A grocery chain is considering the installation of a set of 4 self-checkout lane
ID: 427211 • Letter: A
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 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. (Total 10 Points)
Old
New
No. of Employees
4 per shift = 8 per day
1 per shift = 2 per day
No. of lanes
2
4
Checkout time
45 seconds per co
1.25 min per co
Electricity
0.06 per co
0.06 per co
Bags
0.12 per co
0.20 per co
Fix
$25 per day
Revenue
$12 per co
$10 per co
Labor
$10 per hr
$10 per hr
How many checkouts in total did the old system provide in a shift? (2 Points)
How many checkouts in total does the new system provide in a shift? (2 Points)
What is the unit-less multifactor productivity for each system (old or new)? (4 Points)
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)? (2 Points)
Old
New
No. of Employees
4 per shift = 8 per day
1 per shift = 2 per day
No. of lanes
2
4
Checkout time
45 seconds per co
1.25 min per co
Electricity
0.06 per co
0.06 per co
Bags
0.12 per co
0.20 per co
Fix
$25 per day
Revenue
$12 per co
$10 per co
Labor
$10 per hr
$10 per hr
Explanation / Answer
In order to calculate the number of checkouts we need to use the following information
Number of lanes*(Number of minutes or seconds per day available/Number of minutes or seconds per checkout)
In the old system
The number of lanes = 2
Number of seconds available per day = 16hours*60minutes*60seconds = 16*60*60 = 57600 seconds
Checkout time = 45 seconds
Thus the number of checkouts in the old system is = 2*(57600/45) = 2560
In the new system
The number of lanes = 4
Number of seconds available per day = 16hours*60minutes = 16*60 = 960 minutes
Checkout time = 1.25 minutes
Thus the number of checkouts in the old system is = 4*(960/1.25) = 3072
Now that we know the number of checkouts for each system, in order to calculate unit-less multifactor productivity (MFP) we need to convert both the output and input into same units. The simplest way to do this is to calculate the revenue and cost.
In the old system in a day we have
Total cost = total labor cost + total electricity cost + total bags cost
Total labor cost = number of shifts * number of employee per shift * number of hours per shift * cost per hour = 2*4*8*10 = 640
Total electricity cost = electricity cost per co * number of checkouts = 0.06*2560 = 153.6
Total bags cost = bags cost per co * number of checkouts = 0.12*2560 = 307.2
Total cost = 640 + 153.6 + 307.2 = 1108.8
Total revenue = revenue per co * number of checkouts = 12*2560 = 30720
MFP is 30720/1108.8 = 27.70
In the new system in a day we have
Total cost = total labor cost + total electricity cost + total bags cost + fix cost
Total labor cost = 2*1*8*10 = 160
Total electricity cost = 0.06*3072 =184.32
Total bags cost = 0.20*3072 = 614.4
Fix cost = 25
Total cost = 160 + 184.32 + 614.4 + 25 = 983.72
Total revenue = 10*3072 = 30720
MFP = 30720/983.72 = 31.22
Higher the MFP the better the system. The new checkout system is better due to higher productivity. The percentage change in productivity is
((31.22-27.70)/27.70)*100 = 12.70%
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