The business manager of an office building restocks printer ink cartridges for all employees. The demand...

The business manager of an office building restocks printer ink cartridges for all employees. The demand for the cartridges is approximately 30 per month. Let the standard deviation be 5. Cartridges cost $100 each and they require 3 weeks to be delivered from the moment they are ordered. The cost to place an order is $45. The interest rate is 20% per month. a) What are the optimal values for a continuous review policy? Assume a stockout scenario where each stockout event costs $50. b) What are the optimal values for a continuous review policy? Assume a backorder scenario where the additional cost per unit of a backorder is $30. This includes the cost to expedite the shipment from a different supplier.

Solutions

Expert Solution

D = monthly demand = 30
Sd = std. deviation of monthly demand = 5
L = average lead time = 3 weeks
S = ordering cost = $45
H = carrying cost per item per month = 20% x $100 = $20

Std. deviation of lead time demand = Sl = Sd*SQRT(L) = 5*SQRT(3) = 8.66
Average lead time demand = d = (3/4) x 30 = 22.5

(a)

For the stockout option, p = cost of stckout = $50

Q[0] = SQRT(2*D*S/H) = SQRT(2*30*45/20) = 11.61
1 - Q[0]*h/p*D = 1 - 11.61*20/(50*30) = 0.8452
R[0] = F-inv(1 - Q[0]*h/p*D) = F-inv(0.8452) = 22.5 + NORMSINV(0.8452)*8.66 = 31.3

n(R[0]) = Sl*L(Z) = 0.699
Q[1] = SQRT((2*D*K + p*n(R[0]))/H) = SQRT((2*30*45 + 50*0.699)/20) = 11.69
1 - Q[1]*h/p*D = 1 - 11.69*20/(50*30) = 0.844
R[1] = F-inv(1 - Q[1]*h/p*D) = F-inv(0.844) = 22.5 + NORMSINV(0.844)*8.66 = 31.3

Since these values are converging, we can take the (Q, R) policy of Q=12 and R=31 as the optimal policy.

(b)

B = cost of backorder per unit = $30

EOQ (Q*) = SQRT(2*D*S/H) x SQRT((B+H)/B) = SQRT(2*30*45/20)*SQRT((30+20)/30) = 15

b* = optimal backorder level = Q*H / (B+H) = 15*20/(30+20) = 6

So, the optimal ordering policy will be Q=15 and R = -6, So, when the inventory on hand becomes less than 6 units, order 15 units.

keosha answered 1 year ago

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