A method for building a robust strategy map using mathematical programming considering different sce

Abstract

Keywords: Balanced Scorecard; Mathematical Programming Model; Scenario Planning; Strategy Map

Introduction

In today’s world, many organizations and businesses are focusing on issues such as strategic decision-making and planning to address complex environmental issues [1]. Successful companies have realized the need to focus on strategic management, but sometimes strategic management only focuses on a specific part, which does not allow the strategic or operational plan to be achieved or fail in practice. One of the reasons for this failure is the lack of a comprehensive view of the pre-operational stages of strategic plans. The strategy map as a main component of the balanced scorecard (BSC) is a suitable tool for this challenge, which defines the strategic objectives of different dimensions of the company and by communicating them, identifies the paths for the company to succeed in implementing strategies [2]. The strategy map is a comprehensive tool for the correct attitude and the exact direction of the organization’s progress toward its vision. If the organization can properly design and implement a strategy map, the implementation of the strategies will be significantly improved. The main objectives of a strategy map are to facilitate the transfer of strategy to operational conditions and to understand what each person’s duty is to the overall goals of the organization [3]. If a strategy map is created through a collaborative process, the unity and commitment to implementing the strategy can increase. Through strategy maps, one can imagine how different parts of the organization directly or indirectly contribute to the overall performance of the organization. If a balanced scorecard framework is taken into account in a strategy map to describe the strategy’s logic, it enables the organization to succeed both from the perspective of its customers and stakeholders. In addition, strategic objectives from four balanced scorecard perspectives are linked together in a chain of cause-and-effect relationships [4]. Most methods for building a strategy map focus on the current situation of the business and do not attention to the upcoming uncertain event in the future. A strategy map without considering the uncertainty of the world is of no credit, especially in the current unstable situation. In this paper, a method is presented to build a strategy map that points to this gap and considers different situations based on scenario planning. Hence, the proposed method in this paper tends to consider different situations in the future. Therefore, in the beginning, a preliminary strategy map is prepared for each scenario. For this purpose, the pairwise comparisons technique is applied and its results are used as input parameters of linear programming. In fact, in the first phase, the strategy map of each scenario is built, including strategic objectives and important cause-and-effect relationships. In the initial map of each scenario, assumed that each low-level goal has a relationship with all its high-level goals in the balanced scorecard. Then, in the second phase, based on the heuristic method and the judgment of experts, the

final strategy map of each scenario is made. The contribution of the proposed method is the ability to consider the relationship between the low-level goals of the balanced scorecard aspects (growth and learning aspect) on the high-level goals of the balanced scorecard (financial aspect), without considering predecessor and successor strictly constraint between aspects. It has also tried to use the advantages of exact and heuristic methods to present a strategy map that is valid in possible futures. The 2nd section consists of related work to strategy maps by researchers. The proposed method is represented in section three. In the 4th one, this method is applied to a real case study. Finally, the conclusion is presented in section five.

Literature Review

Despite that design and use of strategy maps have advantages, some researchers have also expressed their weaknesses. For example, they argue causal relationships of BSC show a one-way linear approach often with a learning and growth aspect, and they move toward financial results while they should also show non-linear and two-way links [5-7]. From a statistical point of view, testing the relationship between elements of a strategy map can increase its quality. Ittner and Larcker show that less than 30 percent of the companies surveyed create causal models for testing relationships[8]. However, the idea of calculating causeand-effect relationships may be misleading, because the performance index or data of strategic objectives may lead to a positive or negative correlation without necessarily causation. Norreklit [9] points out that strategy maps do not distinguish between logical and causal links. Even if it only focuses on statistical analysis, there is not enough historical data to determine a reliable coefficient. Typically, in many organizations, there is a difference in the frequency of accumulated amounts and the range in which values vary over a period. Although statistical relationships are related to strategy maps, experience has shown that the design of strategy maps is rarely scientific. Often, strategy maps are the result of a collective view of managers identifying business goals and how to achieve them. This mapping approach is not necessarily a mistake. However, a statistical strategy map may be seen as a black box that does not provide an understanding of strong causative relationships. If managers were not part of the mapping process, they could get away from the use and outcome of their strategy maps, especially if their reasons were not in their favor. Ownership is needed but building a strategy map must be done in a collaborative process. There is significant attention that the dependence on the causal model shown in the strategy map may not be enough to reflect the evolution of the strategy over time [10]. Relying on a long-term statistical strategy map is equivalent to assuming that the organization and strategy will remain the same, and competitors will continue to behave in the same way. In addition, if

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strategy maps are supposed to be able to predict, then it would be possible to question the validity of the analysis of past data to predict future situations. Indeed, the validity of a strategy map based on past data may invalidate it. This means that although the development of a strategy map can help the organization to implement its strategy, it cannot enable the organization to face changes that can affect its strategy and ultimately its performance. Linking the design of strategy maps to future scenarios can help reduce this risk, as maps can be linked to the future, rather than simply displaying the current state of affairs. Using a method to imagine a possible future, such as scenario analysis, could solve these concerns and improve current communication and predictability of strategy maps [11]. The scenario is defined as a vision of what might happen in the future. It is not a prediction, but one of the possible future outcomes. Scenario analysis is a tool to regulate its understanding of future alternatives [12]. Similarly, scenario analysis does not mean exact terms about the future. Instead, it helps managers to not consider future performance as a single plan, but as a set of options that they can choose and work to accomplish. In other words, scenarios can prepare an organization for what might happen in the future. Scenario analysis is a qualitative and orderly method to illustrate possible future situations [13]. Scenario planning is used to imagine the world’s future prestigious positions and to consider how to take advantage of opportunities and prevent potential threats [14]. The scenario analysis seeks to resolve two common concerns in decision-making, excessive change prediction, and inadequate changes. To do this, participants in the development of scenarios are encouraged to distinguish between factors that are believed to be aware of it and elements that are unknown to them and indistinguishable from them. Scenario analysis is a different way of looking at the future for two main reasons. First of all, for organizations, creative thinking about the future is necessary to avoid unforeseen risks and the lack of readiness. Second, since the future is inherently uncertain, organizations must be prepared for possible future situations, not just those that are expected to occur [15]. Two or three scenarios are usually created. The first scenario can be an understanding of the current situation. The second scenario may describe a bright future, which can be due to good organization to deal with the disorder. The third scenario can describe a sadder view, for example, confronting a disorder that the organization is not prepared to deal with [12]. Generally, it can be argued that organizations can use scenario analysis with an official approach to designing strategy maps. Strategy maps are tools for anticipating because they seek to show how decisions can now affect future outcomes. Scenario analysis can extend the effectiveness of strategy maps. The common use of the two methods can be an important step in coping with multiple non-compliant versions of the truth, all of which identify the status of management

information in many organizations [1]. Using scenario analysis in building strategy maps can add an uncertain perspective that a standard strategy map design has not considered it. Both scenario analysis and strategy map force executives to identify both the number of opportunities that may occur in the future and the key goals of the organization. When scenarios are built, the main task of managers is to design a strategy that is stable under the conditions specified in the assumed scenario [10]. The combination of strategy maps and scenario analysis has several advantages as follows [4]: • Strategy maps and scenarios are effective tools for communicating the current and future strategy of an organization. • Both tools are based on a comprehensive view of the organization and its environment, and how it is interlinked between key activities and processes. • The internal focus of strategy maps by analysis of the scenario on environmental factors is considerable. • Both tools require the participation of several interest groups. This can increase the credibility and firmness of the organization’s strategy. • Ultimately, probabilities, uncertainties, trends, and opportunities that are rarely anticipated can be identified, evaluated, and entered into strategy maps through scenario analysis. Buytendijk, et al. [11] presented a new approach to designing a scenario-based strategy map. In the following, four steps proposed by them to create a scenario-based strategy map are represented. It is assumed that the organization currently has a strategy map. 1. Consider the strategy map and identify strategic objectives that describe the assumptions of the business model. 2. Create multiple scenarios, for example, using the analysis of political, economic, social, technological, environmental, and legal elements. Identify the new success factors or important changes in each of these scenarios.

4. Integrate goals across multiple scenarios.

Rezaee, et al. [16] presented an intelligent strategy map to evaluate improvement projects in the auto industry using the fuzzy cognitive map and slack-based efficiency model. Verna, et al. [17] worked on quality inspections in manufacturing processes and proposed a general framework for inspection planning by defect prediction models and inspection strategy maps. Jahromi (2021)[18] proposed a novel multi-objective mathematical model for selecting strategic objectives from identified potential strategic objectives and selecting the important relationships between them. This paper presented a goal programming approach to model-building strategy maps and contained three goals: goals related to the relative importance of strategic objectives (G1), number of casual relationships (G2), and relative importance of relationships (G3). The more the goal is among the more scenarios, the more important and

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the probability that the goals will be achieved in a changing environment is higher. To work on this collaborative analysis, strategic objectives must be clear. This means that highlevel dominant goals such as maintaining profitability do not provide practical guidance. Currently, some approaches provide a strategy map combining the analytical hierarchy process(AHP), analytical network process(ANP), decision-making trial and evaluation laboratory (DEMATEL), Balanced Score Cards (BSC), and so on with a mathematical optimization model [19-23]. Moraga et al. presented a method to build a strategy map focused on identifying causal relationships. They present a methodology to improve the identification of causal relationships of an existing strategy map of a company, using a multi-decision criteria method [24]. In another study, a fuzzy cognitive map for the Sustainable Development Goals was constructed so that the Causaleffect links among them were identified and mapped [25]. Taghizadeh, Torabi, and Rajabzadeh [26] developed a decision-making model investigating the outsourcing of complex product systems using SEM and ISM methods. Al-Mawali [27] integrated the sustainability balanced scorecard (SBSC) framework with DEMATEL for proposing a model and identifying the cause-and-effect relationships between the five perspectives of SBSC and then 23 performance indicators within the SBSC framework in a strategy map. Goodspeed et al. [28] urged that Datadriven scenario planning can be effective in resource-limited contexts. Mohammadi [29] showed that strategic foresight is effective in creating dynamic capabilities. In the proposed method in this paper, a strategy map is assumed with some determined strategic objectives and all potential relationships between them. The strategy map is proposed with the least possible causal relationships while maintaining relationships among the most important goals considering different scenarios. Notably, the robustness of the presented strategy map in this paper is dependent on its adaptability and validity in different futures.

The Proposed Approach

As mentioned earlier, in this paper, a hybrid-scenario-based method is presented that uses mathematical programming and pairwise comparisons based on the AHP technique for building a strategy map. While considering different scenarios in the future named robust strategy map, it has the most common features in future scenarios. The proposed method has two phases containing four steps. In the first phase, the optimal strategy map of each scenario is built as a preliminary strategy map. The second phase produces a conclusive strategy map based on the final strategy maps derived from the first one. According to different scenarios and corresponding to each one, in the first step, a preliminary strategy map is designed. In the second step, experts determine the relative importance of goals and the

relationships between them. Employing a linear mathematical programming model, in the third step, the final map is determined for each scenario. The linear mathematical programming model is used to maximize the relative importance between selected goals and minimize the number of relationships. In the fourth step, the conclusive strategy map (i.e., robust strategy map) is developed. It incorporates all the common strategic objectives and semi-common goals. Based on the output of the mathematical model and taking into account the opinions of the experts, the final strategy map is provided in the proposed method. While maintaining simplicity and considering different scenarios, the outcome of the precise design of this method comprises a combination of mathematical linear programming with decision-making based on pairwise comparisons. Linear mathematical programming approaches used in this model pursue the following objectives: • Maximizing relative importance between goals. • Minimizing the number of relationships between goals. In addition, the following assumptions are considered: There is more than one initial strategy map. The number of these maps equals the number of determined scenarios and different scenarios with the same strategy map are considered as a single scenario. • In each strategy map, the importance of relationships is determined by the experts and the model does not play a role. • The existence of causal relationships between goals at one level and all higher levels is possible. • The effect of goals is from lower (growth and learning aspects) to higher levels (financial aspects), and at each specific level, it is possible to consider the two-way relationship between goals. One of the advantages of this method compared with other related research is that based on the BSC logic about lag and led nature between goals, the relation between goals is not limited to two consecutive levels. The relationship between goals at all levels, including a specific level with itself, is considered. As mentioned earlier, the proposed hybrid method that included mathematical programming and experts’ viewpoints has four steps described below. The symbols used in the mathematical programming of the model are shown in Table 1. •

First Step First, preliminary strategy maps are prepared based on different scenarios. This map includes goals and causal relationships that by default all goals are related to all levels from lower to higher considering the principle of BSC so that there are led and lag relations between goals from the learning and growth aspect to goals of the financial aspect. It is noteworthy that the goals appear not necessarily the same in different scenarios.

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Table 1. The symbols and notations used in the mathematical model Notations l

Nodes at nth level, n = 1, …, 4. The importance between nodes i ∈ Jn and j ∈ Jm so that m ≥ n according to Saaty paired comparison.

Relative importance between j ∈ Jm node i ∈ Jn at the nth level so that m ≥ n.

Decision variables Equal to 1 if there is a relation between i ∈ Jn and j ∈ Jm, otherwise, it is zero, as an independent variable.

The number of relationships between the goals of the nth level and the levels of m ≥ n, as a dependent variable. The difference between 1 and the sum of the relative importance of the selected relationships between the goals of level n and level, m ≥ n, as a dependent variable.

Second Step In this step, the importance of the relationship between goals is determined by the experts and described in the following procedure. To obtain the importance of relationships, the paired comparison method is used [30]. Based on the Analytical Hierarchy Process (AHP) logic, presented by Saaty, the summation of goals’ importance in each aspect (Eq. 1) and the importance of goals in each higher aspect (m≥n) of BSC is equal to one (Eq. 2). (1)

(2) In this case, the relative importance between the node i ∈ Jn at the nth level and node j ∈ Jm which is m ≥ n, is shown with kij as Eq. 3. Moreover, the summation of the relative importance of relationships of each aspect is equal to one according to Eq. 4. (3)

Third Step In this step, a linear programming model is presented to minimize the number of relationships and maximize the relative importance between goals in the strategy map for each scenario. It is worth noting this model resembles the model presented by Quezada

and López-Ospina[6]. However, there is a possibility of a relationship between the goals of non-successive aspects of BSC. The binary linear programming model is as follows. (5) Subject to: (6) (7)

(8) Equation (5) represents minimizing the number of relationships and maximizing relative importance of them, simultaneously. The number of relationships between i ∈ Jn and j ∈ Jm in the final map is calculated by equation (6) and the value corresponding to relative importance is calculated by equation (7).The maximum value of is equal to one if all goals and relationships be selected and maximizing it is equal to minimizing . Obviously, have a value between zero and one, but this is not true for . The maximum value of is equal to the number of relationships between the goals of levels n and m (m ≥ n). Thus, is a scale between zero and one and can be summed up with . Equation (8) states that each node must have a relationship at least by one of the goals at its higher level, except for end-level nodes (i.e., n=4) according to BSC. It is noticeable that the mathematical programming model

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unlike previous ones considers the possibility of a relationship between a goal at the higher level with the goals at the lower level. Fourth Step The final strategy map includes fully common goals and semi-common goals. So that fully common goals existed in all scenarios and semi-common goals existed at least in fifty percent of scenarios. Ultimately, goals that existed in one scenario are not considered in the final strategy map. The relationship between the two goals in the final map follows the following logic: A. If two goals, at least in one of the early maps, are related, they will also be related to the final map. B. If two goals do not have casual relations on the same map, the declaration of the relationship between them requires the decision of the experts.

the company’s experts (see Table 2). The first and second scenarios are related to optimistic and pessimistic situations, respectively and the third scenario points to the current situation (i.e., most likely). In Figures 1-3, the initial strategy maps for these three scenarios are respectively depicted. The mathematical optimization introduced in the previous section is applied to this case. In this example, the control value is set to fifty percent (i.e., θ=0.5).

Results And Discussion

In this section, the effectiveness of the proposed method is examined by applying it to a real case. This real case study is solved by the GAMS program on a computer with a 2.10GHz CPU and 4.00 GB RAM. Considering three scenarios, here, a strategy map is developed for each scenario aimed at building a final strategy map. These scenarios belong to a company kept unknown due to some confidential considerations. This information has been received from the strategic planning department of the company. Eighteen strategic objectives are considered by

Increasing return on capital (O2) Increasing in profit (O3) Increasing financial efficiency (O4) Customer

Reduction in costs (O5) Improving pricing (O6) Customer loyalty (O7) Value proposition (O8) Customer satisfaction (O9)

After sales services (O10) Increasing capacity (O11) Improving supply chain (O12) Improving production process (O13)

Improving Logistic (O14) Improving Safety (O15) Job Satisfaction (O16) Job Development (O17) Job Rotation (O18)

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Figure 5. The final strategy map for the second scenario. Figure 3. Third scenario’s strategy map.

Figure 6. The final strategy map for the third scenario. Figure 4. The final strategy map for the first scenario.

The details of choosing goals for the final strategy map incorporating fully common goals and semi-common ones are presented in Table 3 based on the expert’s view. Common goals exist in all scenarios and semi-common ones must be mutually found in two scenarios. In Table 3, all strategic objectives and their status in each scenario (i.e., existed or not existed) in addition to assessing and decisions about them (i.e., reject, strategic choice, or common objectives) are mentioned. In Figures 4-6, the final strategy maps for the first, second, and third scenarios are respectively shown. In Figure 7, the final strategy map is shown based on three scenarios including fully common goals and

semi-common ones. This robust map is based on three scenarios and is expected to be more reliable. Furthermore, relationships between them are based on their existence in the final strategy map in each scenario. If there is a relation between two objectives in the final strategy map of each scenario, this relation will exist in the final strategy map. As it turns out, this strategy map is based on different scenarios and is therefore expected to be more reliable under different situations. In the final strategy map of the mentioned company, there are thirteen strategic objectives out of eighteen identified primary strategic objectives based on the proposed method (Figure 7).

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Table 3. Decision-making results for strategic objectives Levels

Conclusion

One of the purposes of making a strategy map is to solve the problem of most organizations in transferring and translating the strategy into daily work for their internal stakeholders. On the other hand, and in turn, making a suitable map is one of the challenges of organizations. This paper aims at providing a simple yet practical and logical method for making a strategy map. Thus, exact and

heuristic methods and expert judgment have been used in a combined, realistic, and comprehensive manner. Due to the unstable environmental conditions in which organizations operate and compete, this method estimates various future scenarios. First, it builds the strategy map of each scenario optimally, and second, tries to create a conclusive strategy map for a company using the heuristic method and experts’ judgment. This approach is the common point of all identified scenarios. This paper focuses on developing a method that emphasizes maintaining strong relationships while keeping the final strategy map simple. As a consequence, maximizing the relative importance between goals and minimizing the number of relationships among them are included in the objective function of mathematical programming in the first phase. Among the advantages of this paper, is using a simple heuristic method in the second phase of this method. In other words. a combination of exact and heuristic methods has been used to solve one of the challenging problems of companies. In summary, the contribution of the present paper is to develop a method with the following advantages: • It is an interactive method. • It contains a combination of exact and heuristic methods. • It can be easily implemented. • There is no constraint in determining cause-and-effect relationships between goals at different aspects. • It is possible to consider different scenarios and there is no limit in determining future scenarios.

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The conclusive map is presented based on considering the commonality of all possible future states. • The conclusive strategy map is simple, concise, and useful. To mention managerial implication, the presented method was implemented in a commercial company with the cooperation of all stakeholders. The resulting strategy map has met desired demands, according to the acknowledgment of all stakeholders. Further research can be done by utilizing heuristic alternative methods, or the optimization techniques such as GOT, ALO, EHO, etc. instead of the mathematical model.

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