OVERVIEW
It has been always a question of million dollars for the planning function to identify a good schedule considering demand, process constraint, capacity and stock. With advanced planning and scheduling tools it is possible to generate a good feasible schedule but also to create alternate solution for a given set of problem definition.
Once the multiple simulation results are achieved, it becomes even more complex to identify the best out of it for the given problem. We must understand that in any environment, process parameters and constraints are dynamic. Therefore, a good solution for a given set of parameters may not remain a good solution for new set of parameters.
Even further, the questions remains, how one can find a better solution amongst the given set of solution. It is interesting to learn and observe the different parameters, which enables us to compare these results on common platform and identify the ‘best-fit-case’ for current situation.
This knowledge papers is trying to identify few of the parameters, using those one can visualize and generate common platform to compare the simulation results for production scheduling problem.
The core idea here is to present a few core indicators, which are used commonly and provide basic information about these.
(I) MEAN CYCLE TIME
The cycle time is defined as the time units required to complete all operations of an order. One order may comprise of multiple operation with a particular sequence and constraints. The smallest completion cycle time for the order is equal to sum of time required for all operations.
In real life case, the operation may not be sequenced one after the other without a time gap. Therefore the actual cycle time required to complete the order is higher compare the ideal [smallest] cycle time required.
The mean cycle time is a good indicator for global level performance. This indicator provides value for the average cycle time of a group of orders selected / scheduled. The lower the value of the mean cycle time, the better the result is. This indicates the average time value, which an
order will take for completion with current set of orders.
(II) LATENESS OR TARDINESS
The same problem if viewed with respect to orders, the illustration can be as given below:
Here Cj = Completion Time and Dj = Due Date
Therefore Lateness Lj = (Cj – Dj)
a] Total Lateness = [L1 + L2 + L3 + ……………+ Ln]
b] Average Lateness = [L1 + L2 + L3 + ……………+ Ln] / n
Another criteria related to due date is Tardiness. Tardiness means number of jobs those are tardy in a given environment at a particular time, and it is not concerned with how much tardy a job actual is.
The tardiness of a job j is defined as: Tj = max {(Cj-dj), 0}
a] Total Tardiness = [T1 + T2 + T3 + ……………+ Tn]
b] Average Tardiness = [T1 + T2 + T3 + ……………+ Tn ] / n
(III) TOTAL WEIGHTED LATENESS / DELAY
In manufacturing environment with multiple manufacturing orders, the delay for each order has different value. For example, an order with low priority is delayed by good time units may be acceptable compare to a smaller delay for order with high priority.
Therefore, a new indicator can be defined for calculating lateness / delay, which is linked to the priority or importance [weight] of an order. This indicator normalizes the effect of lateness for priority. Consider again the same problem illustration:
Based on these parameters, we can calculate the indicator as given below.
Total Weighted Lateness / Delay = (P1*L1) + (P2*L2) + (P3*L3) + …….. + (Pn*Ln)
Similarly, average value of the weighted lateness / delay can be defined as:
Average Weighted Lateness / Delay = [(P1*L1) + (P2*L2) + (P3*L3) + …….. + (Pn*Ln)] / n
One can set standard indicator to compare these values and to find out whether the value of total weighted delay is good or not good.
For example: Standard Indicator = [average priority]*[k*Average production cycle time]
Here k is a multiplication factor, which is nothing but the acceptable deviation as percentage of average production cycle time. Here, the closer the value of average weighted lateness to the standard indicator, better the performance is.
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