Question

# 4.a) Find the savings between the total cost of the current production run size and the...

4.a) Find the savings between the total cost of the current production run size and the optimal run size.

b) Find the additional savings in production costs and ordering and holding costs with the proposed project. Calculate the payback period for the investment in the project.

The anticipated annual demand for a chemical product distributed by the Seanna Chemical Group is 25,000 tons per year for the coming year. The company is currently producing the product with a capacity of 80,000 tons/year and a production line setup cost of \$4,000/production run. Assume that the variable cost for the production is \$400/ton and the unit holding cost is estimated as 25% of the variable cost. The company operates 250 working days per year.

a) The current production run size is 5,000 tons/run. How much can Seanna save by optimizing the ordering policy (that is, by using the EOQ model with a finite delivery rate)?

b) Suppose that Seanna recently implemented the optimal policy in part (a) and the Engineering Department is now proposing an investment of \$2 million to renovate its facility for this product, which would reduce the variable cost to \$380/ton and the line setup cost to \$3,000/production run. What will be the annual savings that Seanna may achieve from this (in terms of the sum of production and fixed ordering and holding cost)? As the Chief Operating Officer of the company, would you consider this proposal?

We have the following information (in tons)

Demand (D) = 25000

Setup cost (S) = 4000

Holding cost (H) = 100

Current production run (Q) = 5000

a) The current expense incurred are the holding expense and ordering expense.

Annual holding (carrying) cost is given by HQ/2 = 100*5000/2 = 250,000

Ordering cost is given by DS/Q = 25000*4000/5000 =20,000

The total cost is 250,000+20,000 = 270,000

Now let’s find the Economic order quantity (EOQ) using the formula

EOQ = sqrt (2DS/H) = sqrt (2*25000*4000/100) = 1414.21 (we can round it to 1414.

Now let’s determine the total cost using economic order quantity.

Total cost is (100*1414/2) + (25000*4000/1414) = 70700 + 70721 = 141,421

This means through EOQ the savings is 270,000 - 141,421 = 128,579

b) With the new project the changes are

Setup cost (S) = 3000

Holding cost (H) = 95 (25% of 380)

Rest of the information remains the same.

This means the new EOQ will be sqrt (2*25000*3000/95) = 1256.56 (round it to 1256)

The new annual cost will be (95*1256/2) + (25000*3000/1256) = 59660 + 59713 = 119,373

The total saving from the previous operation is 141,421 – 119,373 = 22,048

Considering that this project requires a \$2 million investment, and provides an annual saving of \$22,048 I will not consider this proposal.

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