Development of Analytic Methods for a Class of Decision Problems in Urban Road Transport Organizations for Efficient Operation of City Buses

Abstract

In India, road transport is the dominant mode of transport, accounting for a remarkable 87% of all passenger traffic. The increasing number of private vehicles, such as cars, significantly contributes to traffic congestion and pollution, and is costly for commuters. Whereas public transport, specifically public buses, offers an economical cost for commuting. Importantly, buses use road space more effectively, as a single bus can replace dozens of cars needed to transport the same number of people. Furthermore, they are more fuel-efficient on a per-person basis, achieving significantly more passenger-kilometers for every liter of fuel consumed. Hence, public transport efficiency is crucial for a country like India, where the population is projected to grow from 1.21 billion to 1.52 billion between 2011 and 2036, and most of the population is financially unable to afford private transport. Hence, cities in India are experiencing a significant surge in travel demand. The responsibility for planning urban transport rests primarily with the State Governments. State Road Transport Undertakings (SRTU) dominate the transport sector for passenger mobility, providing inter-state, inter-city, and intra-city services in select cities. Every Indian-Urban Road Transport Organization (I-URTO) is a metropolitan/municipal-based SRTU. From the user perspective, the bus service provided by I-URTO is a prominent mode of conveyance in any urban city, as it is cost-effective. Despite high user dependence on city bus systems, according to the financial performances of each I-URTO from FY 2009-10 to FY 2019-20, it is observed that almost every I-URTO is facing huge losses in operating city buses. The majority of their revenue stream is contributed by bus fares. Therefore, one possible solution to mitigate the significant losses observed could be to increase the bus fares. However, the government puts these I-URTO under contrary pressure to maintain the current fares and provide equitable service to the public. Due to this, the I-URTO finds it challenging to raise its revenue to cover the operational cost of city buses. Furthermore, according to studies on emissions from India’s transport sector, buses contribute approximately 92 percent more CO2 emissions than two-wheelers, passenger light motor vehicles, cars, and jeeps. Considering these significant financial losses and high volume of CO2 emissions, there is a need to identify all potential operational and strategic-level decision-making problems and propose descriptive/predictive/prescriptive methods for making optimal/efficient decisions for the efficient operation of city buses, without increasing the bus fare. Accordingly, minimizing the cost of city bus operations (CCBO) is an important objective of any URTO. After analyzing the existing literature on minimizing the CCBO and discussing it with experts in this domain, the following four research problems and objectives are considered:

1. Research Problem 1: Allocation of City Buses to the Depots (ACBD) problem Research Objective 1 (RO1): To propose and/or to identify method(s) for optimally or efficiently allocating the given number of buses to the given number of depots with an objective of minimizing both economic cost (the sum of Total Dead Kilometer Cost + Total Depot Operating Cost) and Environmental Cost (Total Cost due to CO2) to the ACBD problem 2. Research Problem 2: Location of Depots (for opening new depots and closing some of the existing depots) and Allocation of City Buses to Depots (LD – ACBD) problem Research Objective 2 (RO2): To propose and/or to identify method(s) for optimally or efficiently allocating the buses to depots by integrating the optimal or efficient decision on opening and closing depot(s) decisions with an objective of minimizing simultaneously both economic cost (the sum of Total Dead Kilometer Cost + Total Depot Operating Cost + Fixed Cost incurred due to Opening New Depots – Salvage Cost gained due to Closing Existing Depots) and Environmental Cost (Total Cost due to CO2) to the integrated Location of Depots (LD) and ACBD problem 3. Research Problem 3: Measuring the Relative Efficiencies of the I-URTO and Developing/Suggesting Improvement Areas for Relatively Inefficient I-URTO Compared with Efficient I-URTO Research Objective 3 (RO3): To identify the right set of input and output variables for comparing the relative efficiencies of the selected I-URTO and developing a methodology for measuring the relative efficiencies among the I-URTO using the traditional Data Envelopment Analysis (DEA). 4. Research Problem 4: Identifying and Prioritizing Motivating Factors in the Usage of City Buses to Increase Revenue Research Objective 4 (RO4): To identify and rank unique factors motivating the usage of city buses using a Multi-Criteria Decision Making (MCDM) approach Research Problem 1: The city buses in URTO traverse various types of non-revenue-generating distances, one of which is the 'Dead Kilometers'. The dead kilometers (DK) refer to the total distance traveled by bus from the depot to the starting point of the first trip and from the ending point of the last trip back to the depot. Each DK covered by a bus implies a revenue loss to the URTO, resulting in higher fuel consumption, increased operational costs, and CO2 emissions. So, there is a need for optimal or efficient allocation of city buses to depots (ACBD). Based on a thorough literature review, it is observed that scant treatment has been given in India for minimizing the CCBO in general, and particularly there is no study that addresses the ACBD problem by simultaneously minimizing the economic (dead kilometer cost (DKC) + depot operating cost (DOC)) and environmental cost (EC). Considering the research gaps identified w.r.t. the ACBD problem, the existing (0-1) ILP model in the literature was extended by incorporating both the DOC and the EC. Due to the computational intractability of the (0-1) ILP model and to have very simple to understand and easy to implement efficient methodologies, in this study, heuristic algorithms are identified from the existing literature. Since the ACBD problem can be viewed as a special type of Transportation Problem (TP), 8 best-known heuristic algorithms (that is, 8 best-known Initial Basic Feasible Solution (IBFS) Method) reported in the literature for TP are considered to address ACBD problem. From the computational analysis carried out by solving 30 randomly generated problem instances on the ACBD problem, it was observed that the best-performing IBFS method for TP is not necessarily the best IBFS method for the ACBD problem, which is a special type of TP. These observations motivated us to consider all the best-known heuristic algorithms reported in the literature for TP (a) to test the hypothesis that “Efficient Heuristic Algorithms (that is, IBFS methods) reported for TP are not necessarily the efficient algorithms for the ACBD problem and (b) to identify the efficient algorithms for ACBD. In the analysis of the literature on IBFS methods for TP, it is observed that more than 150 IBFS methods are reported. To avoid considering all the existing IBFS methods for TP, the criteria: (i) Published in High-Impact Journals/ Reputed Conferences/ Books, and (ii) Well-established Computational Experiments carried out in the existing studies are considered for selecting the existing methods for TP for applying to the ACBD problem. Accordingly, 40 heuristic algorithms have been identified from the existing literature, considering the period from 1958 to 2024. Further, 4 new variants of the existing heuristic algorithms were also proposed. All 44 heuristic algorithms have been implemented in Python for testing the proposed hypothesis and to identify the efficient method(s) for the ACBD problem. To test the hypothesis and to identify the efficient method(s) for the ACBD problem, a suitable computational experiment is developed. As per the computational experiment, (a) an experimental design is proposed and 360 large scale real-life sized problem instances with different problem configurations are generated randomly reflecting the ACBD problem, (b) the extended (0-1) ILP model is considered as benchmark procedure, and (c) different performance measures with an intention of following triangulation approach are considered for both empirical and statistical performance analyses of the heuristic algorithms considered for ACBD problems. Based on both empirical and statistical performance analyses, it is observed that (a) efficient performing IBFS method(s) for TP not became the efficient method(s) for ACBD problem, (b) the existing heuristic algorithms: UPCM-TOCM, WUPCM1-TOCM, and VAM-TOCM are relatively top performers for ACBD problem, among the 44 heuristic algorithms considered in this study, (c) top performing methods consistently yielded 9-10% cost savings compared to the current real-life practice, and (d) each of the heuristic algorithms applied to the Total Opportunity Cost Matrix (TOCM) for allocation decisions is either giving improved and/or equal to the total cost yielded by the respective heuristic algorithms applied to Total Cost Matrix (TCM) for allocation decision. Research Problem 2: The LD-ACBD problem is a strategic-level decision problem for URTO, classified as a capacitated Facility Location-Allocation (FLA) problem. Some of the reasons for this decision problem are: (i) need to open new depots: As the city size is continuously increasing due to people migrating for jobs, the public commuting facilities become essential, and the number of existing buses needs to increase and in turn the existing number of depots needs to increase, (ii) need to close existing depots: As a city expands, the existing depots fall in the inner part of the city, and this might create various menace to the public and due to this, the existing depot(s) need to be closed. Based on a thorough literature review, it is observed that (a) only 7 studies have considered both opening and closing depot(s) in the literature, (b) no study has considered minimizing the EC in the LD-ACBD problem, and (c) only one study has considered minimizing the Depot Operating Cost (DOC) in addition to the other economic costs (DKC + Fixed Cost involved in opening new depots (FCNWD) – Salvage Cost gained in closing some of the existing depot(s) (SCED)) as an objective. Considering the research gaps, a (0-1) ILP model was formulated by extending the existing (0-1) ILP Model in the literature to incorporate both the EC and DOC in addition to the existing economic costs (DKC + FCNWD – SCED). The model's workability was verified with a numerical example. Further, the computational complexity was also studied. The results revealed that the computational time increased exponentially with the problem size. This highlighted a major practical challenge for decision-makers and reinforced the need for alternative solution methodologies, such as heuristic algorithms. In this context, the existing-Greedy Heuristic Algorithm (GHA) available in the literature for the LD-ACBD problem was analyzed. Accordingly, the GHA follows a two-stage procedure. In the first stage, it evaluates all feasible combinations of opening new depots and closing existing depots by computing the cost of opening and closing depots, i.e., (FCNWD – SCED), and then selects the single combination with the minimum (FCNWD – SCED) value. Considering the selected combination of opening new depots and closing existing depots, in the second stage of the procedure, the original LD-ACBD problem is reduced to an ACBD problem. This reduced problem on LD-ACBD is solved using the VAM-TOCM method, which is available in the literature. Finally, the net-total-cost is obtained by adding the (FCNWD – SCED) to the total cost (DKC + DOC + EC) obtained from the ACBD problem for the LD-ACBD problem. However, the existing-GHA neither provides a rationale for evaluating only one combination nor offers evidence that this chosen combination always yields the efficient minimum net-total-cost for the LD-ACBD problem. This motivated the need to verify whether the single-combination strategy used in the existing-GHA was superior to a more exhaustive approach of considering each possible combination of opening new depots and closing existing depots, running the ACBD approach, and then obtaining the minimum net-total-cost out of all the possible combinations of opening new depots and closing existing depots. To examine this, the three top-performing heuristic algorithms for the ACBD problem identified in the first research problem: UPCM-TOCM, WUPCM1-TOCM, and VAM-TOCM, were considered to apply across all feasible combinations of openings and closing depots and running ACBD corresponding to each of the combinations for comparing with existing-GHA. A numerical example was developed to illustrate the working mechanisms of all four heuristic algorithms: UPCM-TOCM, WUPCM1-TOCM, VAM-TOCM and the existing-GHA. The solution obtained for the numerical example from each of the four heuristic algorithms indicated that (i) all four heuristic algorithms produced identical minimum net-total-cost values, and (ii) in each of the 4 heuristic algorithms, the best combination of opening new depots and closing some of the existing depots corresponded to the one with the lowest (FCNWD – SCED) value, which was obtained in the first stage of the existing-GHA. To verify the observations noticed in solving the numerical example using each of the four heuristic algorithms, this study randomly generated 90 real-life-sized, large-scale LD-ACBD problems by proposing a suitable computation experiment. All four heuristic algorithms were applied in each of the 90 problem instances and their performance was evaluated empirically and statistically with the (0-1) ILP model serving as the benchmark procedure. From both types of performance analyses, it is observed that across all 90 instances, the four heuristic algorithms consistently produced identical net-total-costs. Furthermore, a focused statistical investigation revealed that in all instances with multiple feasible combinations, the variation in net-total-cost was perfectly explained solely by the variation in the (FCNWD – SCED) cost component. These results establish that, for the LD-ACBD problem, an efficient combination of opening and closing depots can be identified reliably based on the minimum value of (FCNWD – SCED), without needing to solve the ACBD problem for every possible combination of opening new depots and closing existing depots. Based on this insight, an efficient hybrid decision-making strategy was proposed: (i) identify the best combination using the first-stage logic of the existing-GHA and (ii) solve the resulting ACBD problem using any of the three top-performing ACBD heuristic algorithms. This approach dramatically reduces computational effort while preserving solution quality, making it well-suited for implementation by I-URTO that lack advanced analytics expertise. Research Problem 3: Most I-URTO are currently operating at financial losses, and assessing their performance purely based on financial statements does not capture operational inefficiencies. The challenge lies in evaluating the relative efficiency of these organizations using data-driven methods that account for variations in inputs (such as fleet size/ fuel/ material/ labor costs) and outputs (such as passenger-kilometers/ revenue). The Data Envelopment Analysis (DEA) method provides a well-established non-parametric approach for evaluating the relative efficiencies of the URTO. However, a review of the literature on the performance evaluation of the URTO using DEA revealed that (a) considering the developed countries and the developing countries, including India, the total number of uniquely identified (a) input variables is 24, and (b) output variables is 20. However, no study has considered all 24 input variables and 20 output variables together, and (b) there is a lack of clarity/justification for selecting a subset of 24 input variables and a subset of 20 output variables before applying DEA. Considering the research gaps identified in understanding the relative efficiencies of I-URTO, the first objective of this third research problem was to identify a statistically significant set of input and output variables for DEA to apply to I-URTO systems, considering the data availability for the same set of input and output variables. A dataset for ten I-URTO over a nine-year period in 2011-12 to 2019-20 was observed from government reports. From these reports, data were practically obtainable only for 8 out of 24 input variables and 5 out of 20 output variables. Further, some of the data for these variables were identified as Missing at Random (MAR). Due to the non-linear relationships observed in the scatter plots and the missing data identified as MAR, the Random Forest-based Multivariate Imputation by Chained Equations (RF-MICE) technique was employed to impute missing values, resulting in a balanced panel dataset of 90 observations w.r.t. ten I-URTO and nine-year time-period. Subsequently, 2 Quantile Regression Models (QRM) were developed, considering the input variables and output variables, respectively. After checking for normality, multicollinearity, stationarity, cointegrating relationships, and causality, the QRM was developed using 5 input variables out of an initial set of 8 input variables. Based on the regression results, out of the 5 input variables, only 2 input variables, i.e., Labor Cost (LC) and Fuel Cost (FC), were found to be statistically significant (p < 0.05). A similar analysis was performed considering the set of 3 output variables where only 1 output variable, i.e., the Operating Revenue (OR), was identified as statistically significant. Subsequently, input-oriented DEA models (CCR and BCC) were applied using the available data for ten I-URTO, along with the statistically finalized set of two input variables (LC and FC) and one output variable (OR). The I-URTO: Pune Mahanagar Parivahan Mahamandal Ltd (PMPML) was found to be the benchmark I-URTO, achieving 100% efficiency in both models. Other I-URTO: (i) Navi Mumbai Municipal Transport (NMMT), (ii) Bengaluru Metropolitan Transport Corporation (BMTC), and (iii) Thane Municipal Transport Undertaking (TMTU), were found to be scale efficient but technically inefficient at their current scale (i.e., BCC-efficient but CCR-inefficient). Conversely, Delhi Transport Corporation (DTC) and West Bengal Transport Corporation (WBTC) recorded the lowest efficiency scores, indicating a need for fundamental improvements in both technical and scale efficiency. In addition to identifying efficient and inefficient I-URTO, the DEA results also highlight clear pathways for improving performance. The slack-based target values reveal that most inefficient I-URTO can substantially reduce labor- and fuel-related costs without lowering operating revenue levels. For technically inefficient organizations such as DTC and WBTC, improvements must focus on operational reforms, including better deployment of manpower, structured training to enhance fuel-efficient driving, and adopting proven cost-control practices followed by efficient peers. For BCC-efficient but CCR-inefficient I-URTO like NMMT, BMTC, and TMTU, the inefficiency is driven by scale imbalance, and hence strategic resizing, either expansion or consolidation, would be necessary to move toward optimal scale efficiency. PMPML, being efficient under both the models, serves as a benchmark for best practices in resource utilization. These insights provide actionable directions for enhancing the operational and financial sustainability of I-URTO. Research Problem 4: Despite city buses being the most affordable and socially inclusive mode of transport, ridership levels in many Indian cities remain suboptimal. Understanding commuters’ preferences and identifying the factors that motivate commuters to use city buses are crucial for I-URTO to improve service quality and increase revenue. From the focused analysis of the existing literature, it appears that scant treatment is given in general, particularly w.r.t. I-URTO. Due to this, the fourth research problem on the identification and ranking of the factors motivating the usage of city buses is defined, and a three-phase approach is followed to address this problem. The first phase involved a comprehensive analysis of the existing literature for identifying all unique relevant factors considered in existing studies on the adoption of city buses. Accordingly, a review of the relevant literature identified a total of 30 factors w.r.t. developed countries, developing countries, and India. For conceptual clarity and to eliminate redundancy arising from terminological variations across studies, these 30 factors were systematically consolidated into 9 unique factors in this study considering conceptual similarity. That is, several factors reported under different labels were found to represent the same underlying construct; for instance, safety and security, often treated separately in different studies, were unified under the single factor “Safety” in this study. Using this rationale, the 30 factors were grouped into the following 9 unique factors: Fare, Comfort, Reliability, Staff, Safety, Availability, Accessibility, Information, and Environment. In the second phase, an instrument (a questionnaire) was developed to gather opinions on these 9 unique factors related to the successful adoption of city buses by the users. Using convenience sampling, 400 responses were collected from city bus commuters in the Bengaluru East study area. The final phase involved the application of a Multi-Criteria Decision-Making (MCDM) method, specifically the Best-Worst Method (BWM), to rank and prioritize the factors that contribute to the successful adoption of city buses. After the consistency checks, 169 valid responses were retained out of 400 responses. Based on the average priority weights from all valid 169 responses, the factors were ranked in the following order: Fare, Availability, Accessibility, Reliability, Safety, Environment, Comfort, Information, and Staff. The analysis confirmed that Fare was the most critical factor influencing passengers' choice, while Staff behavior was the least important factor. Furthermore, of the 169 valid responses, the results were analyzed based on the respondents’ travel behavior: adopters (those who frequently use city buses) and non-adopters (those who rarely or never use them). Among the total responses, 139 corresponded to adopters and 30 to non-adopters. For the adopters, the top three factors influencing their choice were Fare, Availability, and Accessibility, which are consistent with the overall rankings. However, for the non-adopters, the top three factors were Accessibility, Fare, and Reliability. This variation indicated that while affordability and service frequency are crucial for existing users, potential users place greater emphasis on how easily they can reach bus stops and on the system’s reliability. In other words, fare policies are vital for retaining current users, whereas improving connectivity and ensuring dependable services may be more important for attracting new users. Finally, for both adopters and non-adopters, Staff was identified as the least influential factor affecting bus adoption. Although this study aims to address real-life decision-making problems related to improving the efficiency of city bus operations in I-URTO, it has certain limitations. For the first two objectives, the problems were studied under a deterministic setting, and the input data used were randomly generated based on an experimental design rather than taken from real I-URTO records. For the third objective, the relative efficiency of I-URTO was evaluated using only the DEA method, which, although useful for identifying relative efficiency, does not account for statistical noise, external factors, or temporal variations that may influence performance. For the fourth objective, the primary data were collected only from the eastern part of Bengaluru, a Tier-1 city, which limits the generalization of the findings to other cities.