Abstract

The idea of cyclic scheduling is commonly utilized to address short-term scheduling problems for multiproduct batch plants under the assumption of relatively stable operations and product demands. It requires the determination of optimal cyclic schedule, thus greatly reducing the size of the overall scheduling problems with large time horizon. In this paper a new cyclic scheduling approach is proposed based on the state-task network (STN) representation of the plant [Comput. Chem. Eng. 17 (1993) 211] and a continuous-time formulation [Ind. Eng. Chem. Res. 37 (1998a) 4341]. Assuming that product demands and prices are not fluctuating along the time horizon under consideration, the proposed formulation determines the optimal cycle length as well as the timing and sequencing of tasks within a cycle. This formulation corresponds to a non-convex mixed integer nonlinear programming (MINLP) problem, for which local and global optimization algorithms are used and the results are illustrated for various case studies.

Author Keywords: Cyclic scheduling; Continuous-time formulation; MINLP

Nomenclature

i

tasks

j

units

n

event points representing the beginning of a task

s

states

I

tasks

I_j

tasks which can be performed in unit j

I_s

tasks which produce or consume state s

IS

subset of all involved intermediate states s

J

units

J_i

units which are suitable for performing task i

N

event points within the time horizon

S

set of all involved states s

price_s

price of state s

r_s

average market requirement for state s

ST_s^max

available maximum storage capacity for state s

U

upper bound of cycle time length

V_ij^max

denotes the maximum capacity of unit j when processing task i

V_ij^min

denotes the minimum amount of material processed by task i required to start operating unit j

α_ij

constant term of processing time of task i at unit j

β_ij

variable term of processing time of task i at unit j expressing the time required by the unit to process one unit of material

ρ_si^p,ρ_si^c

proportion of state sproduced, consumed from task i, respectively

B(i,j,n)

amount of material undertaking task i in unit j at event point n

d(s,n)

amount of state s being delivered to the market at event point n

H

time horizon for a single cycle

ST(s,n)

amount of state s stored at event point n

STIN(s)

amount of state s imputed initially

T^f(i,j,n)

time when task i, which starts at event point n finishes in unit j

T^s(i,j,n)

time when task i starts in unit j at event point n

wv(i,n)

binary variables that assign the beginning of task i at event point n

yv(j,n)

binary variables that assign the utilization of unit j at event point n

Article Outline

Nomenclature

1. Introduction

2. Basic concepts of the proposed approach

2.1. Scheduling problem

2.2. Periodic scheduling approach

2.3. Continuous-time approach

3. Motivating example

4. Proposed formulation

4.1. Mathematical model

4.2. Scheduling problem decomposition

5. Case studies

5.1. Results of motivating example

5.2. Results of example 1

5.3. Results of example 2

6. Conclusions and future directions

Acknowledgements

References

Corresponding author. Tel.: +1-732-445-2971.

¹ Tel.: +1-732-4457061; fax: +1-732-4452421.