The consolidated findings from the analysis of land lease combinations for four types of facilities (fuel stations, ground service equipment - GSE, hangars, and porta-cabins) using the Goal Programming model [15, 20] and Excel Solver are presented in Tables 5 and 6 as discussed in the preceding section.
1. For each of the twenty-three airports, the land allotment areas ranging from 1830 sq. meters (0.452 acres) to 19136 sq. meters (4.73 acres) would accommodate all four facilities (refer to Table 5) [12].
2. The lease revenue for each airport location, based on notified annual rates per sq. meter, varies from 0.83 million INR to 28.99 million INR (refer to Table 5, with an exchange rate of 1 US $ = 70 INR in 2018).
3. The expected total lease revenue for the land lease areas of all twenty-three airports sums up to 267.88 million INR, covering 216,285 sq. meters (53.45 acres) (refer to Table 5, with an exchange rate of 1 US $ = 70 INR in 2018).
4. The cumulative increase in total land area and revenue, considering the proposed land lease mix for the four facility types, is 95% for land area and 77% for land lease revenue, compared to the existing land allotment revenue at notified rates (refer to Table 6, with an exchange rate of 1 US $ = 70 INR in 2018) [10].
5. Comparing the ratios of land lease revenue to total revenue between the existing allotment and the proposed model, there is approximately a 95% increase in the latter (refer to Table 6, with an exchange rate of 1 US $ = 70 INR in 2018).
6. The analysis incorporates average values for area requirements and average floor rent per sq. meter per month from six airports. Assumptions include a 20% floor area limitation for commercial outlets and corresponding income, forming the basis for the weighted Goal Programming Model.
7. In Table 4 under Para 5, the Solver Model's output of "0" in the Objective Function Cell signifies the successful minimization of deviations based on the selected weightage for each of the six deviations. The resulting total area is 3,840 sq. meters within the earmarked limit of 4,000 sq. meters, generating total rental revenue of 58.56 lakh Indian Rupees or 5.85 million. Further scenarios can be explored by modifying input target numbers and prioritizing types of allotments, even with minor deviations, without complete depreciation (refer to Table 4, with an exchange rate of 1 US $ = 70 INR in 2018).
8. By adopting the presented methodology and results, the optimal mix of land and space allotments for enhancing revenue from both airport land and space resources can be determined within the given limitations [2, 7, 10].
In a chapter titled "Statistical Methods as Optimization Problems," George Mason University's publication highlights various approaches to accommodate multiple objectives and constraints in optimization problems. The simplest method involves forming a weighted sum, where constraints are incorporated as a weighted component of the objective function, allowing control over the extent to which the constraints are met. In optimization, there often requires interaction between decision-makers and the optimization procedure.
While formulating an optimization problem, careful consideration is essential to ensure it accurately captures the objective of the real problem. The impact of assumptions about the real problem can be magnified in optimization, necessitating caution in both formulating and analyzing the underlying problem. Even when the problem is correctly formulated, difficulties may arise in applying the optimization problem in a statistical method. In contrast to regular regression models, which can be validated using statistical parameters/tests such as sample size, R square, p-values, and assessments of multicollinearity, the validation of multi-objective models like Goal Programming involves addressing practical resource allocation problems under constraints while minimizing deviations from the objective function. The author acknowledges the absence of direct references to specific statistical tests for validating Goal Programming models. Furthermore, emphasizing that interpreting and validating a model solely from a statistical viewpoint may not always be feasible or justified. The above process, including the basis for data (pertaining to twenty-three airports), assumptions, etc., was thoroughly explained in the preceding subsections covering Methods and Data Analysis. The outcomes and validation of the model, presented as an optimal mix of land allotments for each of the twenty-three airports, were summarized in Tables 3 and 6 and discussed above.