Lexicographic multi-period resources allocation problem with weighted substitutable resources

Lexicographic multi‐period resources allocation problem with weighted substitutable resources is concerned with the allocation of m resources among n users during t periods such as certain weighted substitution between resources is possible in the objective to minimise lexicographically the performances functions vector. In this work, we point that there is proportional answered of the minmax approach to the principle of need. We propose the lexicographic approach to avoid this problem and realise fairness in the allocation of limited resources. For this reason, we study some variants of lexicographic resources allocation problem (LRAP) and we propose the model to formulate the lexicographic multi‐period resources allocation problem with weighted substitutable resources (LMRAPWSR). Also, we propose an exact algorithm to solve our formulated model and we apply this algorithm to treat a case study that concerns the allocation of eight fertilisers among six agri‐agricultures during three periods.