1. The annual demand for an item is 10,000 units, each order costs $120 and the annual holding cost is 35 percent of unit cost. The unit cost depends on the quality ordered as follows:

• $3 for order quantities less than 1000
• $2.60 for quantities between 1000 to 2999
• $2.50 for quantities of 3,000 or more.

What is the optimal order size?

2. Demand for an item is constant at 10,000 units a year. The item can be made at a constant rate of 12,000 units a year. Unit cost is $120. The set-up time takes 1 week and batch set-up cost is $300, and holding cost is 35 % of value a year.

a) What is the optimal batch size for the item?

b) If production set-up time is 2 weeks, what is the stock level to make the company start to produce?

3. a) Why do some companies allow shortages and back orders, even though they know the demands?

b) How do we measure the cost for losing customers and lost sales?

4. The reorder cost for the items is constant at $1,000, and holding cost is 20% of value a year. The following table shows the unit costs and demands and the space required for each unit. The company wants to allocate an average space of 350 cubic meters to the items.

a) Show that the optimal order quantity for each item does not satisfy the space limits.

b) What would be the best ordering policy? Hint: The value of AC (additional cost) is 7 to meet the space limits.

c) How much does the constraint on space increase variable inventory cost?

5. The reorder cost is $1,200 and the holding cost is $50 a unit a week. Find an ordering pattern that gives a reasonable cost for the item. The following is the production schedule over the next 11 weeks.