This paper proposes a new concept on transportation problem in which, we maximize the profit and minimize the transportation time while transporting an amount of quantity from a source to the destination. Here, we design two transportation models, in both the models; we maximize the profit and minimize the time of transportation. Here model-I having the unit purchase cost, unit selling price, unit transportation cost and transportation time as trapezoidal interval type-2 fuzzy number, while in model-II all the parameters are trapezoidal interval type-2 fuzzy number. To reduce these model-I and model-II into crisp equivalent, we use the expected value of a trapezoidal interval type-2 fuzzy number. Then the crisp equivalent problems are solved by employing the Interactive fuzzy satisficing method and LINGO 13.0 software to get the optimal solution. A numerical example is provided to demonstrate the models.

This study attempts to establish an innovative solid transportation problem that intends to maximize profit under the rough interval approximation methodology. Two transportation problems were constructed in this regard with interval coefficients corresponding to the upper approximations and the lower approximations of the rough intervals under study. Furthermore, from the contingent solid transportation problems, four different classical solid transportation problems were derived, which were subsequently solved on the LINGO iteration platform. The concepts of completely satisfactory solution and rather satisfactory solution, surely optimal range, possibly optimal range, and rough optimal range have been discussed with a perspective to its relevance to real-world practical problems. The rough chance-constrained programming and the expected value operator for rough interval have been applied to solve the problem under study. The distinct advantages of the proposed method over those existing have been outlined. Numerical examples have also been provided to illustrate the solution procedure and the methodologies adopted.

The occurrence of a sudden, calamitous, and unfortunate event requires a quick response that can reduce damage and save lives, fulfilling the basic humanitarian needs of the affected population. National or international organizations and agencies may be initiated to provide assistance but local agencies need to act as soon as possible, because they are familiar with the geographical location as well as the local conditions of the affected areas. Effective coordination of disaster assistance is often crucial, particularly when resources are limited in the local agencies and the demands are more. In such conditions, it becomes a challenging job for the agencies to distribute resources so that the resources are optimally used. This article is initiated to address the challenging fact by introducing the concept of priority measure for demands. In this regard, ranking of the affected areas based on resource requirement for a disaster scenario is evaluated through a multicriteria decision-making process. A formula is developed to find the numerical value of priority factor collecting the responses of requirement of relief materials using information crowdsourcing. To this contingent, a three-echelon emergency solid transportation problem is formulated, in which the demand with the most priority is fulfilled by the local agencies in echelon-I, and the remaining demand is fulfilled by the other national or international agencies in echelon-II along with a restoration of local agencies in echelon-III. A numerical example is presented for the sake of model performance and to test the convergence using LINGO and CPLEX optimization solvers. The model is also designed using a genetic algorithm to obtain the optimal solution. Moreover, a brief analysis of the model is presented by considering 11 different numerical instances to enhance the efficacy of the model in real-life applications.