b.ivanov, k.mintchev institute of chemical engineering- bulgarian academy of sciences

B.Ivanov, K.MintchevInstitute of Chemical engineering- Bulgarian academy of sciences

ul. Acad. G.Bonchev, 103, Sofia 1113

Fax: +(359)(2) 8-70-75-23

e-mail: [email protected]

Optimal loading the systems for resource consumption in case of multiproduct and multipurpose batch chemical plants

(theoretical aspects and software realization)

1

The objects which are considering using ECAM to solve the problem about operative management are:

These systems are the most frequently used in :

1. Pharmaceutical industry

2. Fine chemical plants

3. Food industry

4. Paint and varnish manufacturing.

1. Multipurpose batch chemical systems

2. Multiproduct batch chemical systems

3. Manufacture plants including Multiproduct and Multipurpose batch chemical systems, which have shared consumption systems

Steam plant Electricity plant Water

5 Batch size=250kg

Cycle time=15h

1

2

3

4

5

V=5m3

V=8m3

V=12m3

V=15m3

V=15m3

Technology 2

Technology 1

1 Batch size=250kg

Cycle time=15h

Steam plant

Electric plant

Water

4 Batch size=100kg Cycle time=15h





1

2

3

4

5

6

V=5m3

V=8m3

V=12m3

V=15m3

V=15m3

V=5m3

No= Stage 1 Stage 2

Technology 1 S11=0.005

t11=2h

S12=0.09

t12=5h

Technology 2 S21=0.008

t21=7h

S22=0.004

t22=2h

Technology 1 Technology 2






1514132353431

2454341545351

Multipurpose batch chemical systems

1

4

G1 - Planed minimal quantity , which have to be manufactured for product 1

G2 - Planed minimal quantity , which have to be manufactured for product 2

The task of Optimal synthesis of manufacture scheduling is arrived to identify the campaigns, which are participate and working time,

so that the optimal criteria to be satisfied. The criteria are:1. Minimum time duration programm. 2. Maximum profit for planning horizon.

MIN(ts1+tc1+ts2+tc2+...+ ts14+tc14) MAX(P1r + P2r)

(ts1 + tc1 + ts2 + tc2 + . . . + ts14 + tc14) < H

In case of performed the constraints :

G1r > G1) G2r > G2)

Service time

S1

ts1

Service time

S2

ts1

Service time

S14

ts14

Campaign 1

tc1



Campaign 2

tc2



Campaign 14

tc14



H - Planning period /horizon/

Production scheduling model

Loading the consumption systems in case of manufacture campaigns

Steam plant

Electric plant

Water


1

2

3

4

5

6V=5m3

V=8m3

V=12m3

V=15m3

V=15m3

V=5m3

Technology 1 Technology 2


No= Stage 1 Stage 2

Tehnology 1 S11=0.005 t11=2h S12=0.09 t12=5h

Tehnology 2 S21=0.008 t21=7h S22=0.004 t22=2h

Optimal wait time after each batch

Optimal batch sizeOptimal start time of manufacture

Optimal loading of steam station in case of simultaneous work of two

manufacture5

7

Steamplant

Electricplant

Water


1

2

3

4

5

V=5m3

V=8m3

V=12m3

V=15m3

V=15m3

Technology 2

Technology 1


iproduktjstageforpprocespawrepijp ..............

iproductofjstageinpprocessofdurationtijp ............. .

1. Data Let be introduced the following sets:

Set I{i1,i2,…,iN} set of productsSet J{j1,j2,…,jN} set of stagesSet P{p1,p2,…,pJ} set of processes

Also the following data are known:

Mathematical formulation of the problem DATA

Stage duration can be calculated for each stage each product

JjIittp

ijpij ,for

The required demand for each product per a horizon H.

IiGi for

Time horizon H.The cycle time can be calculated for each product

Expression for connecting:

PpJjIiFt tijpijp ,,for )(Bi

PpJjIiFp pijpijp ,,for )(Bi

Max or Min batch size can be calculated for each product

IiBMINi for IiBMAXi for

IiX i for

IiSi for

Mathematical formulation of the problem CONTINUOUS VARIABLES

1. Shifting time for the entire product

These variables present the time of shifting the beginning of each product with regard the horizon beginning.

2.The waiting time between different batches

3. Batch size

IiBi for

The batch size for each product could be changed in the pointed upper and lower boundaries determined from the technologies. These variables

affect on the power of energy consumption and/or the time of waiting between batches.

IiBBB MAXii

MINi for

Ii

N

t

Si

ijj

i for

.N-H

0maxi

Mathematical formulation of the problem CONSTRAINTS

The following constraints are introduced:

1.The batch size constraints:

2.The waiting time between different batches

IiBi

for

GN i

iWhere Ni present the minimum batch numbers that must be manufactured into a time horizon H.

3.The products shifting time constraints

IiSijX i

j

i t

for 0 max

4. The production constraints

IiB

GG

i

ii

for .Bi

5. The horizon constraints

IiSij i

j

t

for H

B

G.

i

imax

6. Energy consumption constraints for simultaneous manufacturing of products

IiSP ii

consti for P )( MAX

Mathematical formulation of the problem Mathematical model of energy consumption

The energy consumption curve for each stage of given product can be written, by using the Fourier transformation as:

PpJjIiXtSt

k

XtSt

ktBX

iii

iii

ii

,,for )(

2cosB

)(

2sinA

2

A,,,SP

kmax

kijp

kmax

kijp

0ijp

iijp

Where:

PpJjIi ,,for A0ijpPpJjIi ,,for Ak

ipj PpJjIi ,,for Bkijp

PpJjIittpFj

jijpijpijp

,,for ,,A1

10

0ijp

PpJjIittpKFj

jijpijpijpA

,,for ,,,A1

1

kijp

PpJjIittpKFj

jijpijpijpB

,,for ,,,B1

1

kijp

are the respective Fourier coefficients for the function distributing stage j o product I. These coefficients are introduced for the cases when the energy

consumption has the constant power as it was shown on the pictures.


Based on the Fourier transformation of the functions of energy consummationswe are able to present the following functions.

1. Energy consumption of stage j of product I

JjIitBXBtBX iiiconst

ii ,for ,,,SP,SP,,,SP ivar

ijiijiij

JjIiBp

iconstij ,for

2

A,SP

0ijp

iWhere:

JjIi

XtSt

k

XtSt

k

tBXp

iii

iii

ii

,for

)(

2cosB

)(

2sinA

,,,SP

kmax

kijp

kmax

kijp

ivar

ij

2. Energy consummation of product I:

IitBXBtBX iiiconst

ii for ,,,SP,SP,,,SP ivar

iiiii

IiBBj

iconst

iconst for ,SP,SP iijii

IitBXtBXj

iiii for ,,,SP,,,SP ivar

ijivar

i

Where:


3. Energy consumption of entire campaign:

,,,SPBS,P,,,SP var tBXtBX const

,SPBS,P iii

constconst B

,,,SP,,,SP ivar

ivar

iii tBXtBX

Where:

The constant part of the power of energy consumption distribution in case of simultaneous product processing presents the ideal case that must be reached.

The variable parts of the above functions present the variation of the real curve around the ideal one. For the variable parts the following is valid:

0,,,SPH

0

var dttBX

dttBXJH

0

var ,,,SPmin

dttBXtBXsignJH

0

varmaxvarmax ,,,SP-P,,,SP-Pmin

Mathematical formulation of the problem

Objective function

Case1. The minimum variation of the real curve with regard to the ideal one to be ensured.

Case 2. The minimum of energy consumption over the given determined in advance level of energy consumption.

Case 3. Maximum profit of the product manufacturing

i

iii BNCJ max

The offered software package is created on the base of original author’s methods published in international journals. Its present version uses MATLAB 6.5 and is adopted for WINDOWS-XP.

1

The software package ECAM solves two main problems:

1.Control problem - for a group of compatible batch products

2.Simulation problem - for such of product group aiming to determine load parameters of resources supply systems.

ECAM could be used for investigation of different manufacturing states and as well as for evaluation the affect of energy integration processes on the resources supply systems. Thus, the technology changes could be properly assessed that provides opportunities for creation of proper production schedules ensuring optimal load of resources supply systems.

2

Main principles during the build up of ECAM

• The menus principle is used • The principle of choices the data is used so

that the human mistakes be reduced. • Logical control about correctness the data• The results are visualized• All functions consist of subsidiary information

ECAM working under Windows’XP area• “Matlab 6.50” is used to build up the product

7

Exit programme

Help InformationAbout authors

RUN PROGRAMME

6

After activating (push the button ) the necessary information

(data base) is charged in the operative memory (RAM).

ECAM is started.

Information about authors and description of the theoretical base in which ECAM is made of.

Information gives a detailing account about different task classes and objects in which ECAM can be used.

INPUT DATA BATCH PLANTSINPUT DATA TECHNOLOGY

INPUT DATA CAMPAIGNOPTIMAL

SHEDULINGVIZUALIZATION OF SHEDULING

PRINT SHEDULING

Module for creation a date base for a production system.

It ensures a proper description of the existing plant units and connection between them

Module for creation a date base for technologies.

It ensures description of different technologies available

For processing in the plant.Module for automatically generation or customization of production campaign (group of compatible products) available to fulfill a given production demands.

Module for formulation of different classes controlling problems.

It involves definition of criteria for optimal control and set of constraints.Module for graphical interface for visualization the results obtained under optimal scheduling of campaign.

Module for formulation of different classes controlling problems.

It involves definition of criteria for optimal control and set of constraints.

7

8

Data for the apparatus and connection between each other in material flow.

Charging the data base about existing apparatus and connection between them.

1.Short name of plant.2.Full name of plant.3.Number of apparatus in Data Base.Visualization of apparatus which include:

-short name of apparatus;-image of apparatus;-basic characterizations;-image of type apparatus;Creation the new connect or imaging of

the existing connects between apparatus.

Rule buttons:-add new apparatus;-delete the apparatus;-edit data base of current apparatus;-save data base of current apparatus;-exit form this module;-help.

9

Data technology.

Buttons which charge data base of chosen technology:-number of stages;-obtainable profit for unit product.Description the data for each stage of

technology:-name of stages;-time of stage;-size factor;-type of apparatus.

Information about resources:-quantity of each resourcerequired to one unit final product;-apportionment of resources in time;-consumption quantity for the stage.

Rule buttons:-add new apparatus;-delete the apparatus;-edit data base ;-save data base ;-exit form this module;-help.

10

Rule module for synthesis tasks of production variants and campaign.

Generation of given technology.Calculating available disposing in a given technology and parameters which are consist of:-Minimum batch size;-Maximum batch size;-Cycle time;-Minimum available manufacturing quantity;-Maximum available manufacturing quantity;

Manuel generation campaign;Design of manufacturing campaigns which a determinate group of manufacture.The program gives possibility to define the stages of each apparatus on given manufacture.After successful defining of all stages and manufactures the next step is to calculate evaluation of each variant which are included in given campaign.

Automatically generation campaign maximum lengthDefine the available manufacturing campaign , each one consist of :-maximal number manufactures which the manufacture program is made of.For obtainable manufacture campaign evaluate are given and also the variants of every manufacture which are included in relevant campaign.

Automatically generation sets full campaign Define maximal number of campaign in case that the manufacture are given.For each variant of manufacture campaign variant which are consist of are given.

11

Define the variants of disposing of given technology

Lead in the data base of technology: -Short name of technology;-Full name of technology;-Number of stages.

Lead in the data base about planning horizon.

Lead in the data base about production demand: -Minimum demand of product;-Normal demand of product;-Maximum demand of product;

Lead in the data base about work regime:-Whit overlapping the cycle;-Without overlapping the cycle.

Define the variants in case of given data base.

Rule buttons:-delete the technology;-edit data technology ;-save technology to data base ;-exit form this module;-print variant;-help.

List of apparatus which are disposing on every stage of technology of considering variant.That also include information about:-Maximum batch size;-Minimum batch size;-Cycle time;

-Maximal and minimum product demand.

12

Design the manufacturing campaign from the customer.

Read the campaigns data base

Choise the existing campaign from data base or lead in the data for new one. Choise of relevant product who will be

manufactured simultanuasly in campaign. Lead in the stage into relevant apparatus.

Choise tha apparatus in which the stage will carry out.

Vizualization of apparatus in which the stage will carry out.

Output information about the campaign:-Maximum batch size;-Minimum batch size;-Cycle time whitout overlapping;-Cycle time whit overlapping;

Rule buttons:-add new campaign;-delete campaign;-edit data base;-save to data base;-exit;-help.

13

Synthesis of variants of campaigns with relatable size to number of manufacture which are included in a plan.

Lead in the data base of existing manufacture plan or including the new one. Choice the regime of manufacture:

-With overlapping the cycle or without overlapping the cycle;-Production demand for the product:

-minimum product quantity;-normal product quantity;-maximum product quantity;

-Include the planning horizont.

Calculating the all available campaigns which are consist of the maximum number manufacture working at the same time.

Output information about obtained variant of campaign:-list of apparatus which have to placed in relevant stage-basic characterization:

-maximum batch size, minimum batch size;-cycle time;-maximum demand,minimum demand;-maximum number of variants.

Rule buttons:-delete campaign;-edit data base of given campaign;-save to data base;-exit;-help.

Synthesis of maximal number independent campaigns.

14

Lead in the data base of existing manufacture plan or including the new one. Choice the regime of manufacture:-With overlapping the cycles or without overlapping the cycles;-Production demand for the product:

-minimum product quantity;-normal product quantity;-maximum product quantity;

-Include the planning horizon.

Calculating the all available campaigns which are consist of the maximum number manufacture working at the same time.

Generalize information of found campaign,Gives the maximum number of in depended campaign.


Output the result of procedure of synthesis of maximal number independent campaigns in given manufacture plan.

15

Output the obtained results for given variants of campaign.

Choice the manufacture variant included in given campaign which will be show on.

List of apparatus in which have to placed the relevant stages.


Module explaining different optimizing tasks.

16

Optimal use of resource.Optimal sheduling for given variant of canpaign-one criteria formulation.Optimal use of resource.Optimal sheduling for full variant of canpaign.One criteria formulation.Optimal scheduling.Optimal scheduling with possible one criteria.1.Minimum time poduction plane.2.Maximum profit.Restriction:1.Minimum demand;2.Minimum resource.

Optimal use of resource.Optimal sheduling for given variant of canpaign.Multicriteria formulation.

Optimal use of resource.Optimal sheduling for full variant of canpaign.Multicriteria formulation.

Optimal scheduling.Optimal scheduling multicriteria formulation.1.Minimum time production plane.2.Maximum profit.Restriction:1.Minimum demand;2.Minimum resource.

Optimal loading the system. /formulation the task/

17

Read the data base for existing plans and available campaign.

Choise the variant of campaign who will search optimal rule, in case of choosen criteria and defineded restrictions. Define the planning horizon in which a given

campaign have to be done. Define the quantity demand of each product.

Define the optimization criteria for chosen campaign who consist of:-resource for optimization;-choice the regime:

-variation-constant

Define the restrictions which are consist of:-restrictions about another resources;-minimum and maximum quantity in case of constant;-minimum and maximum quantity in case of variation.Start the optimization procedure

Output the results:-included technologies;-optimal start time;-optimal wait time;-optimal batch size.Of each manufacture

Optimal loading the system in case of given manufacture program.

18

Read the data base for existing plans and available campaign.

Choise the variant of campaign who will search optimal rule, in case of choosen criteria and defineded restrictions. Define the planning horizon in which a given

campaign have to be done. Define the quantity demand of each product.

Define the optimization criteria for chosen campaign who consist of:-resource for optimization;-choice the regime:

-variation-constant

Define the restrictions which are consist of:-restrictions about another resources;-minimum and maximum quantity in case of constant;-minimum and maximum quantity in case of variation.Start the optimization procedure

Output the results:-included technologies;-optimal start time;-optimal wait time;-optimal batch size.Of each manufacture

Optimal loading the system in case of given manufacture program.

Output the optimal parameters of each

campaign which are consist of: -Service time;-Time duration campaign;-List of manufacture included in campaign;-Start times;-Wait time;-Cycle time;-Optimal batch size;-Optimal batch number;-Quantity which are manufactured during campaign.

Lead in the nesesary information which are consist of:-DB for existing plants;-Planning horizon;-Production demands for each product;-Optimization criteria;-Restrictions.

20

Visualization of obtainable scheduling.

19

Read data of manufacture plan.

Input the number of campaign

Choice the resource

Choice the solution which have to be vizualizated

Visualization the sum consumption curve of chosen resource in case of simultaneous working of all productions in given campaign.

The average curve of loading

The real curve of loading

Summarize data :-variation;-max pic;-min pic

Choice the production of given campaign

Choice the resource for visualization

The average curve of loading

The real curve of loading

Summarize data :-Batch size;-Start time;-variation;-wait time;-constant production;-horizon

Manual input the data :-Batch size;-Start time;-wait time;-horizon

Thank you for your attention

b.ivanov, k.mintchev institute of chemical engineering- bulgarian academy of sciences

Documents

cycle time

batch sizethe batch

15h1 batch size

15h2 batch size

waiting time

5m34 batch size

10h3 batch size

12h5 batch size