The demand for motorcycle tires imported by Dixie Import-Export is 40,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $400, and the cost of storing each tire for a year is $2. Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized.
Let n be the number of tyres per shipment, but consider the example n 1000 to help set up the equation There will be 40,000/n 40,000/1000 40 shipments Stock for 1 shipment ideally starts at 1,000 and reduces to zero in 1/40 th of a year Mean stock level during period is 1000/2 500 Storage charge for 1 shipment: 500 * 1/40 * $2 1000/40 Storage charge for 1 shipment: (n/2) * (n/40,000) * $2 (n^2)/40,000 Storage charge for all shipments: 40 * 1000/40 1000 Storage charge for all shipments: (40,000/n) * (n^2)/40,000 $n Ordering costs for year: 40 * $400 Ordering costs for year: 40,000/n* $400 16,000,000/n Total costs for year, T n + 16,000,000/n dT/dn 1 - 16,000,000/n^2 0, when n 4,000 tyres per shipment, with 10 shipments and total cost T $8,000 Regards - Ian
