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A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

  • Nikolaos Rakovitis
  • Nan Zhang
  • Jie LiEmail author
  • Liping Zhang
Open Access
Research Article
  • 13 Downloads

Abstract

The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

Keywords

scheduling multipurpose batch processes simultaneous transfer mixed-integer linear programming 

Nomenclature

Task-specific event-based model Indices

i,i′

tasks

j,j′

units

n,n′, n″

event points

s

states

Sets

I

tasks

Ij

tasks that can be performed in unit j

ISC

tasks that consume state s

ISP

tasks that produce state s

IR

tasks considered as recycling tasks

J

units

N

event points

S

states

SFP

states that are final products

SIN

states that are intermediate products

SR

states that are raw materials

Parameters

Bimax

maximum batch size that can be processed in task i

Bimin

minimum batch size that can be processed in task i

DS

demand of state s

H

scheduling horizon

ps

price of state s

αi

coefficient of constant term of processing time of task i

βi

coefficient of variable term of processing time of task i

Δn

maximum number of event points that task i is allowed to be active

ρi,s

portion of state s consumed/produced by task i

Binary Variables

wi,n,n

binary variable which takes the value 1 if task i starts at time event point n and finishes at time event point n⩾ n.

Continuous Variables

bi,n,n}′

batch size of task i that is active from time event point n to time event point n′ ⩾ n

ST0s

initial amount of state s (sSR)

STs,n

excess amount of state s that needs to be stored at time event point n

Ti,nf

finish time of task i at time event point n

Ti,ns

start time of task i at time event point n

Unit-specific event-based model Indices

i,i′

tasks

j,j′

units

n,n′,n″

event points

s

states

Sets

I

tasks

Ij

tasks that can be performed in unit j

ISC

tasks that consume state s

ISP

tasks that produce state s

IR

tasks considered as recycling tasks

J

units

N

event points

S

states

SFP

states that are final products

SIN

states that are intermediate products

SR

states that are raw materials

Parameters

Bi,jmax

maximum batch size of task i processed in unit j

Bimin

minimum batch size of task i processed in unit j

DS

demand of state s

H

scheduling horizon

ps

price of state s

αi,j

coefficient of constant term of processing time of task i in unit j

βi,j

coefficient of variable term of processing time of task i in unit j

Δn

maximum number of event points that task i is allowed to be active

ρi,j,s

portion of state s consumed/produced by task i processed in unit j

Binary variables

wi,j,n,n

binary variable which takes the value 1 if task i is processed in unit j from time event point n to time event point n

Continuous variables

bi,j,n,n′

amount of materials that are processed in unit j processing task i from time event point n to time event point n′ ⩾ n

STs,n

amount of state s that has to be stored at time event point n

Tj,ns

start time of unit j at time event point n

Tj,nf

end time of unit j at time event point n

Ti,j,ns

start time of task i in unit j at time event point n

Ti,j,nf

end time of task i in unit j at time event point n

Notes

Acknowledgements

Nikolaos Rakovitis would like to acknowledge financial support from the postgraduate award by The University of Manchester. Liping Zhang appreciates financial support from the National Natural Science Foundation of China (Grant No. 51875420).

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© The Author(s) 2019

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Authors and Affiliations

  • Nikolaos Rakovitis
    • 1
  • Nan Zhang
    • 1
  • Jie Li
    • 1
    Email author
  • Liping Zhang
    • 2
  1. 1.Centre for Process Integration, School of Chemical Engineering and Analytical ScienceThe University of ManchesterManchesterUK
  2. 2.Department of Industrial Engineering, School of Machinery and AutomationWuhan University of Science and TechnologyWuhanChina

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