Question

Quarter-inch stainless-steel bolts are consumed in a factory at a fairly steady rate of 60 per week. The bolts cost the plant two cents each. It costs the plant $12 to initiate an order, and holding costs are based on an annual interest rate of 25 percent.

Now, however, suppose the minimum reorder interval is one month and all order cycles are placed on a power-of-two multiple of months (that is, one month, two months, four months, eight months, etc) in order to permit truck sharing with orders of other parts.

(a) What is the least-cost reorder interval under this restriction?

(b) How much does this add to the total cost?

(c) How is the effectiveness of powers-of-2 order intervals related to the result of the pre­vious problem regarding the effect of demand forecasting errors?

Answer 1

Extract the data as shown below: Consumption rate of stainless-steel bolts = 60 per week Annual demand of bolts (D) = 6052 = 3,120 Cost of each bolt = 2 cents = $0.02 Order cost for each order = $12 Holding cost per year = 25% = $0.02 x 0.25 = $0.005 (a) Calculate the optimal order quantity (E0Q) as shown below: EOQ = 12:08 2x3,120x$12 V $0.005 = 3.869.88 - 3.870 bolts Calculate optimal reorder point as shown below: 1 ROP= Frequency of order EOQ D _3.870 3.120 = 1.24 year = 14.88 months The closest power of two to 14.88 months is 16 months or 1.33 years. Calculate the total cost of ordering as shown below: TC = IDh S 11.33=2* 1.33 x 3,120x0.005 12 1.33 20.748 +9.022 2 = 10.374 +9.022 = $19.367 per year

The power of two on the other side of 14.88 months is 8 months or 0.67 years. Similarly, calculate cost of ordering as shown below: TDh S TC067 =-2 0.67x3,120x0.005 12 0.67 10.425 +17.91 = 5.226+17.91 = $23.136 per year (6) Calculate the optimal cost without the restriction of power of 2 as shown below: TC = 120Sh = V2x3,120x12x0.005 = 374.4 = $19.35 per year Calculate the cost difference for the optimal cost and the cost for 16 months as shown below: Cost difference = $19.367 - $19.35 = $0.017 Calculate the cost difference for the optimal cost and the cost for 8 months as shown below: Cost difference = $23.136-$19.35 = $3.786 From the above calculations it can be concluded that the total cost of 16 months or 1.33 year is only 0.1% more than that of the optimal cost. Whereas, for the 8 months, the total cost is approximately 20% more than that of the optimal cost. NOTE: Part (c) cannot be answered as the previous problem is not provided.