Question

Consider the following information on an inventory management system:

            Item Cost:                                $10

            Order Cost:                              $250

            Annual Holding Cost:              33% of item cost

            Annual Demand:                     25,750

            Average Demand:                   515 per week

            Std. Dev. of Demand:              125 per week

            Leadtime:                                2 weeks         

1. Ignoring the uncertainty in the demand (i.e. looking only at average values), find the optimal order quantity and the reorder point. What is the annual inventory holding and ordering cost for this policy?

2. Consider now the uncertainty. The order quantity remains the same. If the target is to have a 98% fill rate, what should be the reorder point? What is the safety stock? How much additional inventory cost is incurred due to the safety stock? What should be the reorder point?

Answer 1

Given details..

Annual demand = D = 25750

Ordering cost = Co = $250

Annual unit holding cost = Ch = 33% of $10 = $3.3

Optimal order quantity

= square root ( 2 x Co x D / Ch )
= Square root ( 2 x 250 x 25750 / 3.3)

= 1975.22 ( 1975 rounded to nearest whole number )

OPTIMAL ORDER QUANTITY = 1975 UNITS

Annual ordering cost

= Ordering cost x Number of orders annually

= Ordering cost x Annual demand / Optimal order quantity

= $250 x 25750 /1975

= $3259.49

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= $3.3 x 1975/2

= $3258.75

Annual unit inventory holding and ordering cost for this policy

= $3259.49 + $3258.75

= $6518.24

ANNUAL INVENTORY HOLDING AND ORDERING COST = $6518.24

Z value for 98% fill rate = NORMSINV ( 0.98 ) = 2.0537

Standard deviation of weekly demand = 125

Lead time = 2 weeks

Therefore , Standard deviation of demand during lead time

= Standard deviation of weekly demand x Square root ( Lead time )

= 125 x Square root ( 2 )

= 125 x 1.414

= 176.75

Therefore ,

Safety stock = Z value x Standard deviation of demand during lead time = 2.0537 x 176.75 = 362.99 ( 363 rounded to nearest whole number )

Reorder point

= Average weekly demand x Lead time ( weeks ) + Safety stock

= 515 x 2 + 363

= 1030 + 363

= 1393

REORDER POINT = 1393

SAFETY STOCK = 363

Additional inventory cost incurred due to safety stock

= Safety stock x annual unit inventory holding cost

= 363 x 3.3

= $ 1197.9 ( $1198 rounded to nearest whole number )

ADDITIONAL INVENTORY COST INCURRED DUE TO SAFETY STOCK = $1198