1. B.Ivanov, K.Mintchev Institute of Chemical engineering- Bulgarian academy of sciences ul. Acad. G.Bonchev, 103, Sofia 1113 Fax: +(359)(2) 8-70-75-23 e-mail: bivanov@bas.bg Optimal loading the systems for resource consumption in case of multiproduct and multipurpose batch chemical plants (theoretical aspects and software realization)

2. 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 plantWater 5 Batch size=250kg Cycle time=15h 1 2 3 4 5 V=5m 3 V=8m 3 V=12m 3 V=15m 3 Technology 2 Technology 1 1 Batch size=250kg Cycle time=15h

3. Steam plant Electric plant Water 4 Batch size=100kg Cycle time=15h 1 Batch size=80kg Cycle time=10h 3 Batch size=150kg Cycle time=15h 2 Batch size=70kg Cycle time=12h 5 Batch size=250kg Cycle time=15h 1 2 3 4 5 6 V=5m 3 V=8m 3 V=12m 3 V=15m 3 V=5m 3 No=Stage 1Stage 2 Technology 1S 11 =0.005 t 11 =2h S 12 =0.09 t 12 =5h Technology 2S 21 =0.008 t 21 =7h S 22 =0.004 t 22 =2h Technology 1Technology 2 4 Batch size=250kg Cycle time=15h 5 Batch size=250kg Cycle time=15h 3 Batch size=250kg Cycle time=15h 1 Batch size=250kg Cycle time=15h 2 Batch size=250kg Cycle time=15h 15 1 4 1 3 2 35 34 3 1 2 45 43 4 1 54 53 5 1 Multipurpose batch chemical systems 1

4. 4 G 1 - Planed minimal quantity, which have to be manufactured for product 1 G 2 - 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(t s1 +t c1 +t s2 +t c2 +...+ t s14 +t c14 )MAX(P 1r + P 2r ) (t s1 + t c1 + t s2 + t c2 +... + t s14 + t c14 ) < H In case of performed the constraints : G 1r > G 1 )G 2r > G 2 ) Service time S1 t s1 Service time S2 t s1 Service time S14 t s14 Campaign 1 t c1 5 Batch size=250kg Cycle time=15h 1 Batch size=250kg Cycle time=15h Campaign 2 t c2 4 Batch size=100kg Cycle time=15h 1 Batch size=250kg Cycle time=15h Campaign 14 t c14 1 Batch size=80kg Cycle time=10h 5 Batch size=250kg Cycle time=15h H - Planning period /horizon/ Production scheduling model

5. Loading the consumption systems in case of manufacture campaigns Steam plant Electric plant Water 5 Batch size=250kg Cycle time=15h 1 2 3 4 5 6 V=5 m 3 V=8m 3 V=12m 3 V=15m 3 V=5m 3 Technology 1Technology 2 1 Batch size=250kg Cycle time=15h No=Stage 1Stage 2 Tehnology 1S 11 =0.005 t 11 =2hS 12 =0.09 t 12 =5h Tehnology 2S 21 =0.008 t 21 =7hS 22 =0.004 t 22 =2h Optimal wait time after each batch Optimal batch size Optimal start time of manufacture Optimal loading of steam station in case of simultaneous work of two manufacture 5

6. 7 Steam plant Electric plant Water 5 Batch size=250kg Cycle time=15h 1 2 3 4 5 V=5m 3 V=8m 3 V=12m 3 V=15m 3 Technology 2 Technology 1 1 Batch size=250kg Cycle time=15h

7. 1. Data Let be introduced the following sets: Set I{i1,i2,…,iN}set of products Set J{j1,j2,…,jN}set of stages SetP{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 The required demand for each product per a horizon H. Time horizon H. The cycle time can be calculated for each product Expression for connecting: Max or Min batch size can be calculated for each product

8. 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 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.

9. Mathematical formulation of the problem CONSTRAINTS The following constraints are introduced: 1.The batch size constraints: 2.The waiting time between different batches Where Ni present the minimum batch numbers that must be manufactured into a time horizon H. 3.The products shifting time constraints 4. The production constraints5. The horizon constraints 6. Energy consumption constraints for simultaneous manufacturing of products

10. 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: Where: 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.

11. Mathematical formulation of the problem Mathematical model of energy consumption 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 Where: 2. Energy consummation of product I: Where:

12. Mathematical formulation of the problem Mathematical model of energy consumption 3. Energy consumption of entire campaign: 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:

13. 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

14. 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.

15. 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

16. 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

17. Exit programme Help Information About 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.

18. INPUT DATA BATCH PLANTS INPUT DATA TECHNOLOGY INPUT DATA CAMPAIGN OPTIMAL SHEDULING VIZUALIZATION 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

19. 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.

20. 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 resource required 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.

21. 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 length Define 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.

22. 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.

23. 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.

24. 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.

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

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

27. 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.

28. 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

29. 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

30. 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

31. 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

32. Thank you for your attention