Question

2. Ogunmodede Medical Company stocks medical devices for hospitals in the state of Colorado. The average rate of demand for the prostheses is 100 per month and appears to be described quite well by a Normal distribution with standard deviation of 10. The procurement lead-time τ = 6 months. Each medical device costs $2,000. The cost of placing an order with the manufacturer, incoming inspection, etc. is estimated to be $100.00. The annual inventory carrying cost rate is 0.20. All stock outs are backordered. It is difficult to estimate the cost of being out of stock. Instead, it is required that the probability of being out of stock not be greater than 0.0005.

(a) If the facility is to operate as a [Q,r] system, determine Q∗ and r ∗ .

(b) What is the imputed cost of a backorder π?

(c) What is the cost of uncertainty?

Answer 1

Given data

Ogunmodede Medical Company stocks medical devices average monthly demand, d = 100
described quite well by a Normal distribution with standard deviation is σ = 10
The procurement average lead-time τ = 6 months

Cost of each medical devices is C=$2,000

The annual inventory carrying cost rate is % i= 0.20.

Estimated cost is K=$100

In-stock probability of the devices = 1 - 0.0005 = 0.9995.

So, Z = normsinv(0.9995) = 3.29

a)determine Q∗ and r ∗ as follows:

The medical devices annual demand

D = 12*d = 1,200
The unit carrying cost per annum of the stock medical devices

h = i.C = 0.2*2000 = $400

determination of Optimal order size as follows:

Q* = (2.D.K / h)1/2 =

sqrt(2*1200*400 / 100)

= 98 units

The Safety stock calculation as follows:

SS = Z * σ * √t

= 3.29*10*√6

= 81 units

The Reorder point calculation as follows:

r* = d.t + SS

= 100*6 + 81

= 681 units

b) The imputed cost of a backorder π determination as follows:

The Imputed cost of backorder is

p = h ((1/α) -1)

= 400*((1/0.0005) - 1)

= $799,600

c) The cost of uncertainty calculation as follows:

The Cost of uncertainty is equal to cost of holding the safety stock

= SS*h

= 81*400

= $32,400