Question

Please consider the demand and cost information shown below. Note that the order quantity shown (2,000 units per order) is not optimal.

• What is the total logistics cost in this current scenario?

• What would be the economic order quantity?

• By how much (in % terms) could total logistics costs be reduced if the firm used the EOQ rather than an order quantity of 2,000 units?

• Finally, the firm is considering one of two options: Option A would allow the firm to reduce order placement costs to $850 per order (all else equal). Option B, in turn, would allow the firm to reduce physical warehousing charges, thus bringing inventory holding costs down to $41 per unit per year (all else equal). Given the choice between Option A and Option B, which one would you recommend? By how much (in % terms) could total logistics costs be reduced (relative to the initial optimal scenario) if the preferred option was implemented?

Current Annual demand, D = 28,540 units/year

Order placement costs, K = $1,230 per order

Holding cost, h = $68.00 per unit per year

Order quantity, Q = 2,000units per order

Answer 1

Economic order quantity = [ 2 x annual demand x ordering cost / cost of holding one unit per year]^1/2

   = [ 2 x 28540 x1230 /68]^1/2 = 1016

cost with EO quantity = cost of holding + cost of ordering

= (1016/2) x 68 + ( 1230x (28540 /1016)

=34544+ 34551= 69095

Cost with 2000 quantity

   = (2000/2 ) x 68 + 1230 x 28540 / 2000 = 85552

If the order size reduces to 1016, the cost will decrease by ( 85552-69095) = 16457

Cost with option A ( reduction or ordering cost)

EO quantity = [ 2 x 28540 x850 / 68]^1/2 = 845

cost = (845 /2 ) x68 + 850 x ( 28540 / 845) = 57439

Cost with option 2

=EO quantity = [ 2 x 28540 x1230 / 41]^1/2 = 1308

cost = 1308/2 x41 +1230x ( 28540 / 1308) = 26814+26838 = 53652

Option b is better as it has lower cost.

percentage reduction of the original cost =( 69095-53652) / 69095 = 0.2235

= 22.35%