Uncertain four-dimensional multi-objective multi-item transportation models via GP technique

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In this paper, a new type of four-dimensional multi-objective multi-item transportation problem is established using uncertain theory. We formulate and derive the expected value goal programming model and chance-constrained goal programming model based on the uncertain theory, where unit transportation cost, availabilities, capacities of conveyances, demands, unit transportation time, unit loading and unloading time are represented as uncertain matrices. Based on some properties of uncertain theory, the expected value goal programming model and chance-constrained goal programming model are transformed into the corresponding deterministic equivalents form via the soft computing technique, i.e., generalized reduced gradient technique named by LINGO-14.0. After that, a real-life numerical example is given to illustrate the performance of the models. Finally, the sensitivity analysis of the proposed model is presented through chance-constrained goal programming method with respect to different confidence levels.