- Email: [email protected]
Tools for effective decision making
Tools for
Effective
Decision Making Guy D’Andrea, MBA
D
ecision making is one of the most important responsibilities of organizational leaders and managers. Effective decision making is critical to organizational success. This is as true for case management organizations (CMO) as it is for any organization. CMO managers face many difficult and complex decisions—whether to expand services to a new area, how to plan for growth, how to provide adequate staffing to meet expected demand, among others. This article explores issues and techniques regarding decision making and then applies these techniques to a specific CMO management scenario. January/February 2006
TCM 43
The Unknown Factor Many organizational managers do not use all the available tools when making a decision, even a very important one. This is especially true of decisions made under uncertainty, when the future outcome of key variables is unknown. For example, a decision’s success might depend on how large a new market will grow or how quickly. It might depend on the level of demand for a certain service or any number of other variables. Usually, the decision maker is aware of these variables and that the outcome is uncertain. Often, decision makers just make their best guess or forecast for each variable and a base a decision on that. Such an approach has obvious flaws. Each variable has a range of possible outcomes. Forecasts are just estimates; actual values will almost certainly vary from what is predicted. Yet many important decisions are based on simple estimates and predictions. A decision made based on these predictions might be the wrong decision that never would have been made with a more complete picture of all possible outcomes. There is a better way. A decision analysis technique called simulation helps to understand and combine all the uncertainties and unknowns in a decision situation. Simulation does not require a decision maker to make an absolute prediction of the outcome for each relevant variable. Instead, each variable can represent a range of possible outcomes. The decision maker considers such issues as, “What is the best outcome for this variable? What is the worst? What data do I have about the probability of different outcomes within this range?” Simulation combines all the uncertainty for every variable into a single model and then repeats the scenario over and over until a picture of the possible outcomes emerges. It is like running hundreds or thousands of what-if scenarios all at once. Simulation allows decision makers to see the full range of outcomes from their decision, as though they could live through the situation over and over again, each time under a different set of conditions and a different set of results.
TCM 44
January/February 2006
A decision analysis technique called simulation helps to understand and combine all the uncertainties and unknowns in a decision situation. To demonstrate the value of simulation and decision analysis, we will consider a scenario of a fictional CMO called Reliant Case Management. Reliant is faced with a budgeting decision: what is the optimal number of staff case managers to hire for the next year in the face of uncertain demand? Any demand for services not met by staff case managers will be handled by more expensive consultants. This is the crux of the CMO’s decision. Hire too many staff and there will be wasted staff capacity; hire too few and too much work will be delegated to outside consultants. As we shall see, simulation and decision analysis can provide tools important to effective decision making in this scenario. The facts of our fictional scenario are as follows: • Reliant currently employs 35 case managers at an average salary of $70,000 (and a 45% fringe + overhead rate). Because effective case management requires familiarity with each patient’s needs and issues, individual case managers can handle only a limited number of cases per month. • Reliant’s maximum monthly case load for a staff case manager is 40. • Reliant can also bring in external case managers as consultants as needed to manage any cases that exceed inhouse capacity. On average, these consultant case managers charge $325 per case per month. • For the following year, Reliant projected a demand of between 2000 and 3100 cases each month. Demand will randomly fluctuate in this band
from one month to the next, with 2500 cases being the “most likely” volume. An illustration of possible month-by-month demand is provided in Figure 1. The green bars represent total case volume for each of 12 months. Volume varies from one month to the next between the upper limit (3100 cases) and the lower limit (2000 cases), represented by the gray bars. The critical decision Reliant must make is whether to hire additional staff case managers, and if so, how many. This decision will have a direct impact on the volume of cases outsourced to consultants. The more staff case managers, the fewer cases referred to consultants. However, hiring additional staff adds to fixed costs and could lead to overcapacity, which would result in idle case managers. A secondary question for Reliant is how much to budget for consultant case managers. As noted above, the decision will depend on how many staff case managers are hired. Hire many additional staff case managers, spend less on consultants. Hire just a few new staff and consultant costs will be higher. Still, it is important to develop a specific and accurate figure for how much to budget for consultants. Budget too high and it will tie up capital that might be used for other purposes. Budget too low and there might be a shortfall in finds available to pay the consultants. Reliant must optimize case management staffing for the next year in the face of uncertainty about the demand for services. This is a situation faced by many organizations in preparing their budgets. While Reliant can make its best guess for the correct staff size, there are decision tools available that do better than guess. We will first examine some of the more basic approaches Reliant might use and then move on to advanced techniques. We can start to analyze this scenario by first comparing the unit costs of staff vs. consultants. The scenario tells us that the average case manager earns $70,000 plus a rate of 45% overhead, to cover benefits, office space, and other
administrative overhead. The total annual cost for a staff case manager is $70,000 × 1.45 = $101,500. The case also tells us that the maximum monthly case load for a staff manager is 40, yielding maximum annual “case months” of 40 × 12 = 480 per case manager. (For example, in the course of a year, a case manager might handle 150 cases, each lasting 2 months and 60 cases each lasting 3 months [150 × 2 + 60 × 3 = 480]. Other case managers would have different case mixes, but the total case months cannot exceed 480 over a 12-month period.) The cost per case per month, therefore, is $101,500/480 = $211.46. The cost per case per month for consultant case managers is $325 (given in the facts for the scenario). Based on this initial analysis, Reliant could reason that because staff costs are less per unit than consultants, it should make sure to use staff for all case management. In this scenario, the maximum monthly demand is 3100 cases. Given an individual case manager maximum of 40 cases, Reliant needs to hire 78 case managers (3100/40 = 77.5). Total annual costs for this approach are $7,917,000. A staffing level that is equal to the maximum possible monthly demand is illustrated in Figure 2. This approach produces cost certainty, because staff members represent fixed costs and no cases are referred to consultants. But it also yields significant wasted staff capacity, because the actual volume in any month is typically less than peak volume. In Figure 2, excess staff capacity is represented by the blue sections of the bars. An opposite approach would be to hire enough staff to meet minimum monthly case volume and to use consultants for any excess case volume. This approach is illustrated in Figure 3, where the black line signifies minimum monthly volume. Because the minimum monthly volume is 2000, Reliant would need to hire 50 case managers at an annual cost of 50 × $101,500 = $5,075,000. In addition, Reliant would have to bring in consultants for every case above 2000 per month, at a cost of $325 per case. These cases are represented by the red parts of the bars in Figure 3. The actual amount of the con-
Figure 1. Monthly case volume. This is an example. Actual monthly case volume would vary between the upper and lower limits, represented by the gray bars.
Figure 2. Maximum staffing. Staffing is set to a level to meet maximum monthly case volume, represented by the black line. All monthly demand is handled by staff. The blue bars represent unused staff capacity.
Figure 3. Minimum staffing. Staffing is set to a level to meet minimum monthly case volume, represented by the black bar. The green portion of monthly demand is handled by staff; the red portion is outsourced to consultants.
Figure 4. Optimal staffing. Staffing is set a level to somewhere between maximum and minimum case volume. In months of high volume, work is outsourced to consultants (red bars). In months of low volume, there is some idle staff capacity (blue bars).
sultant costs cannot be predicted with certainty, because monthly demand for case management fluctuates. However, we can build a model and use simulation to predict what this cost will be. The 12 variables in our model are case volume for each of the 12 months of the year, which we are told ranges from 2000 to 3100 cases, with 2500 the most likely value. By running a simulation, we find that the average of cases in a month is 2564. (Recall that the scenario facts told us that the most likely value for monthly demand is 2500, which may seem at odds with an average value of 2564. But “most likely value” refers to the mode, not the mean or the average. In the case, a skewed distribution produces an average that is different than the mode.) This means that, with 50 staff case managers, consultants would have to handle an average of 564 cases a month, at a total annual cost of $2,199,600. Add this to the staff cost of $5,075,000, and the total expected
annual cost to Reliant is $7,274,600. As noted above, Reliant’s actual costs would likely vary a bit because of the random fluctuation of monthly demand. Still, this is clearly a better approach than the maximum staffing approach, yielding a relative savings of about $642,000. But is this the best Reliant can do? What if Reliant hired some number of staff case managers between 50 and 78? This approach is illustrated in Figure 4. The gray lines indicate maximum and minimum possible case volume; the black line indicates a staffing level somewhere in between. In some months, the cases exceed the staffing level and consultants are used (the red bars). In some months, case volume falls below staffing levels and capacity goes to waste (the blue bars). Visually, we can see this approach might work— our graph has less red and blue areas continued on page 59 January/February 2006
TCM 45
Decision Making continued from page 45 (i.e., less waste) than the other approaches. The question then is, “What is the right level of staffing?” This is a calculation that is very difficult to do by hand. Reliant’s managers could plug in every possible number of case management staff between 50 and 78, and see which yields the lowest possible costs. But remember, Reliant is also subject to an uncertain monthly case volume. To be most effective, any calculations or predictions should also account for this uncertainty. Trying different combinations of staffing levels with different monthly volumes for every month would become very tedious very quickly. This is where computer technology is very useful. As mentioned earlier, we can build a model that simulates the monthly uncertainty of case volume. Listing the specific features of such a model is outside the scope of this article, but such a model had the following features: • It randomly generates demand for each of the 12 months. For each month, this value is between 2000 and 3100, with 2500 cases being the most likely. • It contains all the other inputs for the scenario, such as staff case manager salary and fringe costs, consultants’ costs. • It relates all the variables to each other in a way that mimics real life. In the model, when a new staff case manager is hired, staff costs go up and consultant costs go down. Once we have built our model, we can instruct the computer to run a simulation to optimize the number of case management staff so that expected total costs are minimized. (For this simulation, we used RISKOptimizer 1.0 for Excel from Palisade Software.) As the simulation runs, the computer tries millions of different combinations of demand levels in combination with different staff levels. In other words, we can leave it to the computer to do the tedious work of trying all the different combinations of staffing and demand levels.
When we run the simulation, we get the result that the optimal staffing level is 62 case managers. This is the staffing level that will minimize total costs. At this staffing level, the expected annual cost of staff case managers is $6,293,500. The simulation tells us that the expected cost of consultants is $335,400, yielding a total cost of $6,628,400. This is well below the cost of either the maximum or the minimum approach described earlier. Moreover, Reliant can be confident that 62 is the optimal staffing level. There is no staffing level that will produce better results for the company. Reliant would budget for 62 staff case managers at a total cost of $6.293 million and budget $335,400 for consultant case manager fees. By using simulation and optimization, Reliant will make the best budgeting decision and will have confidence in that decision. This case study focuses on a simple optimization problem, in which one factor (the number of staff case managers) varies to optimize another factor (total cost). Simulation and optimization can easily be applied to more complex scenarios with multiple variables that combine to optimize the outcome. In fact, these techniques become progressively more valuable as complexity increases, because doing the math manually goes from merely tedious to nearly impossible. Simulation provides decision makers a much more accurate vision of the likely outcomes and risks of a decision. Besides just providing a most likely value for the decision, simulation also provides a clear picture of downside risk and upside potential. Simulation also identifies the variables most critical to the decision outcome, empowering management to better focus resources. The information provided through simulation improves decision making and helps organizations achieve their goals.❑ Guy D’Andrea, MBA, is the founder of Discern Consulting in Baltimore, Maryland. Reprint orders: E-mail [email protected] or telephone (toll free) 888-834-7287; reprint no. Y M C M 3 3 7 doi:10.1016/j.casemgr.2005.09.004
January/February 2006
TCM 59
Effective
Decision Making Guy D’Andrea, MBA
D
ecision making is one of the most important responsibilities of organizational leaders and managers. Effective decision making is critical to organizational success. This is as true for case management organizations (CMO) as it is for any organization. CMO managers face many difficult and complex decisions—whether to expand services to a new area, how to plan for growth, how to provide adequate staffing to meet expected demand, among others. This article explores issues and techniques regarding decision making and then applies these techniques to a specific CMO management scenario. January/February 2006
TCM 43
The Unknown Factor Many organizational managers do not use all the available tools when making a decision, even a very important one. This is especially true of decisions made under uncertainty, when the future outcome of key variables is unknown. For example, a decision’s success might depend on how large a new market will grow or how quickly. It might depend on the level of demand for a certain service or any number of other variables. Usually, the decision maker is aware of these variables and that the outcome is uncertain. Often, decision makers just make their best guess or forecast for each variable and a base a decision on that. Such an approach has obvious flaws. Each variable has a range of possible outcomes. Forecasts are just estimates; actual values will almost certainly vary from what is predicted. Yet many important decisions are based on simple estimates and predictions. A decision made based on these predictions might be the wrong decision that never would have been made with a more complete picture of all possible outcomes. There is a better way. A decision analysis technique called simulation helps to understand and combine all the uncertainties and unknowns in a decision situation. Simulation does not require a decision maker to make an absolute prediction of the outcome for each relevant variable. Instead, each variable can represent a range of possible outcomes. The decision maker considers such issues as, “What is the best outcome for this variable? What is the worst? What data do I have about the probability of different outcomes within this range?” Simulation combines all the uncertainty for every variable into a single model and then repeats the scenario over and over until a picture of the possible outcomes emerges. It is like running hundreds or thousands of what-if scenarios all at once. Simulation allows decision makers to see the full range of outcomes from their decision, as though they could live through the situation over and over again, each time under a different set of conditions and a different set of results.
TCM 44
January/February 2006
A decision analysis technique called simulation helps to understand and combine all the uncertainties and unknowns in a decision situation. To demonstrate the value of simulation and decision analysis, we will consider a scenario of a fictional CMO called Reliant Case Management. Reliant is faced with a budgeting decision: what is the optimal number of staff case managers to hire for the next year in the face of uncertain demand? Any demand for services not met by staff case managers will be handled by more expensive consultants. This is the crux of the CMO’s decision. Hire too many staff and there will be wasted staff capacity; hire too few and too much work will be delegated to outside consultants. As we shall see, simulation and decision analysis can provide tools important to effective decision making in this scenario. The facts of our fictional scenario are as follows: • Reliant currently employs 35 case managers at an average salary of $70,000 (and a 45% fringe + overhead rate). Because effective case management requires familiarity with each patient’s needs and issues, individual case managers can handle only a limited number of cases per month. • Reliant’s maximum monthly case load for a staff case manager is 40. • Reliant can also bring in external case managers as consultants as needed to manage any cases that exceed inhouse capacity. On average, these consultant case managers charge $325 per case per month. • For the following year, Reliant projected a demand of between 2000 and 3100 cases each month. Demand will randomly fluctuate in this band
from one month to the next, with 2500 cases being the “most likely” volume. An illustration of possible month-by-month demand is provided in Figure 1. The green bars represent total case volume for each of 12 months. Volume varies from one month to the next between the upper limit (3100 cases) and the lower limit (2000 cases), represented by the gray bars. The critical decision Reliant must make is whether to hire additional staff case managers, and if so, how many. This decision will have a direct impact on the volume of cases outsourced to consultants. The more staff case managers, the fewer cases referred to consultants. However, hiring additional staff adds to fixed costs and could lead to overcapacity, which would result in idle case managers. A secondary question for Reliant is how much to budget for consultant case managers. As noted above, the decision will depend on how many staff case managers are hired. Hire many additional staff case managers, spend less on consultants. Hire just a few new staff and consultant costs will be higher. Still, it is important to develop a specific and accurate figure for how much to budget for consultants. Budget too high and it will tie up capital that might be used for other purposes. Budget too low and there might be a shortfall in finds available to pay the consultants. Reliant must optimize case management staffing for the next year in the face of uncertainty about the demand for services. This is a situation faced by many organizations in preparing their budgets. While Reliant can make its best guess for the correct staff size, there are decision tools available that do better than guess. We will first examine some of the more basic approaches Reliant might use and then move on to advanced techniques. We can start to analyze this scenario by first comparing the unit costs of staff vs. consultants. The scenario tells us that the average case manager earns $70,000 plus a rate of 45% overhead, to cover benefits, office space, and other
administrative overhead. The total annual cost for a staff case manager is $70,000 × 1.45 = $101,500. The case also tells us that the maximum monthly case load for a staff manager is 40, yielding maximum annual “case months” of 40 × 12 = 480 per case manager. (For example, in the course of a year, a case manager might handle 150 cases, each lasting 2 months and 60 cases each lasting 3 months [150 × 2 + 60 × 3 = 480]. Other case managers would have different case mixes, but the total case months cannot exceed 480 over a 12-month period.) The cost per case per month, therefore, is $101,500/480 = $211.46. The cost per case per month for consultant case managers is $325 (given in the facts for the scenario). Based on this initial analysis, Reliant could reason that because staff costs are less per unit than consultants, it should make sure to use staff for all case management. In this scenario, the maximum monthly demand is 3100 cases. Given an individual case manager maximum of 40 cases, Reliant needs to hire 78 case managers (3100/40 = 77.5). Total annual costs for this approach are $7,917,000. A staffing level that is equal to the maximum possible monthly demand is illustrated in Figure 2. This approach produces cost certainty, because staff members represent fixed costs and no cases are referred to consultants. But it also yields significant wasted staff capacity, because the actual volume in any month is typically less than peak volume. In Figure 2, excess staff capacity is represented by the blue sections of the bars. An opposite approach would be to hire enough staff to meet minimum monthly case volume and to use consultants for any excess case volume. This approach is illustrated in Figure 3, where the black line signifies minimum monthly volume. Because the minimum monthly volume is 2000, Reliant would need to hire 50 case managers at an annual cost of 50 × $101,500 = $5,075,000. In addition, Reliant would have to bring in consultants for every case above 2000 per month, at a cost of $325 per case. These cases are represented by the red parts of the bars in Figure 3. The actual amount of the con-
Figure 1. Monthly case volume. This is an example. Actual monthly case volume would vary between the upper and lower limits, represented by the gray bars.
Figure 2. Maximum staffing. Staffing is set to a level to meet maximum monthly case volume, represented by the black line. All monthly demand is handled by staff. The blue bars represent unused staff capacity.
Figure 3. Minimum staffing. Staffing is set to a level to meet minimum monthly case volume, represented by the black bar. The green portion of monthly demand is handled by staff; the red portion is outsourced to consultants.
Figure 4. Optimal staffing. Staffing is set a level to somewhere between maximum and minimum case volume. In months of high volume, work is outsourced to consultants (red bars). In months of low volume, there is some idle staff capacity (blue bars).
sultant costs cannot be predicted with certainty, because monthly demand for case management fluctuates. However, we can build a model and use simulation to predict what this cost will be. The 12 variables in our model are case volume for each of the 12 months of the year, which we are told ranges from 2000 to 3100 cases, with 2500 the most likely value. By running a simulation, we find that the average of cases in a month is 2564. (Recall that the scenario facts told us that the most likely value for monthly demand is 2500, which may seem at odds with an average value of 2564. But “most likely value” refers to the mode, not the mean or the average. In the case, a skewed distribution produces an average that is different than the mode.) This means that, with 50 staff case managers, consultants would have to handle an average of 564 cases a month, at a total annual cost of $2,199,600. Add this to the staff cost of $5,075,000, and the total expected
annual cost to Reliant is $7,274,600. As noted above, Reliant’s actual costs would likely vary a bit because of the random fluctuation of monthly demand. Still, this is clearly a better approach than the maximum staffing approach, yielding a relative savings of about $642,000. But is this the best Reliant can do? What if Reliant hired some number of staff case managers between 50 and 78? This approach is illustrated in Figure 4. The gray lines indicate maximum and minimum possible case volume; the black line indicates a staffing level somewhere in between. In some months, the cases exceed the staffing level and consultants are used (the red bars). In some months, case volume falls below staffing levels and capacity goes to waste (the blue bars). Visually, we can see this approach might work— our graph has less red and blue areas continued on page 59 January/February 2006
TCM 45
Decision Making continued from page 45 (i.e., less waste) than the other approaches. The question then is, “What is the right level of staffing?” This is a calculation that is very difficult to do by hand. Reliant’s managers could plug in every possible number of case management staff between 50 and 78, and see which yields the lowest possible costs. But remember, Reliant is also subject to an uncertain monthly case volume. To be most effective, any calculations or predictions should also account for this uncertainty. Trying different combinations of staffing levels with different monthly volumes for every month would become very tedious very quickly. This is where computer technology is very useful. As mentioned earlier, we can build a model that simulates the monthly uncertainty of case volume. Listing the specific features of such a model is outside the scope of this article, but such a model had the following features: • It randomly generates demand for each of the 12 months. For each month, this value is between 2000 and 3100, with 2500 cases being the most likely. • It contains all the other inputs for the scenario, such as staff case manager salary and fringe costs, consultants’ costs. • It relates all the variables to each other in a way that mimics real life. In the model, when a new staff case manager is hired, staff costs go up and consultant costs go down. Once we have built our model, we can instruct the computer to run a simulation to optimize the number of case management staff so that expected total costs are minimized. (For this simulation, we used RISKOptimizer 1.0 for Excel from Palisade Software.) As the simulation runs, the computer tries millions of different combinations of demand levels in combination with different staff levels. In other words, we can leave it to the computer to do the tedious work of trying all the different combinations of staffing and demand levels.
When we run the simulation, we get the result that the optimal staffing level is 62 case managers. This is the staffing level that will minimize total costs. At this staffing level, the expected annual cost of staff case managers is $6,293,500. The simulation tells us that the expected cost of consultants is $335,400, yielding a total cost of $6,628,400. This is well below the cost of either the maximum or the minimum approach described earlier. Moreover, Reliant can be confident that 62 is the optimal staffing level. There is no staffing level that will produce better results for the company. Reliant would budget for 62 staff case managers at a total cost of $6.293 million and budget $335,400 for consultant case manager fees. By using simulation and optimization, Reliant will make the best budgeting decision and will have confidence in that decision. This case study focuses on a simple optimization problem, in which one factor (the number of staff case managers) varies to optimize another factor (total cost). Simulation and optimization can easily be applied to more complex scenarios with multiple variables that combine to optimize the outcome. In fact, these techniques become progressively more valuable as complexity increases, because doing the math manually goes from merely tedious to nearly impossible. Simulation provides decision makers a much more accurate vision of the likely outcomes and risks of a decision. Besides just providing a most likely value for the decision, simulation also provides a clear picture of downside risk and upside potential. Simulation also identifies the variables most critical to the decision outcome, empowering management to better focus resources. The information provided through simulation improves decision making and helps organizations achieve their goals.❑ Guy D’Andrea, MBA, is the founder of Discern Consulting in Baltimore, Maryland. Reprint orders: E-mail [email protected] or telephone (toll free) 888-834-7287; reprint no. Y M C M 3 3 7 doi:10.1016/j.casemgr.2005.09.004
January/February 2006
TCM 59