Multi-Criteria Decision-Making in the Transport Sector

Abstract

The transportation sector stands within a highly competitive environment, continuously seeking for effectiveness and efficiency. In the logic of decision-making processes, optimization—the selection of the best element, with regard to some criterion, from some set of available alternatives—appears central. In addition to traditional decision making, there is the technique of Linear Programming, which is an optimization problem in which the objective function is a linear function subject to linear constraints, which may be equalities and/or inequalities. Many real-life problems can be modeled in terms of Linear Programming, highlighting its strong practical interest. Therefore, Linear Programming can be a useful tool to support management in decision-making activities, helping both to reduce human effort and to provide quantitative results to optimization problems, such as revenue maximization or cost minimization. The aim of this research is to highlight how the combination of qualitative methods and quantitative techniques is an ideal combination for identifying the best solution in the decision-making process, contributing to research in the fields of organizational behavior and management. The chapter analyzes the whole decision-making process in transportation organizations seeking competitive advantage. Through a practical application of Linear Programming, presented using a case study, the chapter results demonstrate the importance of an instrument supporting decision-making process.

1. Introduction

The transport sector is of great importance for the economic development of a country, both with regard to the transport of people and goods [1, 2, 3]. It follows that the ability to easily offer services also increases the productivity of companies.

There are many innovative elements brought about by the rapid change increasingly evident to society, but also elements that could be improved.

The future prosperity of the industry will depend on the ability of all companies to remain competitive within the global economy [4]. It is therefore necessary to remain efficient by examining problems that may arise and, in turn, seeking innovative and optimal solutions [5].

In response to this need, organizations have to make decisions and it is precisely in organizations that decision-making processes are a very difficult aspect to evaluate.

Both in the case of individual decision-makers and in the case of groups, in fact, making the correct decision is very complex.

The definition of the problem, the alternatives, the method of evaluation, and the limitations and errors of the decision-makers, push organizations toward decisions that are not always optimal [6].

With this purpose, using multiple criteria decision-making appears to be one of the best solution for organizations in order to be competitive and to take the best decision, facing a continuously changing environment, such as in the transport industry [7].

Multiple criteria decision analysis is a structured process for evaluating options with conflicting criteria and choosing the best solution in a similar way to a cost-benefit analysis but evaluating also numerous criteria, rather than just cost [8].

Furthermore, conducting an MCDA aims to help the organization determine which options are most effective, increasing the efficiency of the decision-making process [9]. In addition to provide an ordered list of alternatives, it addresses the social aspects of decision-making to encourage discussion between different decision-makers.

The chapter, therefore, aims to analyze how more scientific models of analysis can complement the organizational decision-making approach, allowing decisions to be made that are more correct for creating value and gaining an advantage over competitors.

The paper is structured as follows. In Section 2, the methodology of the research review is set out. Next, the findings of the literature analysis on the decisions in the organizations and the related decision-making models are shown in Sections 3 and 4. In Section 5, Linear Programming is described. In Section 6, the discussion and the case study, drawn from this method, are presented. In Section 7, the results of the research are shown. Finally, conclusions and implications for future research are presented in Section 8.

2. Methodology

The methodology used in the paper approaches a literature review analysis on decision-making in complex organizations, such as aviation.

Following the description of qualitative methods of decisions, quantitative methods, such as Linear Programming—LP and Analytic Hierarchy Process—AHP are presented.

To verify the hypothesis a case study is presented [10]. The case study demonstrates that the addition of quantitative methods to qualitative ones can be considered the best solution in order to take proper decisions in organizations.

3. The decisions in the organizations

Organizational life is marked by a series of decisions taken at different hierarchical levels. For example, the relational climate, short- and long-term strategies, process trends, and the quality of working life [11].

The main characteristics of an organization constitute the decision dimensions. The latter influence each other and identify both the nature and the type of the decision itself.

The three main dimensions of a decision are relevance, temporality, and context:

Relevance: It is important to specify that organizational decisions can be simple routine matters but also changes in the whole strategy. Therefore, it can be deduced that the relevance of a decision can specify the impact on the whole organization.

Temporality: It expresses the period of time in which its consequences will be felt, given that a decision can have an immediate or distant effect in time.

Context: The environmental conditions in which a decision is made can vary significantly, influencing the possibility of finding the information necessary to define the problem and possible solutions.

In this regard, it is important to specify that there are different types of situations: certainty, risk, and uncertainty. In situations of certainty, it is possible to foresee the outcome of the decision in advance, as there is total knowledge of the information; in risk situations, it is only possible to make projections on the possible outcome of the decision, as there is partial knowledge of the information; in situations of uncertainty, it is not possible to project the possible outcome of the decision, as there is not enough information.

Starting from the interaction of these three dimensions, the economist Herbert Alexander Simon has identified two large families of decisions: planned decisions and unplanned decisions [12].

On the one hand, the planned decisions are repetitive and routine, addressing structured, well-known, and familiar problems. In fact, it is possible to elaborate a defined procedure, related to problems that occur with a certain repetitiveness and frequency. Furthermore, planned decisions are also defined as operational decisions because they have short-term effects and therefore can be taken at all hierarchical levels of the organization.

On the other hand, unplanned decisions deal with unstructured problems, that is, unexpected situations about which very little information is available. Consequently, it is not possible to manage them by adopting standard procedures: they require an authentic, original, and innovative solution. Unscheduled decisions deal with matters of great importance to the organization. Unplanned decisions are divided into tactical decisions and strategic decisions: the former address issues with short- and medium-term effects that require a dose of creativity and improvisation; the latter have broad relevance and a high level of risk because they modify long-term strategies, in fact, they require all the attention and creativity available to the organization.

4. Decision-making models

Every day and several times a day each of us makes decisions, and this gives us the possibility to choose between several alternatives: this process is called decision-making. It is a complex process because it involves different cognitive structures in which the individual must evaluate and interpret events in order to choose with greater awareness.

When we have to make a decision, we consider and integrate a lot of information to identify the most appropriate thinking strategies to decide on and to generate choice alternatives [13]. Therefore, deciding means arriving at a definitive judgment after having weighed and taken into consideration a series of alternatives and possible choices.

Decision-making is a reasoning process that can be done in a planned or unplanned way.

The study of decision-making dates back to the early 1950s: the main purpose of the research was to describe how a person should make decisions by behaving rationally. This prescriptive approach, defined as normative or rational, provides for the optimization of available resources and refers to the complete rationality of the decision-making process.

The effectiveness of rational decision-making is based on several assumptions, such as the absolute rationality of the decision-maker, the irrelevance of his emotional state, the availability of resources, and the independence of the decision-maker from the environment in which he operates in order to be able to evaluate more information.

Normative decision models are based on the notion of expected value, which consists of what the decision-maker can expect from each choice option. According to this principle, the rationality of the decision-maker is evaluated on the basis of the maximization of a monetary value intended as an advantage of the choice made.

The principle of expected value has proved to be inadequate as it is not always possible to convert a result into monetary value and the latter can have a different value for different people.

Bernoulli highlighted a concept called “moral value,” according to which decisions are determined by the utility that the outcomes have for the decision-maker and not only by their monetary value [14].

The weakness of regulatory models consists in not considering the limits of the human decision-maker and in not considering the decision-making context and the limited capacity of the cognitive system of the decision-maker in processing information.

On the other hand, since the early 1970s, decision psychology has moved toward a descriptive approach, which produced the first results with a work conducted by Herbert Alexander Simon in 1967 in which the effectiveness of the rationality model was demonstrated limited: Simon represented the decision-maker as an infallible scientist who has limited and intentional rationality. Indeed, according to Simon, individuals are limited by internal and external constraints which can be traced at different levels.

Furthermore, also Lichtenstein and Slovic deepened the so-called phenomenon of the reversal of preferences. Thanks to the deepening of this phenomenon, it has been possible to demonstrate and observe in some experiments that, when subjects have to choose between two bets, they prefer the one with the highest probability of winning, which however guarantees a small win. However, when asked to indicate how much they would pay for these same bets, they set a higher price for the bet with the lowest probability of winning, but which offers a higher payout [15, 16].

Over the years we have witnessed the birth of new theoretical orientations that seek to develop models and theories no longer conditioned by the need to check the validity of the principles underlying the rational and normative behavior of the decision-maker. In fact, starting from prospect theory, the tendency to explain decision-making behavior on the basis of the representation of the decision-making context has been emerging. The latter depends on a series of interconnected factors, such as social, moral, and individual values. It can therefore be deduced that the fundamental nature of the decision-making task is no longer the “choice” between the available alternatives based on the value of their expected utility, but the construction of the reasons for a choice in relation to another possible choice [17].

The centrality of decision-making in the competitive advantage that organizations can achieve certainly includes choices but also the decision not to choose. Such decisions, however, cannot simply refer to the “feeling” of management, although certainly “the idea” remains the constituent engine of the enterprise, but must be supported by increasingly analytical models.

Decision-making processes, at all levels, are incredibly complex and—since not everyone can have a visionary capacity—intelligence in managing information through data analysis becomes a fundamental competitive advantage for all those who want to make a complex organization such as that of a large company function properly.

Indeed, in a market that can hardly be understood in a general overview, given its complexity, the goal of those with real decision-making power is to obtain observations based on data analysis.

Now that various tools have made storage decidedly cheaper and make in-depth analyses of data possible in real time, the use of insights obtained from large samples can provide evidence where even a very good observer would fail to arrive. Therefore, Operation Research could complement normative models.

Operations Research, also known as Decision Theory, is that branch of applied mathematics in which complex decision-making problems, which arise in the management of organizations and enterprises, are analyzed and solved by mathematical models and advanced quantitative methods (optimization, simulation, etc.).

The objective of Operations Research is to support decision-making.

To achieve this goal, Operations Research provides mathematical tools to support decision-making activities in which limited resource activities must be managed and coordinated in order to maximize or minimize an objective function.

5. Linear programming

As previously stated, the purpose of organizations is the creation of value in order to gain a competitive advantage in the reference market.

The affirmation of the market, the stability, and the growth of an organization are closely linked to the critical and strategic decisions of management, such as the choice of prices, the identification of the target market, the specialization in the core activities and the allocation of the necessary resources to carry out the activities efficiently. Management will therefore frequently face optimization problems, defined as the selection of the best element, with regard to some criterion, from a set of available alternatives.

Therefore, the result of the optimization problem is the optimum solution, which represents the best, or most favorable condition, possible under specific sets of comparable circumstances.

Linear Programming (LP) is a subset of mathematical programming that aims to efficiently allocate limited resources to known activities to achieve a desired profit maximization or cost minimization. In statistics and mathematics, Linear Programming is a method for optimizing a linear objective function that may be subject to both linear equality and inequality and constraints.

Practically, Linear Programming represents an instrument to achieve the best outcome in a given mathematical model, composed of a list of requirements described as linear equations and a set of linear constraints [18].

The application of Linear Programming has a very wide domain, from business/economics to engineering problems. Our focus will be on its operational utility in modeling problems concerning planning, routing, and scheduling assignment in strategic operations contexts. To make a practical example, Linear Programming makes it possible to answer the following frequent questions for production management:

• What is the maximal production size?

• What is the structure of the production?

• What are the optimal production size and structure?

• What will be the profit reduction in case of the shortcoming of some units of material?

• Which production material should be bought in order to reach the maximum increase in profit?

• What are the possibilities for price negotiation?

5.1 Linear programming problem

The standard Linear Programming model consists of three main elements:

• Objective function (Eq. (1)), which is the function we want to maximize (profit) or minimize (cost).

$$Min\mathrm{f}\left(\mathrm{x}\right)={\mathrm{c}}_1{\mathrm{x}}_1+{\mathrm{c}}_2{\mathrm{x}}_2+\dots +{\mathrm{c}}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{n}}.$$E1

c = cost coefficient of the objective function, x = decision variables

• Decision variables (x)

• Constraints (v), conditions that must be satisfied when optimizing the objective function, expressed in algebraic equations (Eq. (2)) (equalities or inequalities).

An important assumption to consider is that activities cannot be negative (x > =0).

$${\mathrm{v}}_{\mathrm{i}}={\mathrm{\alpha }}_1{\mathrm{x}}_1+\dots {\mathrm{\alpha }}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{n}}>={\mathrm{b}}_{\mathrm{i}},\mathrm{i}=1,\dots .,\mathrm{m}.$$E2

α = coefficient, b = known terms of constraints.

To formalize the problem in a mathematical form a linear system (Eq. (3)) is constructed, considering n decision variables (x), n cost coefficients (c), m constraints (v), and m known terms (b):

$$\left\{\begin{array}{l}\mathit{min}f\left(x\right)=c_1{x}_1+c_2{x}_2+\dots +c_n{x}_n.\\ {\alpha }_1,1x_1+\dots +{\alpha }_1{,}_n{x}_n>=b_1\\ ⋮\\ {\alpha }_{m,1}{x}_{m,1}+\dots +{\alpha }_{m,n}{x}_n>=b_m.\end{array}\right.$$E3

In the following section, a practical demonstration of how to optimize operations in an airline company will be presented. The aim of this example will be to solve the following problem: optimize the route scheduling for the budget airline operating between five main airports in the US, Atlanta, Los Angeles, Chicago, Dallas, and New York.

6. Discussion

6.1 Case study: airline operations optimization using linear programming

In order to demonstrate what has been presented previously, the following case study deals with optimization of airlines route scheduling, specifically, looking for the best possible solution in order to maximize profits, considering the routes’ fixed and variable costs and profits and some constraints related to the need for providing a connection service between the cities.

Table 1 contains information about the distance between the cities.

Cities	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	—	1942	607	730	759
Los Angeles	1942	—	1741	1232	2469
Chicago	607	1741	—	802	738
Dallas	730	1232	802	—	1389
NY	759	2469	738	1389	—

Table 1.

Distance between the cities.

Table 2 shows the total fuel (in US gallons) required to fly each leg.

Cities	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	—	4097	1623	1851	1906
Los Angeles	4097	—	3724	2782	5073
Chicago	1623	3724	—	1985	1867
Dallas	1851	2782	1985	—	3072
NY	1906	5073	1867	3072	—

Table 2.

Total fuel required for leg (in US gallons).

The cost of fuel is 4.5 USD/gallon. We also consider other fixed costs, such as staff, for 3000 USD for each flight.

Table 3 contains the fare charged for a one-way flight between the cities for one passenger.

Cities	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	—	219$	85$	119$	163$
Los Angeles	219$	—	115$	145$	262$
Chicago	85$	115$	—	125$	105$
Dallas	119$	145$	125$	—	100$
NY	163$	262$	105$	154$	—

Table 3.

Fares for the route.

To simplify the example, we will use the same number of passengers for each flight. Considering the 85% of a common liner jet capacity seat taken, each flight will have 160 passengers.

Another important factor to consider is the number of slots available. Slots are the rights granted by the airport owner to schedule a flight to or from the airport at a specific time. Table 4 shows the number of slots available in our case study.

	Max slots for departure	Max slots for arrivals
Atlanta	18	14
Los Angeles	25	25
Chicago	12	16
Dallas	14	15
NY	17	16

Table 4.

N° of slots available.

Finally, since the airline must provide a public service, we must ensure that at least one flight is granted between the cities.

Our Linear Programming problem may now be defined as (Table 5):

• Aim: Maximize profits (find the best flight schedule which maximizes profits)

• Profits = Total income – Total expenditure

• Total income = Fare per person x N° of seats

• Total expenditure = Fuel required x Cost of fuel + Fixed costs.

Decision variables
	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	0	X12	X13	X14	X15
Los Angeles	X21	0	X23	X24	X25
Chicago	X31	X32	0	X34	X35
Dallas	X41	X42	X43	0	X45
NY	X51	X52	X53	X54	0

Profit coefficients (USD)
	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	0	13,603.5	3296.5	7710.5	14,503
Los Angeles	13,603.5	0	−1358	7681	16,091.5
Chicago	3296.5	−1358	0	8067.5	5398.5
Dallas	7710.5	7681	8067.5	0	−824
NY	14,503	16,091.5	5398.5	7816	0

At least 1 flight per leg constraint
	Atlanta	Los Angeles	Chicago	Dallas	NY
Atlanta	0	1	1	1	1
LA	1	0	1	1	1
Chicago	1	1	0	1	1
Dallas	1	1	1	0	1
NY	1	1	1	1	0

Slots constraint
DV	Atlanta	Los Angeles	Chicago	Dallas	NY	Total departures
Atlanta						<= 18
Los Angeles						<= 25
Chicago						<= 12
Dallas						<= 14
NY						<= 17
Total arrivals	<= 14	<= 25	<= 16	<= 15	<= 16

Table 5.

Linear Programming problem data.

Subject to 30 constraints:

• Number of slots for departure (x 5)

• Number of slots for arrival (x5)

• Each decision variable must be > = 1 (x20), to ensure that at least one flight will connect to each city.

Through a Linear Programming solver tool, it is possible to easily find the optimum solution in order to obtain the maximum possible profit, which in our case study represents the best flight schedule under the abovementioned conditions (Table 6).

Optimum solution: N° of flight for each route
DV	Atlanta	Los Angeles	Chicago	Dallas	NY	Total departure		MAX DEP
Atlanta	0	9	3	4	2	18	<=	18
Los Angeles	11	0	1	1	12	25	<=	25
Chicago	1	1	0	9	1	12	<=	12
Dallas	1	1	11	0	1	14	<=	14
NY	1	14	1	1	0	17	<=	17
Total arrivals	14	25	16	15	16
	<=	<=	<=	<=	<=
Max ARR	14	25	16	15	16

Table 6.

Optimum solution.

Then, the Objective Function will be: Maximize total profit (leg profit coefficient x N° of flights) = 977.482 USD.

6.2 Sensitivity analysis

Based on the results obtained from the resolution of the Linear Programming problem, it is possible to carry out an analysis of the data to verify the sensitivity of the optimal solution to any changes.

This operation is called Sensitivity Analysis. Through this analysis it is possible to obtain important information in practice, allowing the decision maker to know the degrees of freedom of the problem and to answer “What if” type questions [19] such as: if the objective function changes, how does the solution change? If available resources change, how does the solution change?

In particular, we can focus on two main aspects: the analysis of how the variation of the decision variables influences the optimal solution and the impact of the constraints on the objective function.

First, we will analyze the variables sensitivity (Table 7).

Name	Final value	Reduced cost	Objective coefficient	Allowable increase	Allowable decrease
Atlanta Atlanta	0	−12,015	0	12,015	INF
Atlanta Los Angeles	9	0	13,603.5	0	10,307
Atlanta Chicago	3	0	3296.5	4414	386
Atlanta Dallas	4	0	7710.5	3653.5	1618
Atlanta NY	2	0	14,503	1618	0
Los Angeles Atlanta	11	0	13,603.5	INF	0
Los Angeles Los Angeles	0	−15,192	0	15,192	INF
Los Angeles Chicago	1	−6243	−1358	6243	INF
Los Angeles Dallas	1	−1618	7681	1618	INF
Los Angeles NY	12	0	16,091.5	0	1618
Chicago Atlanta	1	−9075.5	3296.5	9075.5	INF
Chicago Los Angeles	1	−15,318.5	−1358	15,318.5	INF
Chicago Chicago	0	−3653.5	0	3653.5	INF
Chicago Dallas	9	0	8067.5	INF	3653.5
Chicago NY	1	−9461.5	5398.5	9461.5	INF
Dallas Atlanta	1	−9075.5	7710.5	9075.5	INF
Dallas Los Angeles	1	−10,693.5	7681	10,693.5	INF
Dallas Chicago	11	0	8067.5	INF	8067.5
Dallas Dallas	0	−12,481.5	0	12,481.5	INF
Dallas NY	1	−20,098	−824	20,098	INF
NY Atlanta	1	0	14,503	0	INF
NY Los Angeles	14	0	16,091.5	INF	0
NY Chicago	1	−386	5398.5	386	INF
NY Dallas	1	−2382.5	7816	2382.5	INF
NY NY	0	−16,991	0	16,991	INF

Table 7.

Sensitivity report: variables analysis.

The final value represents the optimal resource allocation solution. This is the number that will replace the decision variable X in the objective function.

Reduced cost is the decrease of the objective function value for the production of one unit of the product. Reduced cost is a negative amount for maximization problems and represents the loss in profits if one unit of the activity is forced into the solution.

There might be situations where not producing one product (activity) is more profitable. In this case, the final value will be zero.

In our case study, we can identify routes where reduced cost is a negative number, which means that removing that flight from the schedule will improve the total profit. However, this decision is incompatible with the “at least one flight per city” constraint and therefore cannot be taken into account.

The allowable increase or decrease shows the range between the objective coefficient can change so that the optimum solution remains unchanged. Referring to the case study, the objective coefficient is the profit per route, which can fluctuate between an upper and a lower limit indicated by the allowable increase/decrease number.

If the objective coefficient varies outside the allowable interval, there will be a new optimum solution, different from the original one.

Now we can move to the constraints analysis (Table 8).

Name	Final value	Shadow price	Constraint R.H. side	Allowable increase	Allowable decrease
Atlanta	14	8718.5	14	2	0
Los Angles	25	10,307	25	2	0
Chicago	16	0	16	INF	0
Dallas	15	4414	15	2	0
NY	16	11,206.5	16	2	0
Atlanta	18	3296.5	18	0	2
Los Angeles	25	4885	25	0	2
Chicago	12	3653.5	12	0	2
Dallas	14	8067.5	14	0	10
NY	17	5784.5	17	0	2

Table 8.

Sensitivity report: constraints analysis.

The shadow price, also known as opportunity cost, is the amount by which the value of the objective function will improve or decrease if the availability of the resources associated with the related RHS (right-hand side) constraint is increased or reduced by a unit.

This information is very useful because it allows decision makers to know the effective impact on the profit of a change in terms of constraints just by multiplying the shadow price by the increase or decrease quantity of the RHS constraint, without having to solve a new Linear Programming problem.

Also, in this case, there is a range of feasibility, identified by the allowable increase and decrease value, within which the RHS constraint may vary, maintaining the shadow price unchanged. If the variation of the RHS constraint falls outside the upper or lower limit, the shadow price will no longer be reliable, making it impossible to evaluate the impact on the profit of that change unless we build up a new Linear Programming problem.

The sensitivity analysis, therefore, reveals to be an essential tool for the post-optimal evaluation of possible new scenarios. For example, in our case study, the strategic need to buy or sell a slot could be a plausible scenario.

Through this analysis, it is quite easy to take the best decision that allows the company to maximize the increase in profits or minimize losses in case of sale.

6.3 Analytic hierarchy process vs. linear programming

In high complexity and uncertainty contexts, such as the transport industry, especially when facing different alternatives that must meet multiple objectives and different stakeholders’ needs, it is necessary to rely on analysis methods that support the decision-making process in order to take the best decisions.

Depending on the context, the needs and the objectives to be achieved, it is essential to choose the most appropriate method to support decision-making.

The Analytic Hierarchy Process (AHP) is a multi-criteria decision analysis methodology capable of suggesting the best solution among a discrete set of alternatives, using mathematics and psychology. The method attributes priority values to individual alternatives, determined through a multilevel hierarchical structure that weighs their importance through quantitative and qualitative judgments.

The structure of the Analytic Hierarchy Process is developed on three levels:

• The final goal to be achieved (the problem to be solved);

• The set of possible solutions called alternatives;

• The decision-making criteria through which the goodness of the alternatives to achieve the goal is evaluated.

The choice of criteria and the judgments used to evaluate the characteristics of the alternatives are subjective interpretations, often of a qualitative nature and expressed in verbal language, which is subsequently transformed into numerical values using the Saaty ratio scale [20].

This conversion table (Table 9) assigns a value from 1 to 9 to the evaluation criteria, where 1 represents the equality between the criteria and 9 the clear superiority of one over the other. The final value is calculated using the weighted average of all judgments.

Intensity of importance	Definition	Explanation
1	Equal importance	Two activities contribute equally to the objective.
3	Weak importance of one over another	Experience and judgment slightly favor one activity over another.
5	Essential or strong importance	Experience and judgment strongly favor one activity over another.
7	Demonstrated importance	An activity is strongly favored and its dominance is demonstrated in practice.
9	Absolute importance	The evidence favoring one activity over another is of the highest possible order of affirmation.
2, 4, 6, 8	Intermediate values between the two adjacent judgments	When compromise is needed.

Table 9.

Saaty’s scale of pairwise comparison (compiled by the author. Source: ([20], p. 246)).

All the decision-making elements belonging to the same hierarchical level are then compared in pairs, thus obtaining a preference ratio that will highlight the local priorities. Considering all the local priorities of the single levels, the principle of hierarchical composition is applied [20] to calculate the priorities of the alternatives, called global priorities.

The Analytic Hierarchy Process is therefore structured in a series of steps that allow the initial problem, complex and unstructured, to be broken down into a rational framework that is simpler to understand and evaluate.

However, this method expects people, as decision-makers or stakeholders, to express preferences. Therefore, the judgments will vary from person to person and the final result will also be influenced by the subjectivity in the preferences of those who participated in the assignment of judgments.

Summarizing, we can state that the Analytic Hierarchy Process helps decision-makers to identify the alternative that best suits their values and their understanding of the problem.

Unlike the Analytic Hierarchy Process, Linear Programming provides an objective optimal solution, calculated exclusively on the final goal and on the conditions imposed on the system, which is not influenced by the subjectivity of the decision maker.

However, this characteristic is not necessarily positive; depending on the needs of the individual cases, it may sometimes be necessary to insert a preference criterion for selecting the various alternatives, thus making the Analytic Hierarchy Process preferable to Linear Programming.

To obtain more precise results and better adapt the quantitative decision support model to the problem, it is possible to integrate the two models, so obtaining an integrated Analytic Hierarchy Process-Linear Programming model (AHP-LP), which allows to insert a degree of flexibility in the search for the optimal solution, represented by the subjective weights attributed in the Analytic Hierarchy Process.

Analytic Hierarchy Process is capable of evaluating both quantitative and qualitative factors, and is used to build a priority scale according to the subjective judgments of decision-makers. Afterward, the priority ratings obtained from the Analytic Hierarchy Process model are used as coefficients of the decision variables in a Linear Programming model to find an optimal solution that maximizes the desired benefits [21].

7. Results

The study demonstrated how qualitative and quantitative methodologies work well together to find the optimal option throughout the decision-making process. The methodology employed in the study concerns the research on decision-making in complex organizations, such as the aviation industry.

After describing qualitative decision-making techniques, quantitative techniques, such as Linear Programming (LP) and the Analytic Hierarchy Process (AHP), are introduced.

Then, the paper analyzed the entire decision-making process in transport companies in search of competitive advantage, the study results illustrate on one hand the importance of a quantitative instrument to support the decision-making process; on the other hand, how the latter helps to identify some choices that turned out to be better than others, through a practical application of Linear Programming.

Linear Programming, as proved in the case study, is able to effectively distribute precious resources to well-known activities in order to maximize profits or minimize costs.

The case study “Airline operations optimization using Linear Programming” has been presented to support the theory: this example addressed the issue of route schedule optimization for the low-cost airline that travels between the five major US airports of Atlanta, Los Angeles, Chicago, Dallas, and New York. The case study indicates that the most effective method for making informed decisions in companies is to combine quantitative and qualitative decision-making techniques.

The optimal flight schedule has given the aforementioned criteria, and the corresponding value of profit, may be easily discovered using a Linear Programming solver tool. In our case study, this answer is represented as the best flight schedule. It is feasible to do an analysis of the data to confirm the sensitivity of the optimal solution to any modifications based on the outcomes acquired from the resolution of the Linear Programming issue. The name of this procedure is Sensitivity Analysis. Through this analysis, crucial information can be acquired that will help the decision-maker to understand the problem’s degrees of freedom and provide them with the answers to hypothetical questions. Therefore, it turns out that the Sensitivity Analysis is a crucial instrument for the post-optimal evaluation of potential new situations, as seen in the case study [22].

It is vital to rely on analysis methodologies that help the decision-making process in high complexity and unpredictable situations, such as the transportation sector, especially when faced with options that must satisfy numerous objectives and the interests of many stakeholders. It is crucial to select the most effective approach to support decision-making based on the situation, the requirements, and the desired outcomes [23].

Furthermore, using mathematics and psychology, the Analytic Hierarchy Process has been described as a multi-criteria decision analysis process that may recommend the optimal solution from a limited number of options, weighed on the preferences of the decision maker. The technique assigns priority values to specific options, which are decided by a multilevel hierarchical structure that evaluates each option’s significance using both quantitative and qualitative criteria. Analytic Hierarchy Process supports decision-makers in locating the option that most closely aligns with their beliefs and perception of the situation.

Contrasting the Analytic Hierarchy Process, Linear Programming offers an objective optimal solution based only on the final goal and the constraints on which the system is subject are unaffected by the decision maker’s subjectivity. A preference criterion may sometimes be required to be inserted in order to choose among the many possibilities, making the Analytic Hierarchy Process preferred to Linear Programming.

Finally, the research described how the two models can be combined to produce an integrated Analytic Hierarchy Process-Linear Programming model (AHP-LP), which enables the inclusion of some flexibility in the search for the optimal solution, represented by the subjective weights attributed to the Analytic Hierarchy Process, in order to obtain more precise results and better adapt the quantitative decision support model to the problem. Analytic Hierarchy Process is used to create a priority scale based on the subjective assessments of decision-makers and is capable of evaluating both quantitative and qualitative elements. In order to discover the best solution that maximizes the intended benefits, the priority ratings acquired from the Analytic Hierarchy Process model are then employed as coefficients of the decision variables in a Linear Programming model.

8. Conclusion and future findings

Reviewing the definition of strategy, we can certainly recall that it has been seen by Chandler as the determination of long-term organizational goals, objectives, lines of conduct, and criteria for resource allocation [24].

In addition, the studies of Hofer and Schendel have highlighted how strategy means the identification of the means or rather the “system of current and planned use of resources and interaction with the environment” that the company plans to use to try to achieve its objectives [25].

It is then worth highlighting the centrality that Grant gives to the link between strategy and value, that is, arguing that strategy is concerned with success, or rather with guiding the decision-making process of the management toward the achievement of the success of the company or rather the creation of value.

Finally, strategy, in the view of Boschetti, is shown as an integrated set of decisions aimed at ensuring the company’s competitive advantage over time and in comparison with competitors [26].

Taken as a whole, these definitions describe the complexity of the function of an organizational strategy, leading to the observation of a fundamental element, namely that strategy is the model of the pursuit of entrepreneurial success that the company has in fact adopted or intends to adopt, in order to excel in the competitive confrontation [27].

Strategy concerns both the choice of ends and the choice of means to achieve them because under conditions of limited rationality, it is not always possible to completely separate means from ends (Simon), strategy is sometimes improvisation and, finally, objectives can sometimes be discovered after starting to operate [28].

For this reason, possessing more decision-making elements makes it possible to direct decision-making processes in a more analytical manner.

Thus, reviewing what has been discussed, the literature certainly provides us with an analysis of how unavoidable decision-making is for organizations and how the correct decision, although complex to make, can determine the success of the company’s objectives.

Sometimes, only qualitative decision-making processes are not enough to efficiently support the management in the definition of the operative scenario and in identifying business opportunities and possible solutions [29].

Hence, this paper later introduces some analytical and multi-criteria models, such as Linear Programming and Analytic Hierarchy Process, which allow us to reach apparently more correct and complete decisions.

Through the case study presented in the discussion section, it has been demonstrated the importance and the utility of Linear Programming in both planning and operational decision-making processes. In fact, this tool provides a numerical solution to the optimization problem, directly providing the best possible solution under a set of conditions. Without this instrument, an enormous human effort would be required to identify a solution that would not be so precise anyway.

With the aim of completing the analysis, the Analytic Hierarchy Process method has also been described, without however presenting any practical applications.

As discussed in the section above, it is possible to obtain an integrated Analytic Hierarchy Process-Linear Programming model to merge their best features into a single tool.

Further research may be conducted on this application of the mathematical models focusing on the possibility of creating a tool capable of supporting the decision-making process by solving problems of a different nature than the one analyzed in this paper.