Optimal discounts for the online assignment problem

We prove that, for two simple functions $d_{rlt}$ , solving the online assignment problem with $c_{rl}‐d_{rlt}$ as the contribution for assigning resource $r$ to task $l$ at time $t$ gives the optimal solution to the corresponding offline assignment problem (provided the optimal offline solution is unique). We call such functions $d_{rlt}$ optimal discount functions.