The Bankston fulfilment center of Universal Logistics is a large warehouse that packs and ships customer orders from client on-line retailers. Five employees have been nominated for a productivity award, although there is disagreement about who should receive the award. These employees, known as pickers, fill incoming orders by locating the requested items and placing them in plastic bins with computer- generated shipping labels, to be transferred to a packing area where other employees put the items in cardboard boxes, add padding, seal the boxes, and arrange postage. Bankston awards bonus payments to the two most productive pickers each quarter, based on the total number of items the warehouse information system recorded picked during that time. At the end of this quarter, however, some employees have argued that Bankston needs to define "productive" more carefully, because the total number of items picked also depends on the total number of shifts an employee was assigned to work during the quarter, an amount that the employee doesn't control. Other employees point out the warehouse information system always assigns the next order to be picked, and a picker who happens to be assigned many small orders will look less productive, because that employee must walk to the packing area and back more often. Furthermore, the pickers don't control the distance they must walk between items in the warehouse, so an unlucky picker might be assigned items that are widely spaced, taking more time to gather. To settle the dispute, Bankston gath- ered all the relevant data that the warehouse information system could provide on the five top pickers and disguised their names before submitting this information to the regional manager for a decision. The report looked like this:

Each shift worked represents 8 labor hours, and the total miles traveled includes all walking between items in the warehouse, as well as walking to and from the packing area.

a. Calculate the labor productivity of the five pickers, in terms of the total items picked this quarter. Who are the top two performers according to this measure, and do they differ from the pair of employees who would win the bonus under Bankston's old rules?

b. Calculate the labor productivity of the five pickers, in terms of the total shipments picked this quarter. Is the top performer according to this measure also the picker who picked the most shipments?

c. The regional manager recommends a new system for the bonus competition: pickers will earn points from three categories: labor productivity in terms of total items picked, labor productivity in terms of total shipments picked, and labor productivity in terms of total miles traveled, which is also the average walking speed of the picker throughout the quarter. In each case, a picker earns 2 points for being the top performer in the category, and 1 point for being the second-best performer in the category. The two pickers who earn the two highest point scores overall will be awarded the bonus payments. Which pickers will earn those bonuses under this new system, and is this different from the pickers who would have won under Bankston's old system?

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Bankston Top Five Pickers Quarterly Statistics Total Items Total Shipments Total Shifts Picked Picked Worked Total Miles Traveled Picker A 119,417 33,251 128 3,840 Picker B 127,782 29,631 140 3,080 Picker C 168,376 40,078 126 3,150 Picker D 118,978 35,562 95 2,280 Picker E 110,998 32,345 130 3,250