Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest moving inventory item has a demand of 6000 units per year. The cost of each unit is $100.00, and the inventory carrying cost is $10.00 per unit per year. The average ordering cost is $30.00 per order. It takes about 5 days for an order to arrive, and demand for 1 week is 120 units (this is a corporate operation, there are 250 working days per year).
a. What is the EOQ? b. What is the average inventory if the EOQ is used?
c. What is the optimal number of orders per year? d. What is the optimal number of days in between any two orders?
e. What is the annual cost of ordering and holding and holding inventory?
f. What is the total annual inventory cost, including cost of the 6,000 units?

Answer 1

A) 
To determine the Annual Set-up Cost 
Annual set-up cost = (# of orders placed per year) x (Setup or order cost per order)  = Annual Demand # of units in each order ¡Á (Setup or order cost per order)  = (D/Q) ¡Á(S) 
           = (6000/Q) x (30) 

To determine Annual holding cost = Average inventory level x Holding cost per unit per year = (Order Quantity/2) (Holding cost per unit per year) 
                           = (Q/2) ($10.00) 

 
To determine Optimal order quantity is found when annual setup cost equals annual holding cost:  (D/Q) x (S) = (Q/2) x (H) 
                          (6,000/Q) x (30) = (Q/2) (10) 
                                                    =(2)(6,000)(30)
                                                    = Q2 (10) 
Q2 = [(2 ¡Á6,000 ¡Á30)/($10)]
      = 36,000 
       =([(2 ¡Á6,000 ¡Á30)/(10)])
       =189.736 ¡Ö 189.74 units 
Hence, EOQ = 189.74 units 

B)  
Average inventory level = (Order Quantity/2) 
                                      = (189.74) /2
                                      = 94.87 
Average Inventory level =94.87 units 

C)  
N= ( Demand/ order quantity)
    = (6000/ 189.736)
    =31.62 
Hence, the optimal number of orders per year = 31.62 

D) 
T = (Number of Working Days per year) / (optimal number of orders) 
   = 250 days per year / 31.62
   = 7.906 
So, the optimal number of days in between any two orders = 7.91 

E) 
Using, (Q) x (H) : (189.736 units) x ($10) =$1,897.36 
So, The annual cost of ordering and holding the inventory = $1,897 

F)
TC = setup cost + holding cost 
      = (Dyear/Q) (S) + (Q/2) (H) 
      = (6,000/189.74) ($30.00) + (189.74/2) ($10.00) 
      = $948.67 + $948.7 
      = 1,897.37
Purchase cost = (6,000 units) x ($100/unit)
                       = $600,000 
Total annual inventory cost = $600,000 + $1,897
                                            = $601,897