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Transportation and assignment models are two important subclasses of linear programming problems in Operations Research. They are widely applied in logistics, supply chain management, scheduling, and resource allocation. Both models seek optimal solutions under constraints and share certain structural and procedural similarities in their solution techniques. Though they differ in scope and problem size, their underlying mathematical foundation and algorithmic strategies overlap significantly. The transportation model involves determining the most cost-efficient way to transport goods from several sources to several destinations while satisfying supply and demand constraints. The assignment model, on the other hand, deals with assigning a set of tasks to a set of agents on a one-to-one basis in such a way that the total cost or time is minimized. Despite this difference in objectives, the solution procedures for both models exhibit significant similarities in terms of problem formulation, use of tabular representations, feasibility checks, optimization methods, and mathematical structure. 1. Linear Programming Formulation Both transportation and assignment models can be formulated as linear programming (LP) problems. In the transportation model, the objective is to minimize total transportation cost subject to supply and demand constraints at sources and destinations respectively. The decision variables represent the number of units to be transported from each source to each destination. In the assignment model, the objective is to minimize the cost or time of assigning agents to tasks, with the decision variables typically being binary (0 or 1), indicating whether an agent is assigned to a task or not. Despite the binary _______ _________ _________ _______ _____ _______ _______ ________ __________ __________ ________ ______.
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