Question

2) Consider the dynamic demand of an end item following the MRP explosion proces3. Time Demand 50 75 The order cost (setup) per order is S125. Inventory carrying charge is assumed to be $1 per unit per time period. Find out the dynamic lot sizes for this problem by using a) Silver-Meal Method b) LUC method c) PPB method d) Solve the problem optimally by using the Wagner Within algorithm e) Compare and contrast the total cost of the obtained solutions.

Answer 1

MRP Explosion a) Silver-Meal Method A $125, h $1/unit/ period m-1K(1) : 125 m 2 K (2) (1/2)*(125+ (1)*75) 100 < K (1) so continue m 3 K (3) (1/3)*(125 (1)*75(2)*30)-86.68 K (4) STOP Q1 175 units m -1, from period 5 K (1) 125 m 2 K (2) (1/2)*(125 (1)*100) 112.50 < K(1) so continue Q5 180 units TC $320$225 $545 b) LUC method A $125, h $1/unit/ period m 1 K (1) 125/50 2.5 m 2 K (2) (125(1)*75)/(50+75) 1.6< K (1), continue m 3 K (3) (200(2)*30) (12530) 1.68> K (2), STOP Q1 125 units m-1, from period 3 K (1) 125/30 4.167 m 2 K (2) (125 (1)20) (3020) 2.9 < K (1), continue m 3 K (3) 145(2)80) (50+80) 2.346< K (2), continue m 4 K (4) (305(3)100) (130+ 100) 2.63 >K (3), STOP Q3 130 units Q6 100 units TC 125($1.6) +130($2.346) +$125 $630

c) PPB method ppF A/h 125 From period 1 PP1-0 PP2 75<125 PP3 75+ (2)30 135 > PPF, STOP Q1 50 75 125 units From period 3 PP1-0 PP2 20 < PPF PP3 20+ (2)80 180> PPF, STOP Q3 30 20 50 units From period 5 PP1-0 PP2 100< PPF Q5 80100-180 units TC $125(3) (75+20+100) $1) $570

d) Solve the problem optimally by using the Wagner Within algorithm? Cij sum of production & inventory costs required to satisfy the entire demand from period i u to and including period (j-1) Ft, t 1 to 6,- minimum cost incurred from period t until end of the planning horizon FT+1, T-6, 0 F7 0 F6 min (c67 f7-min 11251- $125 F5 min [c56 f6min [125 125 $250 (57 + f7)(125 + 1(100) + 0 = $225) = $225 F4 -min [c45 f5 min [125225 $350 (c46 f6] 1125+1(80) +125 $330] [c47f7 [125+1(80) +2(100) +0 $4051 $330 F3 min [c34f4 min [125330 $455) c35f5] 1125+1(20) +225 $370] fc36 + f6)(125+1(20) +2(80) +125 = $430} (c37f7 [125+1(20) +2(80) +3(100) $605 $370 F2 min [c23 f3 min [125370 $495) c24f4 1125+1(30) +330 $460] (c25f5 125+1(30) +2(20) +225 $420] (c26+f6 125+1(30) +2(20) +3(80) +125 $560] (c27+ f7) (125+1(30) +2(20) +3(80) +4(100) $835 $420 F1-min [c12f2 min [125420 $5451 (c13f3 1125+1(75) +370 $570] (c14f4 125+1(75) +2(30) +330 $5901 (c15 + f5] 125+1(75) +2(30) +3(20) +225 S545 (c16 f6 125+1(75) +2(30) +3(20) +4(80) +125 $765] fc17+ f7) (125+1(75) +2(30) +3(20) +4(80) +5(100) $1140 $545 Q1 50+75+30+20 175 units Q5 80+100 180 units TC $125(2) $1((1) (100+75)) (2) (30) (3)(20)) 250+175+60+60 $545 e) Compare and contrast the total cost of the obtained solutions. Silver-Meal: order schedule: (175, o, o, 0, 180, 0), TC $545 LUC: order schedule: (125, 0, 130, 0, 0,100), TC $630 PPB: order schedule: (125, 0, 50, 0, 180, 0), TC S570 Wagner-Within: order schedule: (175, 0, 0, 0, 180, 0), TC $545 The optimal cost is $545 which is produced by the Wagner-Within algorithm and The Silver-Meal heuristic. LUC Method has the highest cost associated with it.