A grocery chain is considering the installation of a set of 4 self-checkout lane

Question

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 $.05 per checkout while bagging (material) costs are $.1 per checkout with the old system and $.15 for the new system. The new lanes also require $100 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?

Explanation / Answer

(a)        2 lanes * 8 hours * 3600 seconds/hour * 1checkout/45 seconds = 1280 checkouts

(b)        4 lanes * 8 hours * 60 minutes/hour * 1checkout/2min = 960 checkouts

(c)        Cost for the old system 4 workers * 8 hours * $10/hour + $.1 * 1280 + $.05 * 1280= $512.

Cost for the new system 1 worker * 8 hours * $10/hour + $.15 * 960 + $.05 * 960 + $100 =$372.

Multifactor productivity for old system = 1280 checkouts / $512 = 2.5 checkouts/$.

Multifactor productivity for new system = 960 checkouts / $372 = 2.6 checkouts/$.

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