Management Engineering - Operations Management

Queueing theory exercises part2/2

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LE 210 EX 4.2 DESPACITO SOLUTION As is to BE III costa Acosta taek compared to old machine µ 1 3.60 20 costi µ 30 costa ME 30 costa pay employees 8h when waiting We will rent the new machine if Coen Cold otherwise we will maintain the old machine COPY A 154h µ 204h OLD Ws 1 µ g e aI e0.2h 12min Cold 8g o.gg 15cg 24 Eh no Wa l c a n s e employees have to wait also when they are doing copies and the company wants to reduce Ya t e s eses µ g gol 0.06h 4min new 8 2 4 0.06 15g 10 14 it is convenient to rent the new machine If we have more than three people waiting for the machine the space is inadequate p mea gr 15 20 31.64 In this case we move to a Mint system where c is the number of small machines with µ Scosta that ensure Wssismin La I e 15min knowing 1 Is 3 and Wa s 15 we can find La from the table Then we put it in the constraint disequation and we have La 1528 53 1 EE 5mh tYInzs1sx Lg 0.354 93 15 60515 713.416515 We see that the constraint is satisfied for ce 7 the minimum number of small machines is 5 Ex 3.2 Meccanica spa solution out 100pct of which outa sopcsl h outb 30p.es h outc 20pes h LA MILL BRILLA OUTA 50pA DRILLB TESTATE 2 PACKABC Out 30pA NON PREEMPT outezoph 204 B PRIORITY letto Mille Cfirst DRILL 10 6 È 0.15.0.2.113 p 0.15.0.1 a Let's consider only one productpertime A la so mill 50 brilla so test Pack to out Soph la input Output la 50pA PATH I Patiti cocci 1 MILL DRILL TEST PACK 100 B la b Mill drills 1dB TEST 0 Pack out 30pA 20 113 0.15.0.2 B Ib sto 30 0.21 0.15 Odb b 3g 30.93pA PATH PATHI OCC 9 1 MILL DRILL TEST PACK IB GRIB O.co 2 Mill DRILL TESTIDRILL TEST pack 0.8950.213 0.17 3 Mill drill TEST Drill test scrap 0.1 fate 0.03 c la Mill drillo test 0 Pack out 20pA 10 la 0.15.0.1 la Ic kto zotodto.ns.o.lk lc ggs 2o 3oplh PATH PATHI OCC 9 1 MILL DRILL TEST PACK K 0.9 2 Mill DRILL TEST DRILL test pack 0.8 01.1 0.085 3 Mill DRILL TEST DRILL test scrap 015 1le 0.015 Putting everything together we have 50 MILLA 50 brilla 50 30.93 37 drills 3712 10945 testa 100 package out 50M Out 3011 6.186 OUTELOPI 30.935123 MILLE 20.30 20.30 22.33 Brilla 22.33 2.03 833 And now we can easily identify the main parameters MILLA BRILLA MILLBC DRILLS DRILL TESTATE PACKABC 784 50 50 51.23 37.12 22.33 109.45 100 µ PA 90 75 90 75 75 160 130 cffffrat.MN 1MIm 1MIm 1MIm 1mIm 1mlm 1 MIMA NON_pre Empt PRIORITY Cfirst IIEIM.mg 26.67 25.85 20 30.30 42.14 18.96 13.85