Èííîâàòèêà è ýêñïåðòèçà. 2015. Âûïóñê 2 (15) АНАЛИЗ ЭФФЕКТИВНОСТИ МЕНЕДЖМЕНТА ПОДРАЗДЕЛЕНИЙ НЕПОСРЕДСТВЕННОЙ РЕАЛИЗАЦИИ УЧЕБНОГО ПРОЦЕССА УЧРЕЖДЕНИЙ ВЫСШЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ С ПОМОЩЬЮ ЭТАЛОНОВ Â.Î. Ãðîïïåí, çàâ. êàô. Ñåâåðî-Êàâêàçñêîãî ãîðíî-ìåòàëëóðãè÷åñêîãî èíñòèòóòà (ÃÒÓ), äèðåêòîð ÍÈÈ Òåîðåòè÷åñêîé è Ïðèêëàäíîé Èíôîðìàòèêè (ÍÈÈÒÏÈ), ä-ð òåõí. íàóê, ïðîô., [email protected] À.À. Áóäàåâà, äîö. êàô. Ñåâåðî-Êàâêàçñêîãî ãîðíî-ìåòàëëóðãè÷åñêîãî èíñòèòóòà (ÃÒÓ), êàíä. òåõí. íàóê, [email protected]  ðàáîòå ïðåäëàãàåòñÿ èñïîëüçîâàòü ìàòåìàòè÷åñêèé àïïàðàò äëÿ îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà, îñíîâó êîòîðîãî ñîñòàâëÿþò ðàíæèðîâàíèå è ïðîãíîçèðîâàíèå. Ê äîñòîèíñòâàì ïðåäëàãàåìîãî ïîäõîäà ìîæíî îòíåñòè åãî èíâàðèàíòíîñòü îòíîñèòåëüíî èñïîëüçóåìîé ñèñòåìû ïîêàçàòåëåé è íåçàâèñèìîñòü îò ñóáúåêòèâíîãî ìíåíèÿ ëèö, ïðèíèìàþùèõ ðåøåíèå. Ïðèâîäÿòñÿ ïðèìåðû, èëëþñòðèðóþùèå ðåàëèçàöèþ îñíîâíûõ ýòàïîâ ïðåäëàãàåìîãî ïîäõîäà. Êëþ÷åâûå ñëîâà: îöåíêà ýôôåêòèâíîñòè, êðèòåðèè, ðàíæèðîâàíèå, ïðîãíîçèðîâàíèå, ýòàëîí. THE ANALYSIS OF EFFICIENCY OF MANAGEMENT OF DIVISIONS OF DIRECT REALIZATION OF EDUCATIONAL PROCESS OF INSTITUTIONS OF HIGHER PROFESSIONAL EDUCATION BY MEANS OF REFERENCE STANDARDS V.Î. Groppen, Head of the Chair, North Caucasian Mining and Metallurgical Institute (NCMMI), Director of Scientific Research Institute of Theoretical and Applied Informatics (NIITPI), Ph.D. of Engineering, Professor, [email protected] À.À. Budayeva, Assistant Professor of Chair, North Caucasian Mining and Metallurgical Institute (NCMMI), Doctor of Engineering, [email protected] We propose to use a mathematical tool for evaluating the effectiveness of management units and members of the immediate implementation of the training, which is based on ranking and forecasting. The advantages of the proposed approach can be attributed to the invariance under the system’s indicators and independence from the subjective opinion of decision-makers. The examples illustrate the main stages of implementation of the proposed approach. Keywords: performance evaluation, criteria, ranking, forecasting model. Ââåäåíèå Öåëÿìè îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà ÿâëÿþòñÿ îïðåäåëåíèå ðåéòèíãà ïðåïîäàâàòåëåé, êàôåäð, äåêàíàòîâ, ôèëèàëîâ è ò. ï. êàê íà îñíîâàíèè êàæäîãî èñïîëüçóåìîãî êðèòåðèÿ, òàê è èíòåãðàëüíî, ñ îäíîâðåìåííûì ó÷åòîì âñåõ êðèòåðèåâ. Òàêîé ïîäõîä ïîçâîëÿåò íå òîëüêî îïðåäåëèòü ìåñòî â èíòåãðàëüíîì ðåéòèíãå êàæäîãî îáúåêòà, íî è âûñâåòèòü ïðè÷èíû, ïðèâåäøèå ê òàêîìó ðåçóëüòàòó.  ñëó÷àå ðàíæèðîâàíèÿ îäíîâðåìåííî ïî ðÿäó ïîêàçàòåëåé çàäà÷à ÿâëÿåòñÿ ìíîãîêðèòåðèàëüíîé, îäíàêî íåïîñðåäñòâåííîå èñïîëüçîâàíèå ïðèíöèïà 293 Èííîâàòèêà è ýêñïåðòèçà. 2015. Âûïóñê 2 (15) Ïàðåòî ïðè ðåøåíèè ïðèêëàäíûõ çàäà÷ ÷àñòî îñëîæíÿåòñÿ ìíîæåñòâåííîñòüþ ñî÷åòàíèé çíà÷åíèé êðèòåðèåâ, ÿâëÿþùèõñÿ îïòèìàëüíûìè [1, 2]. Ïîñëåäíåå ïðèâîäèò ê åñòåñòâåííîìó ñòðåìëåíèþ ê ïåðåõîäó ê îäíîêðèòåðèàëüíîé çàäà÷å ðàíæèðîâàíèÿ, ÷òî ñâÿçàíî ñ âûáîðîì òåõíîëîãèè ñâåðòêè. Ïîñêîëüêó íàèáîëåå ÷àñòî èñïîëüçóåìûå ìåòîäû ñâåðòêè êðèòåðèåâ – èõ ëåêñèêîãðàôè÷åñêîå óïîðÿäî÷åíèå ëèáî èõ âçâåøåííàÿ ñóììà íå ñâîáîäíû îò ñóáúåêòèâíîãî ìíåíèÿ ëèö, ïðèíèìàþùèõ ðåøåíèå [3, 4], íèæå ïåðåõîä ê îäíîìó êðèòåðèþ áàçèðóåòñÿ íà ñî÷åòàíèè ðàíæèðîâàíèÿ è ýòàëîíîâ [5–7]. ¹ Íàèìåíîâàíèå ïîêàçàòåëÿ Êîììåíòàðèè 1 Ïîñåùàåìîñòü Ïðîöåíò ïðîïóùåííûõ àóäèòîðíûõ ÷àñîâ, ïðèõîäÿùèõñÿ íà îäíîãî ñòóäåíòà 2 Óñïåâàåìîñòü Ñðåäíÿÿ àðèôìåòè÷åñêàÿ îöåíêà çíàíèé â õîäå ñåññèè, ïðèõîäÿùàÿñÿ íà îäíîãî ñòóäåíòà 3 Ïðîöåíò íèçêî ìîòèâèðîâàííûõ îöåíîê Ïðîöåíò îöåíîê, ïîëó÷åííûõ â õîäå ñåññèè è ñóùåñòâåííî îòëè÷àþùèõñÿ îò îöåíîê çíàíèé ñòóäåíòîâ, ïîëó÷åííûõ â ðàìêàõ ðóáåæíîãî êîíòðîëÿ è èíûõ ñïîñîáîâ òåêóùåãî êîíòðîëÿ â õîäå ñåìåñòðà 4 Äèíàìèêà òåêóùåé óñïåâàåìîñòè Ïðîöåíò ñëó÷àåâ, êîãäà òåêóùèé è ðóáåæíûé êîíòðîëü çíàíèé ñòóäåíòîâ â õîäå ñåìåñòðà íå âûÿâëÿåò èõ ïîëîæèòåëüíîé äèíàìèêè, ò. å. êîãäà íèçêàÿ óñïåâàåìîñòü â ïåðâîé ïîëîâèíå ñåìåñòðà íå ïðèâåëà ê èñïîëüçîâàíèþ ýôôåêòèâíûõ ïîäõîäîâ, ïðèâîäÿùèõ ê ïîëîæèòåëüíîé äèíàìèêå îöåíîê Îñîáåííîñòè ïðèìåíåíèÿ ýòàëîíîâ â ìíîãîêðèòåðèàëüíîì ðàíæèðîâàíèè Êàê ïðàâèëî, äëÿ îöåíêè ýôôåêòèâíîñòè ìåíåäæìåíòà ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà èñïîëüçóþòñÿ íåîäíîðîäíûå ïîêàçàòåëè, îáùåé ÷åðòîé êîòîðûõ ÿâëÿåòñÿ èõ êîëè÷åñòâåííûé õàðàêòåð. Íèæå, â òàáëèöå, ïåðå÷èñëåíû íåêîòîðûå èç íèõ. Äàëåå áóäåì ïîëàãàòü, ÷òî äëÿ êàæäîãî i-ãî êðèòåðèÿ Êi íå ñîñòàâëÿåò òðóäà îïðåäåëèòü åãî âåðõíþþ Ki max è íèæíþþ Ki min ãðàíèöû. Íàïðèìåð, ïðîöåíò ïðîïóùåííûõ îäíèì ñòóäåíòîì àóäèòîðíûõ ÷àñîâ çàêëþ÷åí â äèàïàçîíå {0 – 100}, à ñðåäíèé áàëë ñòóäåíòà îïðåäåëÿåòñÿ äèàïàçîíîì {2–5}. Ýòî ïîçâîëÿåò ïåðåéòè îò èñõîäíûõ êðèòåðèåâ ê èõ íîðìèðîâàííûì àíàëîãàì Fi, ïîëüçóÿñü óðàâíåíèåì: ∀i : Fi = Ki − Ki min . Ki max − Ki min (1) Ñïðàâåäëèâà ñëåäóþùàÿ òåîðåìà: Òåîðåìà 1. Îïòèìàëüíîå ðàíæèðîâàíèå îáúåêòîâ íà îñíîâàíèè ìíîæåñòâà êðèòåðèåâ {Fi} ñîâïàäàåò ñ îäíèì èç îïòèìàëüíûõ ïî Ïàðåòî ðàíæèðîâàíèé òåõ æå îáúåêòîâ íà îñíîâàíèè ìíîæåñòâà êðèòåðèåâ {Ki}. Äîêàçàòåëüñòâî òåîðåìû ïðèâîäèòñÿ â [5]. Äëÿ òîãî, ÷òîáû âîñïîëüçîâàòüñÿ òåîðåìîé 1, îáîçíà÷èì ñèìâîëîì Fi opt îïòèìàëüíûå çíà÷åíèÿ êðèòåðèåâ Fi, i = 1,2,...n, è îïðåäåëèì «èäåàëüíûé» îáúåêò, ýòàëîí, äëÿ êîòîðîãî ñïðàâåäëèâî: Fi = Fi opt, i = 1,2,...n. Ðåàëüíî òàêîãî îáúåêòà ìîæåò íå ñóùåñòâîâàòü, îäíàêî ýòî ïîçâîëÿåò ðàíæèðîâàòü îñòàëüíûå îáúåêòû ïî âîçðàñòàíèþ «ðàññòîÿíèÿ» òî÷åê, îòâå÷àþùèõ ðàíæèðóåìûì îáúåêòàì â ïðîñòðàíñòâå êðèòåðèåâ, îò ýòàëîíà (ðèñ. 1). 294 Èííîâàòèêà è ýêñïåðòèçà. 2015. Âûïóñê 2 (15) ɉɪɨɰɟɧɬ ɧɢɡɤɨɦɨɬɢɜɢɪɨɜɚɧɧɵɯ ɨɰɟɧɨɤ Ɏ1 1 Ɏ2 ɗɬɚɥɨɧ 0 Ɏ2 Ɏ1 1 2 n 1 ɍɫɩɟɜɚɟɦɨɫɬɶ 1 ɉɨɫɟɳɚɟɦɨɫɬɶ Ðèñ. 1. Ðàíæèðîâàíèå äâóõ ôàêóëüòåòîâ Ô1 è Ô2 ïî òðåì íîðìèðîâàííûì êðèòåðèÿì îòíîñèòåëüíî ýòàëîíà Ïðîãíîç òåíäåíöèé Ïðè ïåðåâûáîðàõ ïðåïîäàâàòåëåé âóçîâ, çàâ. êàôåäðàìè, äåêàíîâ è ò. ï., îñîáîå çíà÷åíèå ïðèîáðåòàåò ïðîãíîç ýôôåêòèâíîñòè èñïîëüçóåìûõ èìè â ïðîôåññèîíàëüíîé äåÿòåëüíîñòè òåõíîëîãèé [8].  ðàìêàõ ïðåäëàãàåìîãî ïîäõîäà ïîâòîðåíèå ïðîöåäóðû ðàíæèðîâàíèÿ íà ïðîòÿæåíèè ðÿäà ëåò ïîçâîëÿåò îïðåäåëèòü ãðàôè÷åñêè äèíàìèêó ìåñòà â ðåéòèíãå ïî âûáðàííîìó êðèòåðèþ (ðèñ. 2), à ïî íåé, àïïðîêñèìèðóÿ ïîëó÷åííóþ çàâèñèìîñòü àíàëèòè÷åñêè, îïðåäåëèòü ïðîãíîç íà ïëàíèðóåìûé ïåðèîä. Òàê, ïðèìåíèòåëüíî ê ôàêóëüòåòó Ô9 (ðèñ. 2), àïïðîêñèìàöèÿ ñ ïîìîùüþ ìåòîäà íàèìåíüøèõ êâàäðàòîâ çàâèñèìîñòè «èíòåãðàëüíûé êðèòåðèé/ãîä» ïîëèíîìîì âòîðîãî ïîðÿäêà: Ì = – 9.940358∙10 –5 – 0.3458189∙Ò + 1.737061∙10–4∙Ò2 , (2) ãäå Ì – ìåñòî ôàêóëüòåòà Ô9 ïî èíòåãðàëüíîìó êðèòåðèþ, Ò – ãîäû (îò 2010 äî 2014), ïîçâîëÿåò ïðîãíîçèðîâàòü «ôèêñàöèþ» ýòîãî ôàêóëüòåòà â ðåéòèíãå ôàêóëüòåòîâ âóçà ïî âûøåíàçâàííîìó êðèòåðèþ íà îäíîì èç ïîñëåäíèõ ìåñò â 2015 ã. ˇ1 ˇ2 ˇ3 ˇ4 ˇ5 ˇ6 ˇ7 ˇ8 ˇ9 0 1 2 3 4 5 6 7 8 9 10 2009 2010 2011 2012 2013 2014 2015 Ðèñ. 2. Ïðèìåð ðàíæèðîâàíèÿ äåâÿòè ôàêóëüòåòîâ âóçà íà ïðîòÿæåíèè ïîñëåäíèõ ïÿòè ëåò ïî èíòåãðàëüíîìó ïîêàçàòåëþ 295 Èííîâàòèêà è ýêñïåðòèçà. 2015. Âûïóñê 2 (15) Çàêëþ÷åíèå Îïèñàííûé âûøå ïîäõîä ê àíàëèçó ýôôåêòèâíîñòè ôóíêöèîíèðîâàíèÿ ïîäðàçäåëåíèé è ó÷àñòíèêîâ íåïîñðåäñòâåííîé ðåàëèçàöèè ó÷åáíîãî ïðîöåññà ïîíèæàåò ñóáúåêòèâèçì â îöåíêàõ òàêîãî ðîäà. Ê åãî äîñòîèíñòâàì òàêæå ñëåäóåò îòíåñòè íåçàâèñèìîñòü îò ÷èñëà è ñïåöèôèêè èñïîëüçóåìûõ ïîêàçàòåëåé, à òàêæå îò ïðèìåíÿåìûõ ñïîñîáîâ àïïðîêñèìàöèè ïîëó÷åííûõ çàâèñèìîñòåé [9]. Áîëüøîé îáúåì îáðàáàòûâàåìîé èíôîðìàöèè è âû÷èñëåíèé, ñâÿçàííûå ñ åãî ïðèìåíåíèåì, ìîãóò îáåñïå÷èâàòüñÿ ïîäñèñòåìàìè ÀÑÓ âóç, ÷òî îáëåã÷àåò åãî ðåàëèçàöèþ è âíåäðåíèå. Ìîæíî òàêæå îòìåòèòü ýôôåêòèâíîñòü àíàëîãè÷íîãî ïðèìåíåíèÿ îïèñàííîãî âûøå ïîäõîäà â äðóãèõ ïðåäìåòíûõ îáëàñòÿõ [7, 10, 11]. Ñïèñîê ëèòåðàòóðû 1. Ãðîïïåí Â.Î. Ïðèíöèïû îöåíêè êà÷åñòâà ðåøåíèÿ ìíîãîêðèòåðèàëüíûõ îïòèìèçàöèîííûõ çàäà÷ ñ ïîìîùüþ ýòàëîíîâ. Ìàòåðèàëû V Ìåæäóíàðîäíîé êîíôåðåíöèè «Óñòîé÷èâîå ðàçâèòèå ãîðíûõ òåððèòîðèé: ïðîáëåìû è ïåðñïåêòèâû èíòåãðàöèè íàóêè è îáðàçîâàíèÿ», 21–23.09.2004 ã., ñòð. 572–580. 2. Ãðîïïåí Â.Î. Ðåøåíèå çàäà÷ ìíîãîêðèòåðèàëüíîé îïòèìèçàöèè è ðàíæèðîâàíèÿ îáúåêòîâ ìåòîäîì ýòàëîíîâ. Òåëåêîìì. èíô. îáðàç. M., ¹ 2 (33), ìàðò–àïðåëü, 2006, ñòð. 14–31. 3. Ëàðè÷åâ Î.È. Òåîðèÿ è ìåòîäû ïðèíÿòèÿ ðåøåíèé. Ì. Ëîãîñ, 2000. 4. Ïîäèíîâñêèé Â.Â. Ââåäåíèå â òåîðèþ âàæíîñòè êðèòåðèåâ â ìíîãîêðèòåðèàëüíûõ çàäà÷àõ ïðèíÿòèÿ ðåøåíèé. ÔÈÇÌÀÒËÈÒ, 2007. 5. Groppen V.O. (2004) New Solution Principles of Multi-Criteria Problems Based on Comparison Standards. Available at: http//:www.arxiv.org/ftp/math/papers/0501/0501357.pdf. 6. Ãðîïïåí Â.Î. Ïðèíöèïû ïðèíÿòèÿ ðåøåíèé ñ ïîìîùüþ ýòàëîíîâ. Èçä. ÐÀÍ, Àâòîìàòèêà è òåëåìåõàíèêà, ¹ 4, 2006, ñòð. 167–184. 7. Groppen V.O. New Solution Principle for Multi-criteria Problems Based on Comparison Standards: Models, Algorithms, Applications. Programme and Abstracts Eurogen 2007. Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems. 11–13 June 2007 Jyvaskyla, Finland, pp. 100–101. 8. Îðëîâ À.È. Òåîðèÿ ïðèíÿòèÿ ðåøåíèé. Ì.: Èçäàòåëüñòâî «Ìàðò», 2004. 9. Ãîëóáèíñêèé À.Í. Ìåòîäû àïïðîêñèìàöèè ýêñïåðèìåíòàëüíûõ äàííûõ è ïîñòðîåíèÿ ìîäåëåé. Âåñòíèê Âîðîíåæñêîãî óíèâåðñèòåòà ÌÂÄ Ðîññèè, ¹ 2, 2007. 10. Âàãèí Â.Ñ., Ãðîïïåí Â.Î., Ïîçäíÿêîâà Ò.À., Áóäàåâà À.À. Ìíîãîêðèòåðèàëüíîå ðàíæèðîâàíèå îáúåêòîâ ìåòîäîì ýòàëîíîâ êàê èíñòðóìåíò îïòèìàëüíîãî óïðàâëåíèÿ. Óñòîé÷èâîå ðàçâèòèå ãîðíûõ òåððèòîðèé, ¹ 1, 2010, ñ. 47–56. 11. Ãðîïïåí Â.Î., Áóäàåâà À.À. Ðàííåå ïðîãíîçèðîâàíèå ðàçâèòèÿ «öâåòíûõ ðåâîëþöèé» ñèñòåìîé êîíòðîëÿ ðîñòà ìåæýòíè÷åñêîé è ìåæêîíôåññèîíàëüíîé íàïðÿæåííîñòè ðåãèîíîâ. «Ïðîáëåìû óïðàâëåíèÿ», èçä. Àêàäåìèè óïðàâëåíèÿ, Ìèíñê, ISSN 2071-3711, ¹ 2 (51), 2014, c. 45–51. References 1. Groppen V.O. Printsipy otsenki kachestva resheniya mnogokriterial’nykh optimizatsionnykh za-dach s pomoshch’yu etalonov. Materialy V Mezhdunarodnoy konferentsii «Ustoychivoe razvitie gornykh territoriy: problemy i perspektivy integratsii nauki i obrazovaniya», 21–23.09.2004 g. [The principles of quality assessment for the optimization of multi-criteria decision-villas via standards. 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