proced. to improve robustness
Aggregation
Level1 – Campaign planning
Level2 – Campaign planning and order scheduling
Level3 – Detailed scheduling
0
1
2
3
12 months
4
5
6
7
8
9
10
11
12
time
Model for level 1
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Forcast errors analysed and a more robust plan
obtained with an iterative MILP + LP procedure
Demand forecast
Statistically
generated
demand samples
MILP solved for
forecasted
demand
LPs solved for
alternative
demand samples
Robustness criteria
depends on the
required service level
Plan meets
robustness
criteria
No
Demand forecast
adjusted
Aggregation
Level1 – Campaign planning
Level2 – Campaign planning and order scheduling
Level3 – Detailed scheduling
0
1
2
3
4
5
6
7
8
9
10
11
12
time
Yes
Campaign plan
Model for level 2
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Objectives: Simultaneous campaign planning and order scheduling,
minimize delays and production cost
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Input: Customer orders, information regarding products, production
process, performance and current status
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Output: Campaign plan, order allocation and confirmed delivery dates
Horizon: 3 months
campaigns with different product groups
Frequency: Every week
Formulation: MILP - Discrete time
Aggregation
Level1 – Campaign planning
Level2 – Campaign planning and order scheduling
Level3 – Detailed scheduling
0
1
2
3
3 months
4
5
6
7
8
9
10
11
12
time
specific orders
Model for level 3
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Objectives: Detailed production scheduling with exact timing of all
setup, production and cleaning tasks, minimize delays and production cost
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Input: Confirmed customer orders, information regarding products,
production process, performance and current status
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Output: Detailed production schedule with exact timing of all tasks
Horizon: 1 month
campaigns with different product groups
Frequency: Every day
Formulation: MILP - Continuous time
Aggregation
Level1 – Campaign planning
Level2 – Campaign planning and order scheduling
Level3 – Detailed scheduling
0
1
2
3
1 month
4
5
6
7
8
9
10
11
12
time
production tasks within campaigns
Integration of levels
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Information is transferred between levels with:

Hard constraints
 Bounds on variables
 Shaping methods
 Penalty functions
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Feasible solutions can
still be obtained when
the guidelines are
violated although they
become less optimal
Formulation – Solution Procedure
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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
subtracts knowledge from data and
makes optimisaiton models tractable
Optimisation
with
decomposition
heuristics
Post-processing
improves the solutions
Computational Results
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Full scale test cases based on data collected in the
production plant

An example of computational results:
Level
Number of
orders
Integer
variables
Constraints
Max computational
time [CPU seconds]
1
400
41844
52478
31716
2
180
31726
46986
21060
3
70
8817
25344
1062
Conclusions
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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 Shah
Centre for Process Systems Engineering
Imperial College London