# OR-Notes

## J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

#### Inventory control tutorial question

On average I sell 150,000 units a year which I obtain from a wholesaler. I estimate that the cost to me of placing an order is £50 with the average inventory storage cost being 20% per year of the cost of a unit (£5). Currently interest rates are 15%.

What would be the optimal order quantity?

I currently order 5 times a year. How much would I save by switching to the optimal order quantity as compared with my current policy of ordering 5 times a year?

To produce a tape recorder doll the Educational Toy Company purchases all the doll material from the same vendor. The annual demand is 10,000 units, ordering cost is £10 and the storage cost per year is 15% of the purchase cost and interest rates are 5%.

• If the purchase cost is £2 per unit what order quantity would you recommend? What is the total annual inventory cost?
• Suppose that the purchase cost falls to £1.75 per unit for an order size of 500 or more. Now what is your recommended order quantity?
• What should the company decide for the order size?
• Would this decision change if the vendor offers the following discount structure:
• Order < 500 units: £2 per unit
• 500 <= Order < 1000 units: £1.75 per unit
• Order >= 1000 units: £1.5 per unit

For a particular component I use 105,000 a year with an order cost of £100 per order. My supplier has a basic price of £0.15 per unit but offers a 10% discount if I order 20,000 components or more. If the cost of storing stock is 20% of the cost of a component per year and interest rates are 10% per year then:

• what would be your recommended order quantity?
• how does your recommended order quantity change if the lead time between an order and delivery of that order is 2 weeks? If there is no change in the recommended order quantity then how can you explain this?
• how does your recommended order quantity change if (in addition to the lead time of 2 weeks) orders are not received instantaneously but at a rate of 25,000 units a month? If the recommended order quantity is more than before, but the total cost is less, then how can you explain this?