Question

Use the northwest-corner method as a starting procedure and the stepping-stone method to find the best shipment schedule/ distribution for the following demand-supply problem. Check for any degeneracy along the analysis and ensure that the solution is optimal. Don't proceed further if degeneracy occurs. Record your answer in text box in given format shown below. Market 1 (M1) Market 2 Market 3 Market 4 Plant (M2) (M3) (M4) Capacity 19 30 50 10 70 Plant 1 (P1) Plant 2 (P2) 70 30 40 60 90 40 8 70 20 Plant 3 (P3) 180 Market Demand 50 80 70 140 340/ 340 Format for answer: Optimal shipment schedule 1) From P1 to M1 = 2) From P1 to M2 = 3) From P1 to M3 = 4) From P1 to M4= From P2 to M1 = 5)

Answer 1

D Stepping - Stanse method ly check degeneracy by lowest Cost Entry methad a M M2 Capacity (suply 19 30 70 2010 $0 10 20301 uolto 60 90/20 180 100/30/0 40130 8180 20 20170 Py Dened 140 so d check Non- segeneracy min-1 = No. of Independent equations, 71 = 6 - 6 son-Degeneracy So Civen pooblem is Non- les

17 North West Cornes method of stepping. stone methan check for degenepacy 2 Market nal plant Mz My plant capacity 2 P 19 3920 HO 70/20/0 so P - -70 .30 40. 4 60- 90/30/0 30 -- PO 40 - not 80/140/0 3 Mo (40 Macket Demand no so 80 60 340/340 To 140 0 40 O Total Transportation Cost by (19x50) + (30120 + (30x60) + ( 4ox 30 North West Comer method + (70X40) + (20x1440) 11 10,150 cs ned witCamScanter

3 Stepping - stone method sor Sol y Given problem is Balanced method. Stepping -stene method howe I can solve by 3 steps Step 1: Intial Basic featible solution. Steps: problem. Degeneracy Calculate Improvement Index value Step Step 1: Obtain by any of 3 methods y NW Corner method 27 Least Cost " 34 Vogel's Approximate, ICS Scanned with Camscanner

3y Vogel's Approxination method :- my Capacityp, P₂ P₃ P4 B 181 Isa 9 9 40 40 Pl 19 30 10 190 40 10 20 2020 60 90 PL 30 60 roog 50 20 180 12 20 70 8 100 1P3 40 340/340 ru 70 80% Dend SD 个 10 21 22 10 B 10 Х 10 २१॥ 2 10. 10 X x ao sor 10 4. 6o. smt5-) no. of allocation 6 = 4+ 3-) sman-) no. of allocation The problem is Degenerate CSS with CamScanner