Tutorial 6 Exercises

Question 1

Brown Manufacturing produces mini-sized refrigeration packs in batches. The firm’s estimated demand for the year is 10,000 units. Because Brown operates for 167 business days each year, this annual demand translates to a daily demand rate of about 60 units per day. It costs about $100 to set up the manufacturing process, and the carrying cost is about $0.50 per unit per year. When the production process has been set up, 80 refrigeration packs can be manufactured daily. Each pack costs $5 to produce. How many packs should Brown produce in each batch?

Question 2

Shakina Harris, who works in her brother’s hardware store, is in charge of purchasing. Shakina has determined that the annual demand for #6 screws is 150,000 and is fairly constant over the 200 days that the store is open each year. She estimates that it costs $30 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is 0.6 cents.

  1. How many #6 screws should Shakina order at a time?
  2. It takes 8 working days for an order of #6 screws to arrive once the order has been placed. Because the demand is fairly constant, Shakina believes that she can avoid stockouts completely if she orders the screws only when necessary. What is the reorder point?
  3. Shakina’s brother believes that she is placing too many orders for screws each year. He believes that orders should be placed only twice per year. If Shakina follows her brother’s policy, how much more would this cost every year over the ordering policy that she developed in part (a)? If only two orders are placed each year, what effect would this have on the reorder point?
  4. Shakina now believes that her estimate of an ordering cost of $30 per order is too low. Although she does not know the exact cost, she believes that it could be as high as $60 per order. How would the optimal order quantity in part (a) change if the ordering cost were $40, $50, or $60?

Question 3

Neha Shah is the purchasing agent for a firm that sells industrial valves and fluid control devices. One of the most popular valves is the KA1, which has an annual demand of 6,000 units. The cost of each valve is $120, and the inventory carrying cost is estimated to be 8% of the cost of each valve. Neha has made a study of the costs involved in placing an order for any of the valves that the firm stocks and she has concluded that the average ordering cost is $45 per order. Furthermore, it takes about two weeks for an order to arrive from the supplier, and during this time the demand per week for KA1 valves is approximately 120. Compute the EOQ, reorder point, optimal number of orders per year, and total annual cost for KA1 valves.

Question 4

Shoes R Us is a local shoe store located in Camden. Annual demand for a popular sandal is 1,000 pairs of sandals, and Gary Cole, the owner of Shoes R Us, has been in the habit of ordering 200 pairs of sandals at a time. Gary estimates that the ordering cost is $20 per order. The cost of a pair of sandals is $10.

  1. For Gary’s ordering policy to be correct, what would the carrying cost have to be as a percentage of the unit cost?

  2. If the carrying cost were 20% of the unit cost, what would be the optimal order quantity?

Question 5

An aircraft company uses rivets at an approximate annual demand rate of 2,500 kg. Each unit costs $30 per kg, the company personnel estimate that it costs $130 to place an order, and the carrying cost of inventory is 10 % per year. How frequently should orders for rivets be placed? Also, determine the optimum size of each order.

Question 6

The annual requirements for a particular raw material are 2,000 units, costing $1.00 each to the manufacturer. The ordering cost is $10.00 per order, and the carrying cost is 16% per annum of the average inventory value. Find the economic order quantity and the total cost of an inventory system.

Question 7

For an item, the production is instantaneous. The holding cost of one item is $1.00 per month, and the set-up cost is $25 per run. If the demand is 200 units per month, find the optimum quantity to be produced per set-up and the total cost of storage and set-up per month.

Question 8

A contract requires cement that amounts to 300 bags per day. No shortages are allowed. Cement costs $2.00 per bag, inventory carrying cost is 25% per annum of the average inventory valuation, and it costs $20 to purchase an order. Find the minimum cost of the purchased quantity for the annual working days of 249 days.

Question 9

The annual demand for a product is 100,000 units. The rate of production is 200,000 units per year. The set-up cost per production run is $5,000, and the variable production cost of each item is $10. The annual holding cost per unit is 20% of its value. Find the optimum production lot size and the total cost of storage and set-up.

Question 10

A product is to be manufactured on a machine. The production rate of that item on the machine is 2500 units per month, and the annual demand is uniform at 18,000 units. The setup cost is $800 per batch, and the annual holding cost in inventory is $18 per unit. Lead time is five days, and the number of working days per month is 20 days. Determine the following:

  1. The most economical batch quantity of a product on a machine
  2. The maximum inventory
  3. The minimum inventory cost.
  4. Reorder point
  5. How will the batch quantity vary if the production rate is infinite?