Question

1. Hayes Electronics stocks and sells a particular brand of personal computer. It costs the firm $450 each time it places an order with the manufacturer for the personal computers. The cost of carrying one PC in inventory for a year is $170. The store manager estimates that total annual demand for the computers will be 1,200 units, with a constant demand rate throughout the year. Orders are received within minutes after placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts of the PCs. The store is open for business every day of the year except Christmas Day. Determine the following:

   1. The optimal order quantity per order

   2. The minimum total annual inventory costs

   3. The optimal number of orders per year

   4. The optimal time between orders (in working days)

2. Hayes Electronics in Problem 1 assumed with certainty that the ordering cost is $450 per order and the inventory carrying cost is $170 per unit per year. However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model parameters: (a) Both ordering cost and carrying cost are 10% less than originally estimated, (b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity and total inventory cost for each of the four cases. Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values.

I need the answer for question 2.

Answer 1

Sol:

Given

        $450 ordering cost per order
         $170 inventory carrying cost per unit per year
        D = annual demand (unknown)

(a)
optimal order quantity = √[2CoD/Cc]
= √[2(450*0.9)D/(170*0.9)]
= 2.3√D

total inventory cost = CoD/Q + Cc*Q/2
= (450*0.9)D/(2.3√D) + (170*0.9)*(450*0.9)/2
= 176√D + 30982.5

(b)
Q = √[2D(450*1.1)/(170*1.1)]
= 5.29√D
Total inventory cost = (450*1.1)D/(2.3√D) + (170*1.1)*(450*1.1)/2
= 215√D + 46282.5

(c)
Q = √[2D(450*1.1)/(170*0.9)]
= 2.54√D
Total inventory cost = (450*1.1)D/(2.3√D) + (170*0.9)*(450*1.1)/2
= 215√D + 37867.5

(d)
Q = √[2D(450*0.9)/(170*1.1)]
= 2.08√D
Total inventory cost = (450*0.9)D/(2.3√D) + (170*1.1)*(450*0.9)/2
= 176√D + 37867.5

Conditions	Q	Total Inventory         Cost
a	2.3 √D	176√D + 30982.5
b	5.29√D	215√D + 46282.5
c	2.54√D	215√D + 37867.5
d	2.08√D	176√D + 37867.5