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# Compare multifactor productivity of the systems

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Question

1. A grocery chain is considering the installation of a set of four self-checkout lanes. The new self-checkout lane setup will replace two old cashier lanes that were staffed by a cashier and bagger on each lane. They work 8-hour shifts. For the new self-checkout system, one cashier staffs all four self-checkouts (answering questions, checkng for unscanned items, taking coupons, etc.) Checkout in the new lanes takes 2 minutes (customers bag their own orders), while checkout in the old lanes took only 45 seconds. In addition, the electricity costs for both setups are \$.05 per checkout, while bagging (material) costs are \$.10 per checkout with the old system and \$.15 for the new system. The new lanes also require \$100 in capital costs per shift. Assume that the lanes are always in use for 8 hours per day (one 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) Evaluate the system. (Compare the multifactor productivity of the systems and assess the new system in a short narrative)

##### Solution Summary

1. A grocery chain is considering the installation of a set of four self-checkout lanes. The new self-checkout lane setup will replace two old cashier lanes that were staffed by a cashier and bagger on each lane. They work 8-hour shifts. For the new self-checkout system, one cashier staffs all four self-checkouts (answering questions, checkng for unscanned items, taking coupons, etc.) Checkout in the new lanes takes 2 minutes (customers bag their own orders), while checkout in the old lanes took only 45 seconds. In addition, the electricity costs for both setups are \$.05 per checkout, while bagging (material) costs are \$.10 per checkout with the old system and \$.15 for the new system. The new lanes also require \$100 in capital costs per shift. Assume that the lanes are always in use for 8 hours per day (one 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

##### Solution Preview

1. A grocery chain is considering the installation of a set of four self-checkout lanes. The new self-checkout lane setup will replace two old cashier lanes that were staffed by a cashier and bagger on each lane. They work 8-hour shifts. For the new self-checkout system, one cashier staffs all four self-checkouts (answering questions, checkng for unscanned items, taking coupons, etc.) Checkout in the new lanes takes 2 minutes (customers bag their own orders), while checkout in the old lanes took only 45 seconds. In addition, the electricity costs for both setups are \$.05 per checkout, while bagging (material) costs are \$.10 per checkout with the old system and \$.15 for the new system. The new lanes also require \$100 in capital costs per shift. Assume that the lanes are always in use for 8 hours per day (one shift) and that a worker makes \$10/hour.

a) How many checkouts did the old system provide in a shift
Old System
Two checkout lanes x 8 hours per shift = 16 hours x 60 =960 minutes
Each Checkout takes 45 seconds = 45/60 = 0.75 minutes
Number of checkouts per shift = 960/0.75 = 1,280 checkouts per ...

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