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OR Spectrum

, Volume 31, Issue 1, pp 141–166 | Cite as

MILP-based campaign scheduling in a specialty chemicals plant: a case study

  • Marcus Brandenburg
  • Franz-Josef Tölle
Regular Article

Abstract

Supply chain management in chemical process industry focuses on production planning and scheduling to reduce production cost and inventories and simultaneously increase the utilization of production capacities and the service level. These objectives and the specific characteristics of chemical production processes result in complex planning problems. To handle this complexity, advanced planning systems (APS) are implemented and often enhanced by tailor-made optimization algorithms. In this article, we focus on a real-world problem of production planning arising from a specialty chemicals plant. Formulations for finished products comprise several production and refinement processes which result in all types of material flows. Most processes cannot be operated on only one multi-purpose facility, but on a choice of different facilities. Due to sequence dependencies, several batches of identical processes are grouped together to form production campaigns. We describe a method for multicriteria optimization of short- and mid-term production campaign scheduling which is based on a time-continuous MILP formulation. In a preparatory step, deterministic algorithms calculate the structures of the formulations and solve the bills of material for each primary demand. The facility selection for each production campaign is done in a first MILP step. Optimized campaign scheduling is performed in a second step, which again is based on MILP. We show how this method can be successfully adapted to compute optimized schedules even for problem examples of real-world size, and we furthermore outline implementation issues including integration with an APS.

Keywords

Supply chain management Campaign planning and scheduling Chemical process industry MILP Advanced planning systems 

Abbrivation

Master data/problem parameters

 

F

Set of facilities

fF

Facility

P

Set of products

pP

Product

A

Set of processes

aA

Process

\({A_f \subseteq A}\)

Set of processes that can be operated on a facility fF

\({F_a \subseteq F}\)

Set of facilities that can operate process aA

za, f

Cycle time of process aA operated on facility fF

ba, f

Batch size of process aA operated on facility fF

apA

Unique process (apart from refinement) that produces product pP

\(P_a^-\), \(P_a^+\subseteq P\)

Set of input, output products of process aA

δa,p and δa,p+

Input, output amounts of product pP for process aA (fractions of batch size b a,f )

Bp = (Ap, Pp, Fp)

Formulation of product pP

\(P_p =\cup_{p\in A_p} P_a^+\)

Set of output products of the processes in A p

Ap

Processes that have to be operated to produce product pP

\(F_p = \cup_{a\in A_p} F_a\)

Set of facilities on which processes of A p can be operated

sta,a'

Duration of the set up activity required between processes a, a'A

\({R \subseteq A}\)

Set of processes which have the refinement property

p*

Off spec product

a*

Refinement process

R*

Set of refinement processes

Transactional data/Instance parameters

 

E

Set of order elements

εE

Order element

πε

Product ordered by order element εE

qε

Order quantity of order element εE

tε

Due date of order element εE

c

Production campaign

ts

Starting time of a campaign

tc

Completion time of a campaign

n

Number of batches of a campaign (“campaign size”)

v

Set up indicator of a campaign (\(v = 1 \Leftrightarrow \) set up activity is performed before campaign c starts)

Cε

Set of all campaigns linked to order element εE (“campaign chain”)

Cε*

Set of all possible campaign chains for order element εE

i(p,t)

Inventory level for product pP at time t≥ 0

tf

Earliest availability date of facility fF

Feasible solution

 

T

Vector of earliest availability times i(t f ) fF

I

Set of initial inventory levels {i(p,0) | pP}

S

Schedule

Algorithm 1

Bπ

Formulation for product π ∈ P

lp

Manufacturing level of product pP

la

Manufacturing level of process aA

lmax

Maximum manufacturing level of all processes aA π

Fε

Set of all possible facility combinations for order εE

Fiε

Set of i-th possible facility combination for order εE

Algorithm 2

ip

Algorithm parameter

ipmin

Algorithm parameter

αn

Algorithm parameter

na

Algorithm parameter

MILP 1

x > (Ci)

Selection indicator for campaign \( C^i \in C_\epsilon\)

w

Workload variable

Algorithm 3

wc,c'

Minimum delay times between campaigns c, c′ ∈ C ε

γk

Algorithm parameter

MILP 2

ts, ts′ ≥ 0

Starting times of campaigns \(c, c'\in \cup_{\epsilon\in E} C_\epsilon\)

tc, tc′ ≥ 0

Completion times of campaigns \(c, c'\in \cup_{\epsilon\in E} C_\epsilon\)

αε ≥ 0

Lateness of order εE

xc,c' ∈ {0, 1}

Sequence indicator

m ≥ 0

Timespan

hc(X)

Holding cost for products in \({X\subseteq P}\)

tc(ε)

Lateness cost of demand element εE

sca,a'

Cost for set up activity between processes a,a′ ∈ A

mc

Timespan cost

T

Duration of all campaigns in the schedule \( T = \sum_{\epsilon \in E}\sum_{c\in C_\epsilon} n\cdot z_{a,f} \)

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Beiersdorf AGHamburgGermany
  2. 2.Bayer Business Services GmbHLeverkusenGermany

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