Question

In: Operations Management

Maxima distributor uses 500 units of an ofﬁce supply per year. The cost of the ofﬁce...

Maxima distributor uses 500 units of an ofﬁce supply per year. The cost of the ofﬁce supply is $60/unit, for orders of less than 50 units; $55/unit for orders greater or equal to 50. The inventory holding cost is 20% of its unit price per year. The procurement order setup cost is $15/order. What is the optimum purchase order quantity that Maxima should place and what is the total cost? (TCO=KD/Q+hQ/2+cD)

Expert Solution

Scenario 1: The cost of the ofﬁce supply is $60/unit, for orders of less than 50 units

Unit cost = $60 / unit

A = Annual Requirement = 500 units

O = Ordering cost / order = $ 15 / order

C = Carrying cost / unit / annum= $ 60 x 20% = $ 12

EOQ = √2AO/C

= √2*500*15/12

=√15000/12

=√1250

=35.36 units

Thus EOQ ≈ 35 units

No. of order = 500 / EOQ = 500/35 =14.29 orders ≈ 14 orders

Ordering cost = No. of orders x Ordering cost per order = 14 x $ 15 = $ 210

Carrying cost = (EOQ/2) x Carrying cost per unit per annum = (35/2) x 12 = $ 210

Total Cost = Ordering cost + Carrying cost = 210+210 = $ 420

Cost of units of Office supply in the year = 500 units x $ 60 = $ 30000

Total cost inclusive of unit cost = 30000+210+210 = $ 30420

Scenario 2: The cost of the ofﬁce supply is $55/unit, for orders of greater than or equal to 50 units

Unit cost = $55 / unit

A = Annual Requirement = 500 units

O = Ordering cost / order = $ 15 / order

C = Carrying cost / unit / annum= $ 55 x 20% = $ 11

EOQ = √2AO/C

= √2*500*15/11

=√15000/11

=36.93 units

Thus EOQ ≈ 37 units

Since in this also EOQ is coming less than 50 so this scenario is invalid (as it was assumed that the order quantity is greater than or equal to 50 units)

Hence, final answer can be drawn from scenario 1:

Optimum purchase order quantity = EOQ of scenario 1 = 35 units per order

Total cost:

Total Cost = Ordering cost + Carrying cost = 210+210 = $ 420

Cost of units of Office supply in the year = 500 units x $ 60 = $ 30000

Total cost inclusive of unit cost = 30000+210+210 = $ 30420

Total cost (inclusive of unit cost) = 30000+210+210 = $ 30420

keosha answered 2 years ago

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