Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

NAME: Givon: An electronic store stock« irni s»l: g an order fortbe, no carrying

ID: 411296 • Letter: N

Question

NAME: Givon: An electronic store stock« irni s»l: g an order fortbe, no carrying cotst for those computcif4% 12 Spa_/com puttst. Required Caiculate the optimal ordor uantity, arus thc, tota cof te rriociel I shortages are ollowed, tre orcder eost is iedticeci by 2s s. and ttna she itia shornaae cost is 12 Spa/unit. Calculate th ptimal order quartity. the opUmai Short c) What ls the cycle time for either option? d) Ir orders are delivered in 72 hours, arnd the store ia open 7 iays tweek.whatlE age quantity, and tho nw tota cost of the model. the lead time demand? Which option is cheape? Why? How are savings achieveci e)

Explanation / Answer

It is given that,

Monthly demand = 100 units

Annual demand, D = 100*12 = 1200 units

Carrying cost (H) = 12

Ordering cost (K) = 50

(a) Optimal order quantity (Q) = (2DK/H)

= (2*1200*50/12)

= 100 units

Total cost of the model = Ordering cost + Carrying cost = (D/Q)*K + (Q/2)*H

= (1200/100)*50 + (100/2)*12

= $ 1200 per year  

(b) The new parameters of the inventory model are :

Ordering cost, (K) = 25

Shortage cost (B) = 12

Optimal order quantity (Q) = [(2DK/H)*(H+B)/B]

= [(2*1200*25/12)*(12+12)/12]

= 100 units

Optimal shortage quantity (S) = Q*H/(H+B)

= 100*12/(12+12)

= 50 units

Total cost of the model = (Q - S)2*H/(2Q) + D*K/Q + S2*B/(2Q)

= (100 - 50)2*12/(2*100) + 1200*25/100 + 502*12/(2*100)

= $ 600 per year

(c) Cycle time = Q/D = 100/1200 = 1/12 year = 1 month

(d) Lead time = 72 hours = 3 days

Lead time demand = Daily demand * Lead time in days = (1200/365)*3 = 9.9 ~ 10 units

(e) The option with shortages is cheaper. The savings are achieved by reducing the order cost with planned shortages.