A grocery chain is considering the installation of a set of 4 self-checkout lanes. The new self-checkout lane setup will replace 2 old cashier lanes that were staffed by a cashier and bagger on each lane

One cashier mans all 4 self-checkouts (answering questions, checking for un-scanned items, taking coupons, etc). Checkout on the new lanes takes 2 minutes (customers bag their own orders) while checkout with the old lanes took only 45 seconds. In addition, the electricity costs for both setups are $0.05 per checkout while bagging (material) costs are $0.10 per checkout with the old system and $0.15 for the new system. The new lanes also require $100/shift in capital costs. Assume that the lanes are always in use for 8 hours per day (1 shift) and that a worker makes $10/hour.
(a) How many checkouts did the old system provide in a shift?
(b) How many checkouts does the new system provide?
(c) What is the multifactor productivity for each system?

(a) (2 lanes)(8 hours)(3600 seconds/hour)(1 checkout/45 seconds) = 1280 checkouts
(b) (4 lanes)(8 hours)(60 minutes/hour)(1 checkout/2 min) = 960 checkouts
(c) Cost for the old system = (4 workers)(8 hours)($10/hour) + ($0.10 )(1280 ) + ($0.05 )(1280 ) = $512. Cost for the new system = (1 worker)(8 hours)($10/hour) + ($0.15 )(960 ) + ($0.05 )(960 ) + $100 = $372. Multifactor productivity for old system = 1280 checkouts / $512 = 2.5 checkouts/$. Multifactor productivity for new system = 960 checkouts / $372 = 2.6 checkouts/$.