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 1.5 minutes (customers bag their own orders) while checkout with the old lanes took only 40 seconds. In addition, the electricity costs for both setups are $0.06 per checkout while bagging (material) costs are $0.12 per checkout with the old system and $0.15 for the new system. The new 4 self-checkout lanes also require $25 in capital costs per lane. Assume that the lanes are always in use for 8 hours per day (1 shift), the average revenue per checkout is $12, and that a worker makes $12/hour

1) What is the unit-less multifactor productivity for each system (old or new)?

2) Which checkout system is more productive and what is the percent change in productivity for the new system relative to the old system ((new-old)/old*100)?

Explanation / Answer

Productivity of old system = (2 lanes x 8 hours x 3600 seconds/hour x 1 checkout) / 40 seconds = 1440 checkouts

Productivity of new system = (4 lanes x 8 hours x 3600 seconds/hour x 1 checkout) / 90 seconds = 1280 checkouts

Cost for the old system = (4 workers x 8 hours x $12/hour) + ($0.12 x 1440) + ($0.06 x 1440) = $643.

Cost for the new system = (1 worker x 8 hours x $12/hour) + ($0.15 x 1280) + ($0.06 x 1280) + $25 = $399.

Revenue from old system = 1440 x 12 = $17280 & Profit = 17280 – 643 = $16637

Revenue from new system = 1280 x 12 = $15360 & Profit = 15360 – 399 = $14961

Multifactor productivity for old system = 1440 checkouts / $643 = 2.24 checkouts/$.

Multifactor productivity for new system = 1280 checkouts / $399 = 3.21 checkouts/$.

The new system is more productive as it gives more checkouts with one dollar.

The percentage change in productivity is ((3.21 – 2.24) / 2.24) x 100 = 43.3 %.

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