DOC PREVIEW
Pitt IE 2100 - hw8sol

This preview shows page 1-2 out of 5 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

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


View Full Document

Pitt IE 2100 - hw8sol

Download hw8sol
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view hw8sol and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view hw8sol 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?