Management Engineering - Operations Management

Queueing theory exercises part1/2

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LE 209 QUEUEING THEORY EXERCISES Ex 1 RINASCIMENTO CLINIC solution Maps 30pA R Ta f f y 30 20pA NBOpth 17pA MIMA MM 0.15.20 3pA 30pA SP 13pA MIMA gang Msp 15pA a Wa 9 usa Ifo 4.5min Wga 20 30 30 20 4min Wasp IIa 26min General steps for modelling a complex system: Shape the system and de fine the main 1. parameters Understand di fferent kinds of customers and 2. their paths Compute the occurrences of the paths 3. Calculate throughput times 4. Decide strategic actions 5. b PATH 1 R Gp out Ws E Wsi E 1 Nsa Wsop 676 12min Mi di PATH 2 R GP SP out Usa Nsa Wsop Wasp 646730 42min PATH 3 R SP out Nsa Usa Wsop 6730 36min C Weegee Occurrence Wsi II 12 tg 42 tg 36 23min d Inactivity time 1 fa 606min47 1 g 60 15min In time ap 1 2g 60 20min In times 1 1g 60 8min E S Mcat Mcat 1 Fsd is the E Sa y g a g g correspondent 1 9 of Ws applie 4 f 1 9 a in case of Els tempt E sa g g a g g priority For R and GP there are not variation whilst there are variations for sp this leads variations for patient of path 2 and 3 Es II 8.33min 1 9 E Sa 1 ELIA 1 4 f 1 g g 36.5min Ws Ws 12min WSI Ws Wsop E Sa 20.33min Wsggere 23min Wsj Usate Sa 42.5min When a server is able to serve two classes of customers that have di fferent service admission, under the hypothesis that customers of class 1 have a service admission priority higher than customers of class 2, we have to take into account two cases: - PREEMPTIVE PRIORITY - NON PREEMPTIVE PRIORITY Ex 2 Sterilisation centre solution 7 0.3.15 4.5kITL 30 usukitthMIMB yysygg.sk h Isi yea 7 1SK.it h M30kit h 20 gen MIMI 7 0.15 03.15 02.15 3.6 skitlhfifjthaxmlm d u 3k.tk MIMA 30 cane È PRE EMPTIVE A 0.3.15 4Skita non urgent S vestita 1Okitth 20 Opht aor.es itin e Yn I t I Y I I s I I GOYNORMAL How many paths 6 urgent 6 non urgent 12 1 Co OR p 8 Cno OR GE p iii 3 Co GE P 9 Cno GE P g quagga 4 Co G P 10 CN G P 6 Cutopnormal 7 12 no OPnorma P OCCURENCES occ 03 0.85 515 8.5 occa 0 085.10 15 1 Occa 015.0 315 15 1.5 Occa 015.0 31 5 34 Occa 02.415 6.674 0cg 021915 13.33 occa 03.5 15 10 Occ 03.10 15 20 0.2.0.610 15 8 ispidi e O.nu s sssx 33.344 66.66 Skitsoutof15 10kitsoutofis ELS Mcat 130 pre EMPTIVE _sgg 0.04h 2.4min 1 1 9 ygyygyyggyggygyyaoyy.am E Sa Incat n orthopaedics table Ewe do a linee f f 45 1.125 74 0.073 considering e 3 and g 1.125 inthe interpolation I E sue Ws Lg I Off f 15.97min GENERAL f 3.675 1.225 7 from the table La 0.744 Ws gig 32.15min 3 GYNAECOLOGY f 4 ge 0.9 La 0.229 Ws gig g 15.053min OPTHALMOLOGY E g that g g IIII 0.3875h 23.25min non_pre Emptive 4 f 1 9 a IL _E 1 1 1 1 3 5 IT 1 p 1 g g a g g g g 0.66875h 40.125min PREPARATION Ws 1 12 7. 5 13.33min µ_a 1 Mean Ws for the whole system Eg E Wsi 0cg 40.51min Possible improvements Gust the main ones 1 Single queue system for preparation 40 Usare impact on all the paths since it is the first phase a Understand the main causes of second working for 15 of kits processed in orthopaedics Ad hoc processor tools to avoid second working More training for orthopaedics operators 3 Improve service process in orthopaedics leg 2 kits in 25min instead of 30min 7 Ns 16min and switch to a MINI system the second operator could be moved to other areas so it is not fired