Question

A company purchases 86 400 items per year for use in its production process. If the unit cost is $9.25, the holding cost for one unit is 60 cents per month, and the cost of making a purchase is $540, determine the following if no shortages are allowed:

(i) The optimum order quantity.  

(ii) The optimum total yearly cost.

(iii) The number of orders per year.  

(iv) The time between orders.  

(b) Suppose they plan to now allow backorders which they estimate at a cost of 20 cents per unit per month. If all other costs are the same determine:

(i) The optimum order quantity and the maximum inventory level.

(ii) The optimum total yearly cost.

(iii) The maximum shortage that will occur.

(iv) The proportion of time that shortages will occur.

Answer 1

Solution:

Annual Purcahsed Quantity = 86,400 Units

Ordering Cost per order = $540

Carrying Cost per unit per annum = Unit Cost * 60% * 12 = $9.25*60%*12 = $66.60

(i) Optimum Order QUantity = ((Annual Purchased Quantity x 2 x Ordering Cost per order) / Carrying cost per unit per annum)^1/2

= ((86,400*2*540)/66.60)^1/2

= 1183.67 Units or 1184 Units

(ii) Optimum Total Yearly Cost = Cost of Purcahsed + Total Ordering Cost + Total Carrying Cost

= (86,400*9.25) + (Number of Orders 86,400 / 1184 * 540) + (1/2*1184*66.6)

= $878,033

(iii) Number of Orders Per Year = Total Purcahsed QUantity / Optimum order quantity

= 86,400 / 1184

= 72.97 or 73 orders

(iv) Time between orders

Assumed a year = 365 days

Time between orders = Days in a year / Number of Orders = 365 / 73 = 5 days

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