Last updated: 22:49:40 IST, 05 January, 2024

A consultant has to make a choice between a mathematical model (MM) and a simulation model (SM) for addressing three types of business decisions.

He decides to do a literature survey and find the number of published papers which propose models for these types of decisions. He finds the following information:

There were 138 papers which proposed mathematical models. Out of this 90 were for addressing operational decisions, 35 were for addressing transactional planning decisions and 13 were for addressing strategic planning decisions.

There were 37 papers which proposed simulation models. Out of this, 9 papers were for addressing operational decisions, 16 were for addressing transactional planning decisions and 12 papers were for addressing strategic policy evaluation decisions.

Solution Approach

Since the number of papers proposing a particular model for a particular decision scenario is an indication of the suitability of the model for the scenario, we can use do a test for proportions and decide.

Operational Decisions:

Out of the papers proposing mathematical models, let \(p_1\) be the proportion of papers addressing Operational Decisions. ie 90/138

Out of the papers proposing simulation models, let \(p_2\) be the proportion of papers addressing Operational Decisions. ie 9/37

\(H_o: p_1 - p_2 = 0\)

\(H_a: p_1 - p_2 \neq 0\)

op_using_mm_or_sm <-prop.test(c(90,9),c(138,37))
op_using_mm_or_sm
## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(90, 9) out of c(138, 37)
## X-squared = 18.23, df = 1, p-value = 1.958e-05
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  0.2323389 0.5855224
## sample estimates:
##    prop 1    prop 2 
## 0.6521739 0.2432432

Tactical Planning Decisions:

Out of the papers proposing mathematical models, let \(p_1\) be the proportion of papers addressing Tactical Planning Decisions. ie 35/138

Out of the papers proposing simulation models, let \(p_2\) be the proportion of papers addressing Tactical Planning Decisions. ie 16/37

\(H_o: p_1 - p_2 = 0\)

\(H_a: p_1 - p_2 \neq 0\)

tp_using_mm_or_sm <-prop.test(c(35,16),c(138,37))
tp_using_mm_or_sm
## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(35, 16) out of c(138, 37)
## X-squared = 3.6932, df = 1, p-value = 0.05464
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.37130628  0.01368779
## sample estimates:
##    prop 1    prop 2 
## 0.2536232 0.4324324

Strategic Policy Evaluation Decisions:

Out of the papers proposing mathematical models, let \(p_1\) be the proportion of papers addressing Strategic Policy Evaluation Decisions. ie 13/138

Out of the papers proposing simulation models, let \(p_2\) be the proportion of papers addressing Strategic Policy Evaluation Decisions. ie 12/37

\(H_o: p_1 - p_2 = 0\)

\(H_a: p_1 - p_2 \neq 0\)

st_using_mm_or_sm <-prop.test(c(13,12),c(138,37))
st_using_mm_or_sm
## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(13, 12) out of c(138, 37)
## X-squared = 10.809, df = 1, p-value = 0.00101
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.40577274 -0.05447011
## sample estimates:
##    prop 1    prop 2 
## 0.0942029 0.3243243