STRATEGIC PLANNING AND DECISION MAKING PROBLEMS IN THE BILEVEL PROGRAMMING FRAMEWORK

Abstract

The journey of this research work got initiated through identification of recent challenges in strategic planning faced by the decision-makers at managerial levels. Through interactions with practitioners of various sectors of the Industry, it started becoming clear that a peculiar situation is predominantly encountered by decision-makers. During a majority of

situations of strategic planning, the selection of a move as a course of action by a decision- maker gets a reaction from one or more concerned parties, which in turn affects the objective

of the decision-maker under consideration. The introspection of the literature in mathematical programming enabled us to realize that the mathematical modelling of such situations is possible through bilevel programming framework. The industrial interactions and literature review provided the motivation to address these challenges of strategic planning by modelling such decision-making issues as bilevel programming problems. For meticulously and precisely modelling the problems and to test the models with appropriate data, we narrowed down our study to the problems of Railways and supply chain management, due to approachability to the practitioners in these two sectors. Subsequent to the task of modelling the addressed issues, another challenge which we faced during our research is the unavailability of solution algorithms to solve the problems modelled as variants of bilevel programming framework. Wherever any algorithms were available for solving such a problem, we discovered those as incapable of handling the problems of a practical scale of ours. This motivated us to work towards the development of solution algorithms for the variants of bilevel programming problems being dealt with, and thus achieve success in our main objective. In our study, we have addressed both of these challenges collectively and contributed towards the development of decision support for some of the identified challenges of decision-makers which can be categorized within the scope of modelling through the bilevel programming. Further, we have supported our study by an implementation of developed algorithms on the relevant data obtained for appropriate cases from firms facing such problems. This has enabled us to contribute to the society through an optimal utilization of available opportunities.

The thesis entitled “Strategic Planning and Decision Making Problems in the Bilevel Programming Framework” comprises of five chapters followed by the bibliography and the list of publications. The precursory Chapter 1 manifests strategic planning and decision-making, and decision-support for the same. The concept of bilevel programming along with its variants is then introduced. A survey of literature on decision-making models using bilevel programming framework developed for assisting managerial decisions of firms from various sectors is presented thereafter. Noting some practical issues in the approaches followed in strategic planning, a scope of research for developing a decision-support is observed to fix the objective of thesis along with the plan of research work. Preliminary concepts from different areas are used in our research work for development of solution algorithms. They need to be introduced with a bit detailed explanation before using them in the presentation of our work in subsequent chapters. All of such relevant concepts are presented in Chapter 2 for providing the readers with a clear understanding of our interdisciplinary work. Additionally, an independent discussion on a special case of a variant of bilevel programming problem is explicated as a ground work for developing a GA-based solution methodology in a later chapter. In Chapter 3, problem of railways is studied for decision-making on an operational issue of running special trains to tackle higher demand on specific routes during seasons of festivals and holidays. The study includes development of decision support for operational decisions on optimal utilization of rolling-stocks and determining optimal fare-price structure in a competitive environment coerced by other travelling service providers. The influence on the demand-shares by the competitors of railways is incorporated in decision making to

utilize the rolling-stock accordingly. The problem is modelled as a mixed integer single- leader-multi-follower bilevel programming problem. A diversified-elitist genetic algorithm is

introduced to solve the constructed model. The suggested methodology is illustrated by taking a test situation from Indian Railways. The work presented in this chapter has been published as a research paper entitled “A Bilevel Programming Model for Operative Decisions on Special Trains: An Indian Railways Perspective”, in Journal of Rail Transport Planning & Management (Elsevier), 8, (2018), 184-206. doi: 10.1016/j.jrtpm.2018.03.001.

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Chapter 4 develops a decision support for strategic pricing and aggregate production distribution planning for a small scale supplier intending to penetrate into a potential market engendered by a single buyer. A novel mixed integer single-leader-single-follower bilevel programming model is developed to formulate the problem in which the supplier is considered as a leader and the buyer as a follower. The proposed model subsumes the assessment of demand share against the price quotation, enabling the supplier to prepare an aggregate production distribution plan accordingly. An integer coded genetic algorithm is developed to solve the model and its implementation is exhibited through a test scenario. The work presented in this chapter is published as a research paper entitled “A Bilevel Programming Model for a Cohesive Decision Making on Strategic Pricing and Production Distribution Planning for a Small Scale Supplier”, in the journal International Game Theory Review (World Scientific Publishing Company), 22(2), 2020, doi: 10.1142/S0219198920400095. Chapter 5 studies a strategic problem of price negotiation of the buyer with its multiple suppliers in an oligopolistic-monopsony market. The problem is studied to develop a decision support for identifying target prices for negotiation through which the common goal of all stakeholders viz maintaining a sustainable business environment can be achieved. For this purpose it is suggested for the buyer to identify the Nash-equilibrium prices of the suppliers’ oligopolistic-competition as target prices, as adopting this strategy helps in avoiding adverse actions from either side. In order to develop a decision support for this strategic issue a mathematical model is formulated as a multi-leader-single-follower bilevel programming problem. A GA-based solution approach is proposed to solve such a bilevel programming problem. The proposed methodology is demonstrated by an implementation of a case of a manufacturing firm of the FMCG sector. The work presented in this chapter is communicated as a research paper entitled “A Bilevel Game Model for Ascertaining Competitive Target Prices for a Buyer in Negotiation with Multiple Suppliers” to the Journal Omega (Elsevier). A summary followed by future scope of the research work is evinced to conclude the thesis. Finally, two independent results on convex optimization are presented in Appendix, which are referred in Chapter 3 for developing a methodology to solve a problem modelled there.