Question

Problem 1: One of the few surviving on-line grocers, Fresh Direct uses 150 trucks to generate delivery within 2 hours. Currently Fresh Direct sells $200 million worth of food per year representing 2 million orders and comprising 60 million items. A major part of the operation depends on how well workers in the warehouse assemble orders. An error caught before a shipment leaves the warehouse costs $0.50 per item, while every error found after shipping costs $6.00 per item. After years of effort, Fresh Direct achieved a level of accuracy in assembly so that 99.6% of its items were correctly filled and shipped (that is, only 0.4% items were not shipped correctly). Recently a software firm offered Fresh Direct a RFID product that would check the items in an order after it was assembled and before it left the warehouse and would catch 75% of the incorrect items, thus improving overall order accuracy to 99.9%. What is the maximum that Fresh Direct should be willing to pay to purchase the new system if it wants to recoup the new system costs within a year? A second option that Fresh Direct is examining is implementing a system to lower the cost of shipping an incorrect item by 45% (i.e., to $3.3 per incorrectly shipped item). Would this system provide more value to Fresh Direct than the system described in part 1? How much of a decrease in error cost is needed under the option described in (2) to produce cost savings equivalent to the software product described in (1)?

Answer 1

Error cost per item before a shipment leaves the warehouse costs = $0.50

Error cost per item after a shipment leaves the warehouse costs = $6.00

Total items = 60 million

The current level of accuracy in assembly = 99.6%

Number of items that are incorrectly shipped = 0.4% of 60 million = 0.24 million

Total error cost for faulty shipments before RFID technology = Error cost per item * Number of items

= 6 * 240000

= $1440000 per year

Level of accuracy after RFID technology = 99.9%

Number of items that are incorrectly shipped after RFID technology = 0.1% of 60 million = 0.06 million

Total error cost for faulty shipments after RFID technology = Error cost per item * Number of items

= 6 * 60000

= $360000 per year

Ans 1)

Difference in error costs before and after RFID technology = $1440000 - $360000

= $1080000

Thus Fresh direct would be willing to pay a maximum of $1080000 if it wants to recoup the new system costs within a year.

Ans 2)

If the second option is chosen, the error cost of the incorrectly shipped item will be reduced to $3.3 per item

Total error cost for faulty shipments = Error cost per item * Number of items

= 3.3 * 240000

= $792000 per year

Such a system would reduce the error costs per year without any additional investment in new technology. Thus in the short time frame, it would be beneficial to adopt this system, but in the longer time frame, investment in RFID technology would result in additional savings of $432000 per year.

Thus if we assume that Fresh direct pays a maximum of $1080000 for the technology, that additional cost of investment would be recovered within a period of (1080000/432000) or 2.5 years

Ans 3)

If we want to produce cost savings equivalent to the software product, the error cost per faulty shipment has to be reduced even further. The total error costs would then be equal to the error costs after RFID technology, i.e.

= $360000 per year

Total error cost for faulty shipments = Error cost per item * Number of items

360000 = x * 240000

x = $1.5

% reduction in error costs = [(3.3 - 1.5) / 3.3]* 100

= 54.54%

Hence we need a 54.54% decrease in error cost as described in the second option