Rahmaniperchkolaei, BijanTaeeb, ZohrehShahriari, MohammadrezaLotfi, Farhad HosseinzadehSaati, Saber2025-04-172025-04-172024Rahmaniperchkolaei, B., Taeeb, Z., Shahriari, M., Lotfi, F. H., & Saati, S. (2024). Discrete and combinatorial optimization. In Decision-Making Models (pp. 177-208). Academic Press.978-044316147-6, 978-044316148-3https://hdl.handle.net/20.500.12713/6185In the realm of practical scenarios, numerous complex situations inherently align with the framework of integer programming (IP). These real-life challenges emerge when the linear programming assumption of divisibility proves inapplicable. An integer programming problem manifests as an extension of linear programming (LP), wherein some or all decision variables are constrained to non-negative integer values. However, the unfortunate reality is that solving integer programming problems tends to be considerably more intricate than addressing standard linear programming challenges. A plethora of vital optimization problems within diverse domains find their most fitting representation through either graphical or grid-based models. These models offer an intuitive approach to understanding and solving intricate optimization quandaries. The focus of this chapter lies in the exploration of integer programming problems and the transportation problem, which emerges as a distinct facet of linear programming. The transportation problem stands as one among the specialized structures of linear programming, garnering extensive applicability in real-world scenarios. It serves as a pivotal tool for efficiently allocating resources, optimizing supply chains, and devising strategies for distribution and logistics. This chapter embarks on a journey to decipher the intricacies of integer programming, uncovering its significance in encapsulating real-life dilemmas where discrete decision-making is fundamental. By delving into the nuances of the transportation problem, we gain insights into a practical manifestation of linear programming's potential, further enriching our understanding of optimization techniques in the context of real-world complexities. © 2024 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessCalculation MethodsColumn Generation MethodCombinational Optimization ProblemsEnumerative MethodsInnovative and Meta-innovative Methods Integer ProgrammingRelaxation MethodTransportation ProblemBook Chapter1772082-s2.0-8520290093210.1016/B978-0-443-16147-6.00005-0N/A