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 per shift. One cashier mans all 4 self-checkouts per shift (answering questions, checking for un-scanned items, taking coupons, etc). Checkout on the new lanes takes 1.25 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 $0.06 per checkout while bagging (material) costs are $0.12 per checkout with the old system and $0.20 for the new system. The new 4 self-checkout lanes also requires a total of $25 in capital costs per day. Assume that the lanes are always in use for 16 hours per day (2 shift), for the old system the average revenue per checkout is $12 and $10 for the new system, and a worker (cashier and bagger) 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. 2560 checkout

b. 3072 checkout

c. Old system = 3.85 checkout/$

New system = 5.56 checkout/$

Explanation:

Given:

Checkout lanes = 4

a.

How many checkouts did the old system provide in a shift?

Given

Lanes = 2

Time in use = 16 hours --- Convert to seconds

Time = 16 * 3600 = 57600 seconds

Checkout = 1 per 45 seconds

Number of check outs is calculated as:

2 lanes * 57600 seconds * 1 checkout / 45 seconds

Number of checkout = 2560 checkouts

b.

How many checkouts does the new system provide?

Lanes = 4

TimeTime in use = 16 hours --- Convert to minutes

Time = 16 * 60 = 960 minutes

Number of check outs is calculated as:

4 lanes * 960 minutes * 1 checkout / 1.25 minutes

Number of checkout = 3072 checkouts

c.

Given

Electricity costs for both setups are $0.06 per checkout

Bagging (material) costs are $0.12 per checkout with the old system

Bagging (material) costs are $0.20 per checkout with the old system

Cost for the old system is calculated by:

$0.06 * 2560 + $0.12 * 2560

= $153.6 + $307.2

= $460.3

Multifactor = 2560 checkout/$460.3

Multifactor = 5.56 checkout/$

Cost for the new system is calculated by:

0.06 * $3072 + 0.20 * $3072

= $184.32 + $614.4

= $798.72

Multifactor = 3072 checkout/$798.72

Multifactor = 3.85 checkout/$

i would have to say its c