# Managing Variability Example

Document Sample

```					                  WHITE CELLS ARE ADJUSTABLE
© Kristoffer Burnett - Certified Management Accountant, 2009-2012
Managing Variability Example

Customer Waiting Time

Employees in sales department                                        4
Average hourly cost for sales dept. employee      \$              26.50 This cost can include wages and benefits
Variable costs (per min)                          \$               0.05 Phone charges and any other variable costs associated with helping customers
2                                                         3                  4                    5                  6
1                                                       Average            Average             Average                            Cost of Line
Employee        Expected Customer        Expected Flow     Customers Being       Customers          Customers in     Cost of Labor Per Charges Per Call       Total Cost Per
Number of Employees                      Utilization     Waiting Time (min)         Time (min)          Helped             Waiting             System           Call Received      Received             Call Received
2                                         98.8%             192.8                 201.3          2.0                      44.8               46.8    \$            3.80 \$          10.07      \$           13.87
3                                         65.9%                2.1                  10.6         2.0                       0.5                 2.5                5.70             0.53                   6.23
4                                         49.4%                0.5                   9.0         2.0                       0.1                 2.1                7.60             0.45                   8.05
5                                         39.5%                0.2                   8.7         2.0                       -                   2.0                9.50             0.44                   9.94
6                                         32.9%                0.1                   8.6         2.0                       -                   2.0   \$          11.41 \$            0.43      \$           11.84

7                    8
Probability That
All Employees Are    Potential Lost
Number of Employees                        Busy         Customers Per Min
2                                        40.0%              0.093
3                                        21.1%              0.049
4                                         9.5%              0.022
5                                         3.7%              0.009
6                                         1.2%              0.003

120.0%                                                                                                                                                                \$16.00
Effect of Staffing Changes

\$14.00
100.0%

\$12.00

80.0%
\$10.00

60.0%                                                                                                                                                             \$8.00

\$6.00
40.0%

\$4.00

20.0%
\$2.00

0.0%                                                                                                                                                              \$-
2                              3                               4                            5                               6

Employee Utilization            Total Cost Per Call Received

Notes:

1   The percent of time employees spend helping customers at different staffing levels
2   Expected Customer Waiting Time + Average Call Length
3   Sum of Average Customers Waiting and Average Customers Being Helped
4   The cost of labor per customer helped, includes idle time.
5   The total variable costs incurred due to wait and activity time.
6   Cost of Labor Per Call + Cost of Line Charges Per Call
7   The probability of a customer calling and not being helped immediately
8   The number of customers that are potentially lost if they do not want to wait
WHITE CELLS ARE ADJUSTABLE                                                                                                                                                             © Kristoffer Burnett - Certified Management Accountant, 2009-
2012
Managing Variability Example

Sales Department Call Log
1                      2
Call Completion                             Interarrival Time                              Call Completion                          Interarrival Time                         Call Completion                         Interarrival Time
Call Arrival Time             Time            Call Length (Min)           (Min)            Call Arrival Time             Time           Call Length (Min)         (Min)          Call Arrival Time          Time          Call Length (Min)         (Min)
8:03:38 AM             8:13:10 AM                 9.53                                  10:59:00 AM              11:13:31 AM               14.51                14.48         2:06:00 PM           2:14:13 PM                 8.22                13.57
8:07:16 AM             8:20:55 AM                13.65                   3.64            11:02:40 AM             11:15:09 AM               12.48                 3.67          2:09:47 PM           2:12:01 PM                2.23                 3.79
8:08:12 AM             8:13:07 AM                 4.91                   0.94            11:06:20 AM             11:11:23 AM                5.05                 3.66          2:12:19 PM           2:21:06 PM                8.78                 2.53
8:11:42 AM             8:18:40 AM                 6.97                   3.48            11:08:59 AM             11:11:20 AM                2.36                 2.65          2:15:22 PM           2:17:52 PM                2.51                 3.04
8:15:18 AM             8:23:32 AM                 8.22                   3.61            11:12:36 AM             11:18:23 AM                5.77                 3.63          2:17:46 PM           2:24:17 PM                6.52                 2.40
8:16:55 AM             8:26:57 AM                10.04                   1.61            11:16:00 AM             11:22:59 AM                6.95                 3.39          2:20:09 PM           2:30:18 PM               10.15                 2.39
8:41:00 AM             8:43:03 AM                 2.04                  24.08            11:16:02 AM             11:24:37 AM                8.61                 0.04          2:23:56 PM           2:38:32 PM               14.60                 3.77
8:44:49 AM             8:53:58 AM                 9.16                   3.82            11:19:42 AM             11:30:19 AM               10.61                 3.67          2:38:00 PM           2:50:04 PM               12.07                14.07
8:48:32 AM             8:56:37 AM                 8.08                   3.71            11:23:23 AM             11:28:05 AM                4.69                 3.69          2:41:47 PM           2:51:24 PM                9.60                 3.79
8:50:00 AM             9:00:42 AM                 8.38                   1.47            11:25:19 AM             11:29:56 AM                4.62                 1.93          2:43:57 PM           2:57:45 PM               13.79                 2.16
8:52:19 AM             9:03:45 AM                10.76                   2.32            11:28:48 AM             11:35:46 AM                6.97                 3.48          2:47:39 PM           3:01:27 PM               13.79                 3.70
8:53:00 AM             9:08:10 AM                11.36                   0.68            11:32:32 AM             11:39:51 AM                7.31                 3.73          2:49:47 PM           2:52:36 PM                2.82                 2.13
8:53:42 AM             8:58:50 AM                 8.84                   0.71            11:40:00 AM             11:44:11 AM                4.19                 7.47          2:53:24 PM           3:04:31 PM               11.12                 3.63
8:55:11 AM             8:59:24 AM                 5.70                   1.48            11:43:44 AM             11:47:27 AM                3.71                 3.73          2:54:57 PM           3:07:26 PM               12.48                 1.54
8:56:36 AM             9:01:30 AM                 6.32                   1.41            11:47:31 AM             11:57:16 AM                9.75                 3.79          3:20:00 PM           3:22:03 PM                2.04                25.05
8:56:49 AM             9:07:17 AM                10.68                   0.22            11:51:07 AM             12:04:21 PM               13.23                 3.60          3:23:38 PM           3:26:11 PM                2.55                 3.63
9:00:13 AM             9:07:10 AM                 6.94                   3.41            11:54:23 AM             12:03:28 PM                9.09                 3.27          3:27:17 PM           3:34:58 PM                7.67                 3.66
9:03:54 AM             9:11:07 AM                 7.21                   3.67            11:55:42 AM             12:09:55 PM               14.23                 1.31          3:29:01 PM           3:36:24 PM                7.39                 1.73
9:07:00 AM             9:14:02 AM                 7.04                   3.10            12:06:00 PM             12:18:15 PM               12.25                10.30          3:32:37 PM           3:38:16 PM                5.64                 3.60
9:10:33 AM             9:14:19 AM                 3.76                   3.56            12:09:08 PM             12:12:50 PM                3.70                 3.14          3:35:03 PM           3:49:24 PM               14.36                 2.43
9:14:23 AM             9:23:15 AM                 8.87                   3.83            12:12:50 PM             12:21:01 PM                8.18                 3.70          3:40:00 PM           3:44:44 PM                4.74                 4.95
9:15:23 AM             9:26:01 AM                10.64                   0.99            12:16:38 PM             12:30:13 PM               13.58                 3.80          3:43:38 PM           3:54:59 PM               11.36                 3.63
9:19:14 AM             9:31:07 AM                11.89                   3.84            12:20:30 PM             12:28:21 PM                7.85                 3.86          3:45:34 PM           3:55:49 PM               10.25                 1.93
9:23:02 AM             9:25:33 AM                 2.51                   3.82            12:24:10 PM             12:27:36 PM                3.44                 3.66          3:49:10 PM           4:02:14 PM               13.06                 3.61
9:29:00 AM             9:35:19 AM                 2.32                   5.96            12:35:00 PM             12:47:01 PM               12.02                10.84          3:52:55 PM           4:04:47 PM               11.86                 3.74
9:32:46 AM             9:41:01 AM                12.01                   3.76            12:38:39 PM             12:43:09 PM                4.49                 3.66          3:54:59 PM           4:04:34 PM                9.58                 2.07
9:33:00 AM             9:35:30 AM                 2.74                   0.24            12:42:25 PM             12:44:48 PM                2.39                 3.76          3:56:37 PM           3:58:54 PM                2.29                 1.63
9:36:30 AM             9:43:04 AM                 6.57                   3.50            12:46:10 PM             12:58:59 PM               12.81                 3.76          4:07:00 PM           4:10:10 PM                3.17                10.38
9:40:06 AM             9:43:01 AM                 2.91                   3.60            12:48:47 PM              1:00:50 PM               12.05                 2.61          4:10:47 PM           4:24:06 PM               13.32                 3.79
9:40:50 AM             9:48:54 AM                 8.06                   0.73            12:52:26 PM             12:57:25 PM                4.98                 3.66          4:12:40 PM           4:25:49 PM               13.16                 1.87
9:51:00 AM             9:58:38 AM                 7.63                  10.16             1:16:00 PM              1:20:44 PM                4.74                23.56          4:14:03 PM           4:19:34 PM                5.51                 1.40
9:54:45 AM            10:03:46 AM                 9.01                   3.74             1:19:31 PM              1:27:57 PM                8.44                 3.51          4:17:02 PM           4:19:50 PM                2.79                 2.98
9:58:33 AM            10:09:32 AM                10.99                   3.80             1:22:05 PM              1:36:07 PM               14.02                 2.58          4:20:47 PM           4:35:46 PM               14.99                 3.74
10:02:18 AM            10:16:09 AM                13.85                   3.76             1:25:44 PM              1:40:33 PM               14.82                 3.64          4:37:00 PM           4:50:42 PM               13.69                16.22
10:06:04 AM            10:18:36 AM                12.54                   3.76             1:26:30 PM              1:29:34 PM                3.07                 0.76          4:40:39 PM           4:45:03 PM                4.41                 3.64
10:09:55 AM            10:19:58 AM                10.05                   3.86             1:30:13 PM              1:37:39 PM                7.44                 3.71          4:44:28 PM           4:52:12 PM                7.75                 3.82
10:13:31 AM            10:24:55 AM                11.39                   3.60             1:32:12 PM              1:46:15 PM               14.05                 1.99          4:48:12 PM           4:58:00 PM                9.79                 3.74
10:26:00 AM            10:40:37 AM                14.61                  12.48             1:38:00 PM              1:44:12 PM                6.19                 5.80          4:49:52 PM           4:57:23 PM                7.52                 1.66
10:29:40 AM            10:40:59 AM                11.32                   3.67             1:40:17 PM              1:54:43 PM               14.43                 2.29          4:53:41 PM           4:59:07 PM                5.44                 3.82
10:33:26 AM            10:38:20 AM                 4.90                   3.76             1:44:02 PM              1:53:06 PM                9.07                 3.74          4:57:28 PM           5:08:58 PM               11.50                 3.79
10:37:09 AM            10:49:32 AM                12.38                   3.71             1:47:41 PM              1:56:36 PM                8.91                 3.66          5:05:00 PM           5:13:13 PM                8.22                 7.54
10:40:55 AM            10:50:59 AM                10.06                   3.77             1:48:47 PM              2:01:38 PM               12.84                 1.09          5:08:40 PM           5:16:50 PM                8.16                 3.67
10:44:31 AM            10:53:00 AM                 8.48                   3.60             1:52:26 PM              1:56:16 PM                3.84                 3.64          5:12:29 PM           5:25:05 PM               12.60                 3.82

Statistics

Average call length (min)                                     8.5
Standard deviation call length (min)                          3.8   This figure represents the volatility of call length
Coefficient of variation - call length                     0.447    Standard deviation call length / Average call length
Average interarrival time (min)                               4.3
Standard deviation interarrival time (min)                    4.1   This figure represents the volatility of interarrival time
Coefficient of variation - interarrival time               0.953    Standard deviation interarrival time / Average interarrival time
Call length:interarrival ratio                                2.0   Average call length / Average interarrival time

Notes:

1 Call Completion Time - Call Arrival Time
2 Call Arrival Time - previous Call Arrival Time

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