Further Business Applications Lesson 6.3. Economic Lot Size A manufacturer can produce its product in varying batch sizes 120 once a year 60 twice a year.

Further Business Applications

Lesson 6.3

Economic Lot SizeA manufacturer can produce its product in varying batch sizes• 120 once a year• 60 twice a year• 10 each month … etc.

Elements to be considered • k = Costs for storage one unit for a year• f = Fixed setup cost per batch• g = Mfg. cost per item• M = Total number of items per year• q = Number of items per batch 2

Economic Lot Size

Manufacturing cost per batch

Number of batchesper year

Total annual manufacturing cost

Inventory goes down linearly q to 0• Average inventory q/2 units per year• Storage costs

3

f g q M

q

M f Mf g q g M

q q

2

k q

Economic Lot Size

Total production cost is sum of• Manufacturing costs• Storage costs

To minimize T(q) we solve T '(q) = 0 for q• Find this solution before proceeding • Check your answer with text book solution

4

( )2

f M k qT q g M

q

2 f Mq

k

Try It Out

LeTourneau Lamps makes 100,000 lamps annually • Costs $1 to store a lamp for a year• Costs $500 to set up factory to produce a

batch

What is the optimum number of lamps to produce in each batch?

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Economic Order Quantity

Suppose we purchase an item for sale• How often should we order• How many do we buy for each order

Elements to be considered • k = Costs for storage one unit for a year• f = Fixed costs to place an order• M = Total number of items per year• q = Number of items per batch

Goal: minimize Total Cost = Storage Cost + Reorder Cost

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Economic Order Quantity

Assume average inventory of q/2• Yearly storage cost•

Number of orders placed annually

Reorder cost

Total cost7

2

k q

M

q

f M

q

( )2

f M k qT q

q

Determine T '(q)Solve T '(q) = 0 for q

Determine T '(q)Solve T '(q) = 0 for q

Sample Problem

The LeTourneau Bookstore hasan annual demand for 100,000 copies of that best seller, Calculus with Applications• It costs $.50 to store the copy for one year• It costs $60 to place an order

What is the optimum number of copies per order?

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Assignment

Lesson 6.3

Page 333

Exercises 5 – 13 odd

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