Inventory Management

Problem $1$

A large law firm uses an average of $10$ packages of copier paper a day. Each package contains

$500$ sheets. The firm operates $260$ days a year. Storage and handling costs for the paper are $$1$

per year per package, and it costs approximately $$10$ to order and receive a shipment of

papers.

a$)$ What order quantity would minimize total annual ordering and holding cost?

b$)$ Calculate the total annual inventory control cost using your order quantity from part a$.$

c$)$ The office manager is currently using an order quantity of $100$ packages. The partners of

the firm expect the office to be managed in a cost$-$efficient manner. Would you

recommend that the office manager use the optimal order quantity instead of $100$

packages? Justify your answer.

Problem $2$

A chemical plant produces sodium bisulfate in $100kg$ bags. Demand for this product is $20$

tonnes per day. The capacity for producing this product is $50$ tonnes per day. Setup cost is $$400,$

and storage and handling costs are $$200$ per tonne per year. The company operates $200$ days a

year. $($Note: $1$ tonne $=1,000kg).$

a$)$ What is the optimal number of bags per production run?

b$)$ What would the average inventory level be for this lot size?

c$)$ Determine the approximate length of a production run, in days.

d$)$ About how many production runs per year would there be$?$

e$)$ How much could the company save annually in inventory control cost if the setup cost

could be reduced to $$200$ per production run and the optimal production quantity is

recalculated and used?