JIT-transportation problem and its algorithm
This article introduces the (just-in-time) JIT-transportation problem, which requires that all demanded goods be shipped to their destinations on schedule, at a zero or minimal destination-storage cost. The JIT-transportation problem is a special goal programming problem with discrete constraints. This article provides a mathematical model for such a transportation problem and introduces the JIT solution, the deviation solution, the JIT deviation, etc. By introducing the B(lambda)-problem, this article establishes the equivalence between the optimal solutions of the B(lambda)-problem and the optimal solutions of the JIT-transportation problem, and then provides an algorithm for the JIT-transportation problems. This algorithm is proven mathematically and is also illustrated by an example.
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