Two-agent order acceptance and scheduling to maximise total revenue

The order acceptance and scheduling problem has attracted the attention of many researchers over the past two decades. Studies dealing with profit calculation in this problem have so far focused only on one type of penalty function. This is while in real life situations each manufacturer can have different customers and may deal with each individual customer through different objective functions. In this pcaper, the order acceptance and scheduling problem has been redefined as a two-agent case for which a new and more practical problem has been considered. The objective is maximising the total revenue from accepted orders by considering an upper bound on the total lateness of the first agent's orders and no tardy orders of the second. A mathematical programming model and a pseudo-polynomial dynamic programming are proposed to optimally solve the problem. Computational results for this problem have shown the capability of the proposed approach.