Schedule Planning Proceeding of Transfer Batches in Flexible Automated Lines While Sets are Forming and Limits are Recognized

The hierarchical approach while solving the problem of complex scheduling of transferred batches of units using flexible transfer lines is considered, when sets and time limits of flexible transfer lines are formed. Mathematical model of hierarchical game to optimize a mixture of transferred batches is developed. The groups of sets are processing during time intervals of definite lengths. The schedules of batches of units are optimized, using the mathematical model. The way of optimizing a mixture of groups of sets while resulting batches are formed, is developed. The output in high-mixed productions recognizes the processing of transferred batches (TB) using Flexible Automated Lines (FAL). The FALs are made as a sequence of flexible technological places (FTP). Each FTP can be rearranged to process different type of units. The increasing of effectiveness is associated with a scheduling planning problem. The result of such problem solving is a project schedule of FAL activity. The input of this task is an industrial program formed by Enterprise’s Automatic Control System (ASC). The ASC gets a set of items to be processed if FAL. The unified items (units) are the units with the same processing time intervals. The time intervals to rearrange the FTP are equal. The time intervals, used to rearrange the FTP to proceed these types of items are equal, too. While time intervals of processing and rearranging FTP are inhomogeneous enough, the effectiveness of scheduling depends on the mixture of transferred batches. In such case the planning of TB assumes the set of batch and the schedule of processing using FAL is considered [1]. The problem of complex processing schedule of TS using FAL while the sets of items are formed and the time limits of FAL acting is developed. The set if items is a set of different kinds of items which are processed in FAL. The number of items of each kind which are included in a set, is preset. The ASC program gets a number of each kind of sets and the time intervals to process a set of batches using FAL. Hierarchical approach is used to solve a problem [1]. It considers to decompose the generalized function in decision support system of FAL. The function if decomposed to a set of sub-functions, which are hierarchically ordered. The problem solving is implemented using the hierarchical levels: – the first (upper) level – defines of solutions of structure TB; * Corresponding author: krotov_k1@mail.ru MATEC Web of Conferences 346, 03094 (2021) ICMTMTE 2021 https://doi.org/10.1051/matecconf /202134603094 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). – the second level – defines the solutions of groups of TB, which are proceed during the given time intervals; – the third level – defines the schedule of TB processing, using FAL for solutions of groups of TB is formed on the second level. To solve a problem of scheduling while sets are proceed and batches are formed, using time interval limits, some subtasks need to be made. The subtasks are: to define of structure TB; to define of structure of groups of TBs, which are proceed, using given time intervals; to define schedules of TBs processing using FAL; to allocate the items, proceed using FAL during given time interval to sets. The modern ways of complex schedules of processing of batches in multi-stage systems (FAL, in particular case), are realizing the scheduling of sets of materials, which are proceeding in non-stop (continuous) productions [2,3]. The ways can define the order of definite batches implementations [4,5] and realize the decisions of a party set and the order of operations using one or several parallel devices [6,7]. The review of articles defines there are no ways to form a structures of TBs in multi-stage systems, when problem order is unlimited. There are no ways to determine a structures of TBs while the sets are formed. There are no ways to solve a scheduling problem, when the time intervals of FAL activity are limited. The purpose of the research is to improve the ways of complex scheduling of TBs proceeding in FAL. The hierarchical game model is developed to solve the problem. Using such a game defines the structures of batches, the structures of groups of batches and the schedule of processing them using FAL; the initial solve of structures of TB and an optimized groups of TB is defined too. The scheduling is realized by three-levels formed solving. The first-level gamer is forming the structures of TB. The second-level gamer is forming the groups of TBs, the third-level gamer is forming the scheduling of groups of TBs processing. The order of the players’ moves is: 1) the first move does the first-level gamer; he defines the structures of TBs and gives the decision to down-sided level; 2) the second move does the second-level gamer; he forms the structures of the groups of batches and gives the decision to the third level;. 3) the third-level gamer makes a decision of the groups of batches scheduling, using FTPs; later the decision is given to the second level to analyze the groups of batches optimality; 4) the second-level gamer takes the groups of batches schedules; he allocates the items from to sets and defines the optimality of the batches of such groups. Steps (2-4) are made, while the best decision of the groups structures is not formed; such decision is given to the first level to analyze the optimality of the solutions of batches; 5) the first-level gamer takes the decision of the groups of batches mixture and defines the optimality of the solutions of batches; 6) the upper-level gamer forms a new decision of the the solutions of batches and gives it to a second-level gamer; the solutions of the structure of batches are optimized in consideration of groups of batches, which are taken from the second level. The gamers’ moves are done while the complex decisions, nearly optimal, are achieved. The model of process of proceeding TB in FAL uses the next keys (see Table 1): MATEC Web of Conferences 346, 03094 (2021) ICMTMTE 2021 https://doi.org/10.1051/matecconf /202134603094

The output in high-mixed productions recognizes the processing of transferred batches (TB) using Flexible Automated Lines (FAL). The FALs are made as a sequence of flexible technological places (FTP). Each FTP can be rearranged to process different type of units. The increasing of effectiveness is associated with a scheduling planning problem. The result of such problem solving is a project schedule of FAL activity. The input of this task is an industrial program formed by Enterprise's Automatic Control System (ASC). The ASC gets a set of items to be processed if FAL. The unified items (units) are the units with the same processing time intervals. The time intervals to rearrange the FTP are equal. The time intervals, used to rearrange the FTP to proceed these types of items are equal, too. While time intervals of processing and rearranging FTP are inhomogeneous enough, the effectiveness of scheduling depends on the mixture of transferred batches. In such case the planning of TB assumes the set of batch and the schedule of processing using FAL is considered [1]. The problem of complex processing schedule of TS using FAL while the sets of items are formed and the time limits of FAL acting is developed. The set if items is a set of different kinds of items which are processed in FAL. The number of items of each kind which are included in a set, is preset. The ASC program gets a number of each kind of sets and the time intervals to process a set of batches using FAL.
Hierarchical approach is used to solve a problem [1]. It considers to decompose the generalized function in decision support system of FAL. The function if decomposed to a set of sub-functions, which are hierarchically ordered. The problem solving is implemented using the hierarchical levels: -the first (upper) level -defines of solutions of structure TB; -the second level -defines the solutions of groups of TB, which are proceed during the given time intervals; -the third level -defines the schedule of TB processing, using FAL for solutions of groups of TB is formed on the second level.
To solve a problem of scheduling while sets are proceed and batches are formed, using time interval limits, some subtasks need to be made. The subtasks are: to define of structure TB; to define of structure of groups of TBs, which are proceed, using given time intervals; to define schedules of TBs processing using FAL; to allocate the items, proceed using FAL during given time interval to sets.
The modern ways of complex schedules of processing of batches in multi-stage systems (FAL, in particular case), are realizing the scheduling of sets of materials, which are proceeding in non-stop (continuous) productions [2,3]. The ways can define the order of definite batches implementations [4,5] and realize the decisions of a party set and the order of operations using one or several parallel devices [6,7]. The review of articles defines there are no ways to form a structures of TBs in multi-stage systems, when problem order is unlimited. There are no ways to determine a structures of TBs while the sets are formed. There are no ways to solve a scheduling problem, when the time intervals of FAL activity are limited. The purpose of the research is to improve the ways of complex scheduling of TBs proceeding in FAL. The hierarchical game model is developed to solve the problem. Using such a game defines the structures of batches, the structures of groups of batches and the schedule of processing them using FAL; the initial solve of structures of TB and an optimized groups of TB is defined too. The scheduling is realized by three-levels formed solving. The first-level gamer is forming the structures of TB. The second-level gamer is forming the groups of TBs, the third-level gamer is forming the scheduling of groups of TBs processing. The order of the players' moves is: 1) the first move does the first-level gamer; he defines the structures of TBs and gives the decision to down-sided level; 2) the second move does the second-level gamer; he forms the structures of the groups of batches and gives the decision to the third level;.
3) the third-level gamer makes a decision of the groups of batches scheduling, using FTPs; later the decision is given to the second level to analyze the groups of batches optimality; 4) the second-level gamer takes the groups of batches schedules; he allocates the items from to sets and defines the optimality of the batches of such groups. Steps (2)(3)(4) are made, while the best decision of the groups structures is not formed; such decision is given to the first level to analyze the optimality of the solutions of batches; 5) the first-level gamer takes the decision of the groups of batches mixture and defines the optimality of the solutions of batches; 6) the upper-level gamer forms a new decision of the the solutions of batches and gives it to a second-level gamer; the solutions of the structure of batches are optimized in consideration of groups of batches, which are taken from the second level.
The gamers' moves are done while the complex decisions, nearly optimal, are achieved. The model of process of proceeding TB in FAL uses the next keys (see Table 1): The parameter purpose The item's type ID ( The number of type i items.

L
The number of FTP ( The number of Transfer Batch of type i items ( The vector of number of TB types i items ( Array of mix of items in TB. l π Proceeding sequence of TB in l FTP.

P
Array of order of sequence of proceeding items of TB in FTP in FAL.   These matrices contain the solve of forming the schedule of proceeding TB in FAL task, when current step of optimizing algorithm is doing.
To give a type of groups of TBs of items, proceeding in FAL, the next keys are used (see Table 2): The expression∑ =1 determines the number of sets, formed from proceeded items in TB in groups z N ( = 1, ). The model of hierarchical game to optimize a decision using a structure of TB, groups of TB and schedules of proceeding TB of groups in FAL is: 1st level: ; 3rd level [1,8,9]: The 1st level criterion follows the integrated number of sets formed., the 2nd level criterion -the number of sets, proceeded in TB, included in groups, not included to forming sets, 3rd level criterion suits to general times of non-functioning of FTM while TB in group is proceeded. The expression (4) recognizes, that the end of proceeding time of last TB in L-th FTM is not more than time of the end of interval of z t ) Z , 1 z ( = of FAL functioning. The optimization of the structure of TB is done using the method, recognized in [1]. of mix of groups of TB is obtained by the next steps: 1) the initial decision of structure of groups [9]; 2) the evaluating of decisions in local area optimal decision and choosing the best of them. The algorithm of initial decision of structure of groups forming z N ( Z , 1 z = ) [9] recognizes the sequential distribution of TB to groups using limit (expression (4) ) is considered. The way to optimize the groups of TB is assumed to do the steps: data are used. The methods of defining the structures of TB are not considered the specifics of task, using a necessity of forming the sets with proceeded in FAL items and time limits of FAL functioning. The hierarchical approach means the definition of the structures of batches, structures of groups of batches and scheduling in FAL, using the hierarchical ordered levels of the planning system (hierarchical games theory). The model of hierarchical game while optimizing the structures of bathes, groups of TB and schedule of proceeding them in FAL are developed. The results showed the ability of significant increasing of forming sets from items, proceeded in TB in groups.