EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING
We consider the problem of finding an order portfolio that maximizes the total profit according to one of five optimization criteria and should fit the beginning date of the planned period and the due dates specified by the customers. Also, we need to build for this order portfolio a feasible (not v...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Technical University Kharkiv Polytechnic Institute
2018-12-01
|
| Series: | Вісник Національного технічного університету "ХПÌ": Системний аналіз, управління та інформаційні технології |
| Subjects: | |
| Online Access: | http://samit.khpi.edu.ua/article/view/2079-0023.2018.44.04 |
| _version_ | 1797760677338677248 |
|---|---|
| author | Taras Nikolayevich Lisetsky |
| author_facet | Taras Nikolayevich Lisetsky |
| author_sort | Taras Nikolayevich Lisetsky |
| collection | DOAJ |
| description | We consider the problem of finding an order portfolio that maximizes the total profit according to one of five optimization criteria and should fit the beginning date of the planned period and the due dates specified by the customers. Also, we need to build for this order portfolio a feasible (not violating the due dates) operational plan of jobs processing that would correspond to the minimum possible processing time of the entire order portfolio. We show that the problem in this formulation is a multi-stage scheduling problem. We describe previously developed methodology for the problem solving: the three-level model of production planning. We substantiate the possibility of applying the methodology for any type of small-series production according to one of the five criteria of optimality. We show that independently of the production type considered, whatever is the original production technology, and no matter how the multi-stage scheduling problem is implemented, we reduce the planning problem solving for any of the five optimality criteria to obtaining a feasible solution of the multi-stage scheduling problem for the criterion of maximizing the start time of the earliest job. We show that the efficiency of the multi-stage scheduling problem solving depends on the efficiency of solving the first level of the three-level model. Therefore, we statistically investigate and prove the efficiency of solving the problem of minimizing the total weighted completion time of jobs with precedence relations on a single machine. We show the efficiency of PSC-algorithm for the problem solving for the case when the weights of only terminal vertices of the precedence graph are non-zero. We have shown that the approximation algorithm for this problem solving allows to solve real practical large size problems (we checked dimensions of up to 10,000 jobs). The solutions obtained by the approximation algorithm coincided with those obtained by the exact PSC-algorithm in 99.97 % cases. |
| first_indexed | 2024-03-12T19:02:02Z |
| format | Article |
| id | doaj.art-262eff2ed9814ed484f5d7b41b3e4762 |
| institution | Directory Open Access Journal |
| issn | 2079-0023 2410-2857 |
| language | English |
| last_indexed | 2024-03-12T19:02:02Z |
| publishDate | 2018-12-01 |
| publisher | National Technical University Kharkiv Polytechnic Institute |
| record_format | Article |
| series | Вісник Національного технічного університету "ХПÌ": Системний аналіз, управління та інформаційні технології |
| spelling | doaj.art-262eff2ed9814ed484f5d7b41b3e47622023-08-02T06:33:03ZengNational Technical University Kharkiv Polytechnic InstituteВісник Національного технічного університету "ХПÌ": Системний аналіз, управління та інформаційні технології2079-00232410-28572018-12-01132044192510.20998/2079-0023.2018.44.042079-0023.2018.44.04EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNINGTaras Nikolayevich LisetskyWe consider the problem of finding an order portfolio that maximizes the total profit according to one of five optimization criteria and should fit the beginning date of the planned period and the due dates specified by the customers. Also, we need to build for this order portfolio a feasible (not violating the due dates) operational plan of jobs processing that would correspond to the minimum possible processing time of the entire order portfolio. We show that the problem in this formulation is a multi-stage scheduling problem. We describe previously developed methodology for the problem solving: the three-level model of production planning. We substantiate the possibility of applying the methodology for any type of small-series production according to one of the five criteria of optimality. We show that independently of the production type considered, whatever is the original production technology, and no matter how the multi-stage scheduling problem is implemented, we reduce the planning problem solving for any of the five optimality criteria to obtaining a feasible solution of the multi-stage scheduling problem for the criterion of maximizing the start time of the earliest job. We show that the efficiency of the multi-stage scheduling problem solving depends on the efficiency of solving the first level of the three-level model. Therefore, we statistically investigate and prove the efficiency of solving the problem of minimizing the total weighted completion time of jobs with precedence relations on a single machine. We show the efficiency of PSC-algorithm for the problem solving for the case when the weights of only terminal vertices of the precedence graph are non-zero. We have shown that the approximation algorithm for this problem solving allows to solve real practical large size problems (we checked dimensions of up to 10,000 jobs). The solutions obtained by the approximation algorithm coincided with those obtained by the exact PSC-algorithm in 99.97 % cases.http://samit.khpi.edu.ua/article/view/2079-0023.2018.44.04планування виробництваПДС-алгоритмточний алгоритмнаближений алгоритмкомбінаторна оптимізаціяскладання розкладів |
| spellingShingle | Taras Nikolayevich Lisetsky EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING Вісник Національного технічного університету "ХПÌ": Системний аналіз, управління та інформаційні технології планування виробництва ПДС-алгоритм точний алгоритм наближений алгоритм комбінаторна оптимізація складання розкладів |
| title | EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING |
| title_full | EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING |
| title_fullStr | EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING |
| title_full_unstemmed | EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING |
| title_short | EFFICIENCY RESEARCH OF THE THREE-LEVEL MODEL OF SMALL-SERIES PRODUCTION PLANNING |
| title_sort | efficiency research of the three level model of small series production planning |
| topic | планування виробництва ПДС-алгоритм точний алгоритм наближений алгоритм комбінаторна оптимізація складання розкладів |
| url | http://samit.khpi.edu.ua/article/view/2079-0023.2018.44.04 |
| work_keys_str_mv | AT tarasnikolayevichlisetsky efficiencyresearchofthethreelevelmodelofsmallseriesproductionplanning |