Natural disasters lead to massive human and financial losses yearly; thus, disaster planning is of critical importance. One of the most crucial measures for disaster planning is developing an efficient disaster relief supply chain (DRSC) network. Thus, many researchers have focused on this field while overlooking some crucial actual conditions as a result of the complexity of the problem. Consequently, this study develops a DRSC network considering the perishability of relief commodities (RCs), the gradual injection of the limited pre-disaster budgets, pre-disaster lateral transportation, and the time value of money. In this respect, a novel multi-period multi-commodity mixed-integer non-linear programming model is presented, which optimizes pre-disaster warehouse location and inventory management and the post-disaster re-procurement and distribution of RCs in each period. Utilizing a new service utility index, the proposed model strives to minimize deprivation cost while maximizing demand coverage and fair service. To provide the required RCs in the pre-disaster phase, a bidirectional quantity flexibility contract (BQFC) is proposed, which is integrated with multi-sourcing and allows for two-part buybacks, installment and delayed payments, and quantity-based discounts on its terms. The applicability and performance of the model are validated via a real case study in Mashhad, Iran. Various sensitivity analyses are provided to highlight the desirable performance of the model and achieve helpful managerial insights.

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