Sarah operates a concession stand at a downtown location throughout the year. One of her most popular items is circus peanuts, selling about 200 bags per month. Sarah purchases the circus peanuts from Peter's Peanut Shop. She has been purchasing 100 bags at a time. However, to encourage larger purchases, Peter now is offering her discounts for larger order sizes according to the following price schedule, where the price for each category applies to every bag purchased.
Sarah wants to use the EOQ model with quantity discounts to determine what her order quantity should be. For this purpose, she estimates an annual holding cost rate of 17 percent of the value (based on purchase price) of the peanuts. She also estimates a setup cost of $4 for placing each order. Follow the instructions of Prob. 19.3-17 to analyze Sarah's problem.
Prob. 19.3-17
Kenichi Kaneko is the manager of a production department which uses 400 boxes of rivets per year. To hold down his inventory level, Kenichi has been ordering only 50 boxes each time. However, the supplier of rivets now is offering a discount for higher-quantity orders according to the following price schedule, where the price for each category applies to every box purchased.
The company uses an annual holding cost rate of 20 percent of the price of the item. The total cost associated with placing an order is $80 per order. Kenichi has decided to use the EOQ model with quantity discounts to determine his optimal inventory policy for rivets.
(a) For each discount category, write an expression for the total cost per year (TC) as a function of the order quantity Q.
(b) For each discount category, use the EOQ formula for the basic EOQ model to calculate the value of Q (feasible or infeasible) that gives the minimum value of TC. (You may use the analytical version of the Excel template for the basic EOQ model to perform this calculation if you wish.)
(c) For each discount category, use the results from parts (a) and (b) to determine the feasible value of Q that gives the feasible minimum value of TC and to calculate this value of TC.
(d) Draw rough hand curves of TC versus Q for each of the discount categories. Use the same format as in Fig. 19.3 (a solid curve where feasible and a dashed curve where infeasible). Show the points found in parts (b) and (c). However, you don't need to perform any additional calculations to make the curves particularly accurate at other points.
(e) Use the results from parts (c) and (d) to determine the optimal order quantity and the corresponding value of TC.
(f) Use the Excel template for the EOQ model with quantity discounts to check your answers in parts (b), (c), and (e).
(g) For discount category 2, the value of Q that minimizes TC turns out to be feasible. Explain why learning this fact would allow you to rule out discount category 1 as a candidate for providing the optimal order quantity without even performing the calculations for this category that were done in parts (b) and (c).
(h) Given the optimal order quantity from parts (e) and (
), how many orders need to be placed per year? What is the time interval between orders?
