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

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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.

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Abbreviations

Master data/problem parameters:

 

F :

Set of facilities

f ∈ F :

Facility

P :

Set of products

p ∈ P :

Product

A :

Set of processes

a ∈ A :

Process

\({A_f \subseteq A}\) :

Set of processes that can be operated on a facility f ∈ F

\({F_a \subseteq F}\) :

Set of facilities that can operate process a ∈ A

z a, f :

Cycle time of process a ∈ A operated on facility f ∈ F

b a, f :

Batch size of process a ∈ A operated on facility f ∈ F

a p ∈ A :

Unique process (apart from refinement) that produces product p ∈ P

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

Set of input, output products of process a ∈ A

δ − a,p and δ + a,p :

Input, output amounts of product p ∈ P for process a ∈ A (fractions of batch size b a,f )

B p = (A p , P p , F p ):

Formulation of product p ∈ P

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

Set of output products of the processes in A p

A p :

Processes that have to be operated to produce product p ∈ P

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

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

st a,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

ε ∈ E :

Order element

π ε :

Product ordered by order element ε ∈ E

q ε :

Order quantity of order element ε ∈ E

t ε :

Due date of order element ε ∈ E

c :

Production campaign

t s :

Starting time of a campaign

t c :

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)

C ε :

Set of all campaigns linked to order element ε ∈ E (“campaign chain”)

C * ε :

Set of all possible campaign chains for order element ε ∈ E

i(p,t):

Inventory level for product p ∈ P at time t≥ 0

t f :

Earliest availability date of facility f ∈ F

Feasible solution:

 

T :

Vector of earliest availability times i(t f ) f ∈ F

I :

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

S :

Schedule

B π :

Formulation for product π ∈ P

l p :

Manufacturing level of product p ∈ P

l a :

Manufacturing level of process a ∈ A

l max :

Maximum manufacturing level of all processes a ∈ A π

F ε :

Set of all possible facility combinations for order ε ∈ E

F i ε :

Set of i-th possible facility combination for order ε ∈ E

i p :

Algorithm parameter

i min p :

Algorithm parameter

α n :

Algorithm parameter

n a :

Algorithm parameter

x > (C i):

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

w :

Workload variable

w c,c' :

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

γ k :

Algorithm parameter

t s , t s ′ ≥ 0:

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

t c , t c ′ ≥ 0:

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

α ε ≥ 0:

Lateness of order ε ∈ E

x c,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 ε ∈ E

sc a,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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Authors and Affiliations

  1. Beiersdorf AG, Unnastr. 48, 20245, Hamburg, Germany

    Marcus Brandenburg

  2. Bayer Business Services GmbH, 51368, Leverkusen, Germany

    Franz-Josef Tölle

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  1. Marcus Brandenburg
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  2. Franz-Josef Tölle
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Correspondence to Marcus Brandenburg.

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Brandenburg, M., Tölle, FJ. MILP-based campaign scheduling in a specialty chemicals plant: a case study. OR Spectrum 31, 141–166 (2009). https://doi.org/10.1007/s00291-007-0084-5

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