IE 2100: Supply Chain Analysis (Fall 2014) Solutions to Homework 8 Question 1 Given: A=3000, h = i*c = 0.36*400 $/unit/year = (0.36*400)/12 $/unit/month = $12/unit/month. 1) Single production run in Jan. ⇒ P1= ΣDj = 1020 and Pj=0 for j=2,3,...,12 Variable costs =3000+12*(960+880+750+630+520+520+420+340+200+100+40+0)= $67,320 J F M A M J J A S O N D ($3000 for setup and $64,320 for holding) 2) Lot-for-lot production ⇒ Pj = Dj for each j=1,2,...,12. Variable Costs = 11*3000 + 0 = $33,000 one setup each month except June (demand=0); no inventories... ($33,000 for setup and $0 for holding) 3) Average monthly demand = (ΣDj)/12 = 1020/12 = 85. Therefore EOQ based on average demand = SQRT(2*3000*85/12) = 206.155 ≈ 206. Thus, we want to keep all production as close to 206 as possible starting January. (60+80) < 206 < (60+80+130), i.e., 140<206<270. Since 270 is closer (than 140 is) to 206, P1=270, P2=P3=0 (120) < 206 < (120+110), i.e., 120<206<230. Since 230 is closer to 206, P4=230, P5=0 (0+100+80) < 206 < (0+100+80+140), i.e., 180<206<320. Since 180 is closer to 206, P6=180, P7=P8=0; however D6=0, so we can do better by P6=0, P7=180, P8=0 (140) < 206 < (140+100), i.e., 140<206<240. Since 240 is closer to 206, P9=240, P10=0 (60+40) < 206 - end of planning horizon! Thus P11=100, P12=0. Variable costs = {3000+12*(210+130+0)}+{3000+12*(110+0)}+ J F M A M {3000+12(80+0)}+ {3000+12(100+0)} + {3000+12(40+0)} = $23,040 J A S O N D ($15,000 for setup and $8,040 for holding) NOTE: You might use a different approach than mine for deciding on how you stay close to 206 each time you produce; this is just a heuristic. Of course, your plans and costs might be a little different if you do so…4) For the POQ method, we need production for as close as possible to T = EOQ/D = 206/85 = 2.423 months at a time - say 2 months... Thus P1=140, P3=250, P5=110, P7=180, P9=240, P11=100, P2=P4=P6=P8=P10=P12=0 Variable cost = 3000*6 + 12*(80+120+80+100+40) = $23,040 (6 prod. runs) J M J S N ($18,000 for setup and $5,040 for holding) NOTE: If you chose to round up to 3 rather than round down to 2 your plan will obviously be a little different; again this is just a (not very good…) heuristic. 5) Silver-Meal Heuristic s=1 t=1 TVCUT(1,1)=3000+12*0 = 3000 t=2 TVCUT(1,2)={3000+12*(80+0)}/2 = 1980 t=3 TVCUT(1,3)={3000+12*(210+130+0)}/3 = 2360 INCREASING !! Thus P1=140, P2=0 s=3 t=3 TVCUT(3,3)=3000+12*0 = 3000 t=4 TVCUT(3,4)={3000+12*(120+0)}/2 = 2220 t=5 TVCUT(3,5)={3000+12*(230+110+0)}/3 = 2360 INCREASING !! Thus P3=250, P4=0 s=5 t=5 TVCUT(5,5)=3000+12*0 = 3000 t=6 TVCUT(5,6)={3000+12*(0+0)}/2 = 1500 t=7 TVCUT(5,7)={3000+12*(100+100+0)}/3 = 1800 INCREASING !! Thus P5=110, P6=0 s=7 t=7 TVCUT(7,7)=3000+12*0 = 3000 t=8 TVCUT(7,8)={3000+12*(80+0)}/2 = 1980 t=9 TVCUT(7,9)={3000+12*(220+140+0)}/3 = 2440 INCREASING !! Thus P7=180, P8=0 s=9 t=9 TVCUT(9,9)=3000+12*0 = 3000 t=10 TVCUT(9,10)={3000+12*(100+0)}/2 = 2100 t=11 TVCUT(9,11)={3000+12*(160+60+0)}/3 = 1880 t=12 TVCUT(9,12)={3000+12(200+100+40+0)}/4 = 1770 END OF P.H. !! Thus P9=340, P10=P11=P12=0 Var. cost = 5*3000 + 12*(80+120+80+200+100+40) = $22,440 J M J S O N ($15,000 for setup and $7,440 for holding)6) The Least Unit Cost Heuristic s=1 t=1 TVCUD(1,1)={3000+12*0}/60 = 50 t=2 TVCUD(1,2)={3000+12*(80+0)}/140 = 28.286 t=3 TVCUD(1,3)={3000+12*(210+130+0)}/270 = 26.22 t=4 TVCUD(1,4)={3000+12*(330+250+120+0)}/390 = 29.23 INCREASING !! Thus P1=270, P2=P3=0 s=4 t=4 TVCUD(4,4)={3000+12*0}/120 = 25 t=5 TVCUD(4,5)={3000+12*(110+0)}/230 = 18.8 t=6 TVCUD(4,6)={3000+12*(110+0+0)}/230 = 18.8 t=7 TVCUD(4,7)={3000+12*(210+100+100+0)/330 = 24 INCREASING !! Thus P4=230, P5=P6=0 s=7 t=7 TVCUD(7,7)={3000+12*0}/100 = 30 t=8 TVCUD(7,8)={3000+12*(80+0)}/180 = 22 t=9 TVCUD(7,9)={3000+12*(220+140+0)}/320 = 22.875 INCREASING !! Thus P7=180, P8=0 s=9 t=9 TVCUD(9,9)={3000+12*0}/140 = 21.43 t=10 TVCUD(9,10)={3000+12*(100+0)}/240 = 17.5 t=11 TVCUD(9,11)={3000+12*(160+60+0)}/300 = 18.8 INCREASING !! Thus P9=240, P10=0 s=11 t=11 TVCUD(11,11)={3000+12*0)}/60 = 50 t=12 TVCUD(11,12)={3000+12(40+0)}/100 = 34.8 END OF P.H. !! Thus P10=100, P12=0 Variable cost = 5*3000 + 12*(210+130+110+80+100+40) = $23,040 J F A J S N ($15,000 for setup and $8,040 for holding)7) Part Period Balancing Method s=1 t=1 HC(1,1) = 12*0 = 0 < 3000 t=2 HC(1,2) = 12*(80+0) = 960 < 3000 t=3 HC(1,3) = 12*(210+130+0) = 4080 > 3000. Since 4080 is closer (than 960 is) to 30, P1=270, P2=P3=0 s=4 t=4 HC(4,4) = 12*0 = 0 < 3000 t=5 HC(4,5) = 12*(110+0) = 1320 < 3000 t=6 HC(4,6) = 12*(110+0+0) = 1320 < 3000 t=7 HC(4,7) = 12*(210+100+100+0) = 4920 > 3000 Since 1320 is closer (than 4920 is) to 3000, P4=230, P5=P6=0 s=7 t=7 HC(7,7) = 12*0 = 0 < 3000 t=8 HC(7,8) = 12*(80+0) = 960 < 3000 t=9 HC(7,9) = 12*(220+140+0) = 4320 > 3000. Since 4320 is closer (than 960 is) to 3000, P7=320, P8=P9=0 s=10 t=10 HC(10,10) = 12*0 = 0 < 3000 t=11 HC(10,11) = 12*(60+0) = 720 < 3000 t=12 HC(10,12) = 12*(100+40+0) = 16 < 3000. END OF P.H. !! Thus P10=200, P11=P12=0 Variable Cost = 4*3000 + 12*(210+130+110+220+140+100+40) = $23,400 J F A J A O N ($12,000 for setup and $11,400 in holding) 8) The Sliver-Meal heuristic yields the best plan (costing $22,440 over the year). Question 2 The data for the problem is as follows: j Dj Pj hj hj′ Aj 1 1500 33,600 4.0 3.82 102 2 1680 52,800 7.4 6.78 68 3 540 24,000 2.4 2.36 187 4 2880 39,600 9.0 8.35 263.5 For consistency, both D and P have been expressed in units of years (×12 for D, and
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