The student advisement office at the University has a student worker who copies

Question

The student advisement office at the University has a student worker who copies and assembles a handbook for students whenever the supply of these runs low. Past observations indicates that these handbooks are given out at the rate of 4 per day. The student worker can copy and assemble 100 per eight-hour day. The student worker is paid 3.75 $/hour and it takes .5 hour to prepare everything to produce a batch of handbooks. The cost of carrying inventory is related to handbooks that are damaged or become obsolete due to changes in the degree requirements. On average, 10% of all handbooks become unusable, and each costs $1 in materials, labor and copying costs.

a)      If the office is open 250 days/year, how many handbooks should the student worker produce at a time in order to minimize costs?

b)      How many days of demand will be supported by this order quantity?

c)       What will be the maximum handbook inventory, assuming the minimum is zero

d)      What is the average inventory of handbooks?  

Explanation / Answer

Given are following data :

Annual demand of handbooks = D = 4 / day x 250 days = 1000

Daily demand of handbook = d = 4

Daily production capacity of handbook = p = 100

Annual unit cost of carrying inventory = Ch = 10% of $ 1 = $0.1

Set up cost ( i.e. preparation cost ) = Cs =$3.75 / hour x 0.5 hour = $1.875

Number of handbooks to be produced at a time ( EPQ = Economic Production Quantity )

= Square root ( 2 x 1.875 x 1000 / 0.1 x ( 1 – 4/100) )

= Square root ( 2 x 1.875 x 1000 / 0.1 x 0.96 )

= 197.64 ( 198 rounded to nearest whole number )

NUMBE ROF HANDBOOKS STUDENT WORKERS SHOULD PRODUCE AT A TIME IN ORDER TO MINIMIZE COST = 198

Number of days of demand will be supported by this order quantity = EPQ/d = 198/4 = 49.5 days

Maximum handbook inventory = EPQ x ( 1 – d/p) = 198 x ( 1 – 4/ 100) = 198 x 0.96 = 190.08 ( 190 rounding to nearest whole number )

Average inventory of handbooks

= ( Maximum inventory + Minimum inventory ) /2

= ( 190 + 0)/2

= 95

NUMBER OF DAYS OF DEMAND SUPPORTED BY THE ORDER QUANTITY = 49.5 DAYS

MAXIMUM HANDBOOK INVENTORY = 190

AVERAGE INVENTORY OF HANDBOOKS = 95

NUMBE ROF HANDBOOKS STUDENT WORKERS SHOULD PRODUCE AT A TIME IN ORDER TO MINIMIZE COST = 198

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