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ECONOMIC ORDER QUANTITY

Sample Problems

Home | What is Economic Order Quantity? | Its Cost Components | EOQ Model with Purchases | Assumptions of the Model | Optimizing Economic Order Quantity | Graphical Solutions | Sample Problems | Answers

 

Sample Problems

  1. ABC company is attempting to minimize total inventory cost. The cost of each unit is $2.25. The cost of capital is 15% and the physical cost of maintaining this inventory is currently running at 7%. The purchasing officer can place an order in 25 minutes with materials and overhead cost of $7.50 per order. The purchase officer is currently paid $18.00 per hour. Records show, average weekly sales to be 12,000 units.  
    1. How many units should ABC order?
    2. How often should ABC place each order?
    3. What is the minimum TIC?


  2. Joe's pizza parlor is attempting to minimize total inventory cost. The cost of each pizza is $1.25. The cost of capital is 18% and the physical cost of maintaining his pizza inventory is currently running at 2% of cost. Joe pays his secretary/bookkeeper $7.50 per hour. Joe's secretary can place an order in 15 minutes with materials and overhead cost of $15.00 per order. Records show, weekly pizza sales as follows:

    Weekly Pizza Sales
    Week Sales(units)
    1 475
    2 515
    3 525
    4 500
    5 485


    1. How many units should Joe order?
    2. How often should Joe place each order?
    3. What is the minimum TIC?


  3. Suppose R & B Beverage Company has a soft-drink product that has a constant annual demand rate of 3,600 cases. A case of the soft drink costs R & B $3.00. If ordering costs are $20 per order and inventory holding costs are charged at 25%, what are the EOQ and cycle time in days for this product?

  4. A general property of the EOQ inventory model is that total inventory holding and total ordering costs are equal or balanced at the optimal solution. Use the above data to show that this result is observed.

  5. The XYZ Company purchases a component used in the manufacturing of automobile generators directly from the supplier. XYZ's generator production operation, which is operated at a constant rate, will require 1,000 components per month throughout the year. If ordering costs are $25.00 per order, unit cost is $2.50 per component, and annual inventory holding costs are charged at 20%, answer the following inventory policy questions for XYZ.  
    1. What is the EOQ for this component?
    2. What the cycle time in months?
    3. What are the total annual inventory holding and ordering costs associated with your recommended EOQ?
    4. Assuming 250 days of operation per year and a lead time of 5 days, what is the reorder point for the XYZ Company?

 

  1. Suppose that XYZ's management likes the operational efficiency of ordering in quantities of 1,000 units and ordering once each month.
    1. How much more expensive would this policy be than your EOQ recommendation?
    2. Would you recommend in favor of the 1,000-unit order quantity? Explain.
    3. What would the reorder point be if the 1,000-unit quantity were acceptable?

  2. Tele-Reco is a new specialty store which sells television sets, videotape recorders, video games, and other television-related products. A new Japanese-manufactured videotape recorder costs Tele-Reco $600 per unit. Tele-Reco's inventory carrying cost is figured at an annual rate of 22%. Ordering costs are estimated to be $70 per order.  Assume 365 days per year and a lead time of 5 days.
    1. If demand for the new videotape recorder is expected to be constant with a rate of 20 units per month, what is the recommended order quantity for the tape recorder?
    2. What is the estimated annual cost for inventory and ordering costs associated with this product?
    3. How many times will orders be placed per year, and what is the cycle time for this product?
    4. What is the reorder point in units?
    5. What impact would a cost increase to $1,200 per unit have on the inventory policy?


  3. DIG4OIL Inc, a large distributor of oil-well drilling equipment has operated over the past two years with EOQ policies based on an annual inventory carrying charge of 22%. Under the EOQ policy, a particular product has been order with a EOQ = 80. A recent evaluation of carrying costs shows that because of an increase in the interest rate associated with bank loans, the inventory carry charge should be 27%.
    1. What would be the new EOQ for the above product?
    2. Develop a general model showing how the economic order quantity changes when the inventory carrying costs is changed from 22% to 27%.
    3. Discuss the effects of changes in unit costs, demand, holding cost per unit and ordering costs pr unit.


  4. Using the general expression for EOQ and total inventory cost draw a graph of ordering, carrying, and total inventory cost as a function of quantity. Explain how EOQ will be effected by changes in demand, ordering costs, and carrying costs.


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