Operations Management Capacity Cushion

Chapter 9  SUPPLEMENT C

1)

Annual demand =2750 rolls

Cost/roll=875

Holding Cost=12%

Order cost=45

a) How many rolls should yellow press order at a time?

The Economic Order Quantity is

EOQ= (2DS/H)1/2

D= Demand in rolls/year

s=Cost/order =45

H= Cost/roll * annual holding cost 

=875*0.12= 105

= (2*2750*45/105)1/2

=48.55

=49 rolls at a time

b) Find time between orders? (Assume 365 workdays/yr)

The time between order (TBO), expressed in days is:

TBOEOQ = EOQ/D (365workdays/year)

= (49 / 2750)*365

=6.503636

=6.5 days

2) Babble Inc buys 425 blank tapes/month

Ordering Cost= 11.75

Holding Cost=0.25/cassette per year

1. How many tapes should Babble order at a time?

Economic Order Quantity= EOQ= ?

Demand in tapes/year = D =425*12= 5100 Tapes

Ordering Cost= S= 11.75

Holding cost/per tape per year =H=0.25

EOQ= (2DS/H)1/2

EOQ= (2*5100*11.75/0.25)1/2

=692.387

=692 Tapes

B) What is the time between orders (TBO)?

TBOEOQ = EOQ/D =692/425 =1.628235 =1.6

Rough:

EOQ50.15 =(2*5100*11.75/0.25)1/2

3)

EOQ = Economic Order Quantity

D= Annual Demand =320 *50

S= Annualset-up cost/lot=100

H= Annual holding cost/unit=38%

• Calculate EOQ for lowest price in table

EOQ= (2DS/H)1/2

           EOQ6.60 = (2*320*50*100/0.38*6.60)1/2

=1129.564

=1130 baseballs

Solution is infeasible as 1130 units corresponds to price of $7.35/unit and not $6.60/unit

• Calculate EOQ for next higher price in table

EOQ7.35 = (2*320*50*100/0.38*7.35)1/2

=1070.383785

=1070 baseballs

Solution is feasible as 1070 units rightly corresponds to $ 7.35/unit

We will now determine whether total cost can be reduced by purchasing 5000 baseballs that corresponds to lowest price/unit. For this, we need to find total annual cost given the lot size is 1070 baseballs.

P= Price per purchased unit

CQ = (Q/2)* H + (D/Q) *S + PD

C1070 = (1070/2)*0.38*7.35 + (320*50)/1070 *100 + 7.35*320*50

=1494.255 + 1495.327103 +117600

=120589.582

=120590

Now, the total annual cost at the lot size of 5000 baseballs

CQ = (Q/2)* H + (D/Q) *S + PD

C5000 = (5000/2)* 0.38* 6.60 + (320*50)/5000 *100 + 6.60*320*50

= 6270 + 320 + 105600

=112190

Thus, Team should buy 5000 baseballs/order

1. If it buys 15000 baseballs or more, price drops to $6.35/unit. Should we revise the order?

Calculate EOQ at lowest price of $6.35/unit

EOQ= (2DS/H)1/2

           EOQ6.35 = (2*320*50*100/0.38*6.35)1/2

=1151.58

=1152

Not feasible as 1152 units corresponds to price of $ 7.35/unit

• We can find whether total cost can be reduced by purchasing 15000 baseballs that corresponds to lowest per unit cost.
• CQ = (Q/2)* H + (D/Q) *S + PD

C15000 = (15000/2)* 0.38* 6.35 + (320*50)/15000 *100 + 6.35*320*50

=18097.5 +106.66 + 101600

=119804.16

=119804

Comparing this result to optimal result we obtained in (a)i.e 112190 concludes that team should buy 5000 baseballs/order

 Chapter 11 –Location

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