The main objective of this paper is to solve a bulk transportation problem (BTP) for optimization of the transportation costs under time constraints. The multi-index bulk transportation problems (MIBTP) are an extended form of bi-criteria bulk transportation issues, which are bulk transportation problems with the goals of minimizing both time and cost. These types of problems occur when products are supplied by different modes of transportation but demands at the destination are exclusively met by one source. The objective of this paper is to get the cost–time efficient solution pairs. A new methodology is proposed in order to generate a set of optimal solutions that maintain both the overall expenses and duration of transportation. If the products are delivered earlier than the specified delivery time, there will be some concession in the costs. If the products are delivered after the specified delivery time, penalty costs must be paid. Therefore, the total transportation cost consists of direct transportation costs, concession costs, and penalty costs. To check the effectiveness of the proposed approach, a numerical problem has been solved.