(1423) On the Transportation Problem with Mixed Constraints عن مشكلة النقل مع قيود مختلطة - omar, Amani (INP, 2024)
The study discusses the standard transportation problem in linear programming, where the goal is to minimize the total transportation cost between supply sources and demand destinations. It notes that standard problems require a balance between available quantities at sources and demands at destinations. In cases of imbalance, a dummy source or destination with zero costs is introduced. The study highlights the need for flexibility in specifying minimum or maximum quantities that can be taken from or received at certain sources. Mixed transportation models, where constraints are inequalities rather than equalities, have been studied, and it has been shown that the mixed model is equivalent to a standard transportation problem with one additional source and destination. This paper aims to provide a proof of optimality for the mixed solution and presents methods for finding alternative basic solutions.