Anyway, last Monday, October 20, 2008, while working on the financial statement of my department, I bumped on a problem that occupied my mind for most of the time this week. I believe this problem is a game-like problem and somehow connected or related to my interest. For a year now, I have been engrossed by the concept of game theory on social sciences. Because of this, I easily recognized that the problem, which stopped me to work on my business plan for a week, is a certain version of social games.
I call it, the Profit-Incentive-Outage Problem. Technically, it is a management/business problem, but I have this gut feeling that its nature is the same as any game. For now, I don’t have any concrete idea of the problem and how it is categorized according to the formal criterion of hard mathematics or economic theories. I treat it is a simple business management.
Here’s the problem:
The Profit-Incentive-Outage Problem
How can the management minimize the expenses on a given Incentive without compromising the satisfaction of the employees on the given incentive as well as their performance?
Actually, this is not a simple problem. It is complicated business management numbers analyses especially when we consider the actual implementation of it.
To simplify my view on this problem, I considered the recent Perfect Attendance incentive we have here in our company. In our company, we give PHP 2,000.00 to all employees who are present (no excused and unexcused absences) and no tardiness in a month. For small-value campaigns, the incentive amount is quite high and it eats out considerable amount of the profit especially majority of the team members are availing this incentive and the monthly revenue is almost constant or the revenue is not directly related to performance.
Thinking on this problem, I realized the following points:
1. This problem has a game-like nature with management and employees as players. The management always focuses on minimizing the incentive expense without compromising the employees. On one hand, the employees will always aim for a higher return of money from the incentive/s.
2. This incentive program will not work and will not give optimized returns if the management won’t manage the paid leaves of the employees very well. If the leaves of the employees won’t be managed carefully, the existence of the incentive program defeats its purpose, which is to increase monthly revenue (for the campaigns being billed on employee per hour attendance).
3. For me to create a model, certain assumptions must be stipulated: (a) given that agents have the option to take leaves at the maximum of 22 days and minimum of 1 day in a month; (a) given that agents have the freedom to choose different combinations of absences every month in a year; (c) given that the management has no control on the management of leaves of the agents (it means no other parametric constraints); (d) given that all other costs as constant and only revenue and incentive costs as dependent variables, dependent on the leaves frequency of the agents in a year; and (e) given that the incentive rate is constant.
With all these assumptions, for several days, I worked my mind on coming up a good model for this (actually until now, I don’t have a good model of this problem). I am actually looking for points where the profit is optimized while giving the employees considerable amount of incentive. Honestly, I did not know where to start.
Just to begin somewhere, I did several combinations of availed leaves of an agent in a year and the table looks like this.
Zero means that for that month the agent did not avail any leave. 600+ combinations (scenarios) were made.
I thought of graphing the numbers resulting from this table expecting to see a pattern or recognizable form. This is the only way to see how things will go and if we can lay out a good model out of the numbers.
Initially, I thought of plotting the % of Revenue spent for the incentive against the Average annual outage (which is the total days out of the office over 12 – total number of months in a year).
And here’s the graph:
The graph is boring except for the visible aspect that the points are in discreet values. If we connect the dots horizontally we can see that for every % revenue the agent can get any combination of leaves. I am not seeing any insight on this graph so, I replotted the numbers using the average monthly leave frequency. Average monthly leave frequency is the average number of days a certain agent being on leave in a month.And I got this graph:
Now, this one looks better. I can clearly see the limits of each line (when the dots are connected horizontally).One example insight I can get here, at 0.00% of Revenue level, an agent is forced only play around the average monthly leave frequency of 1.00-2.50 (this is also the reason why I set the average monthly outage of my team to 2.5).
I am sure this graph can tell me more. But I don’t have the time yet to play around with it, especially now that the company business planning is near.
Also, I must consider the following notes:
1. Things will get complicated if the incentive rate is not constant and it is dependent on performance (as well as revenue dependent on performance).
2. The graph seems discreet (horizontally) because we use discreet values.
3. The graph is definitely discreet vertically. This will change if we used continuous values for all variables.
I guess, blogging it is good for now. At least, I captured my thoughts on this matter and revisit this problem someday.
For those, who has a solution to this problem please PM me. I am dying to know more about this kind of problem.
Also, don’t ask me about the equation. Just like what I told Pow, I have the graph, but I don’t have the equation.
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