Order acceptance and scheduling with consideration of service level

In traditional order acceptance and scheduling (OAS) research, there is no constraint on how many orders are allowed to be rejected in total. We study OAS with consideration of service level in this paper. In our OAS model, there are n orders and m machines available at time zero. To maintain a predefined high service level, the number of orders to be rejected is limited to be no greater than a given value k. The objective is to minimize the completion time of the last accepted order plus the total penalty of all rejected orders. The problem is NP-hard in the strong sense in general. For the special case with a single machine (i.e., when $$m=1$$ m = 1 ), we present an exact algorithm with a complexity of $$O(n\log k)$$ O ( n log k ) . For the general case, we first propose an $$O(n\log n)$$ O ( n log n ) heuristic with a worst-case bound of $$2-\frac{1}{m}$$ 2 - 1 m , followed by a sophisticated heuristic by making use of LP-relaxation and bin-packing techniques. The second heuristic has a worst-case bound of $$1.5+\epsilon $$ 1.5 + ϵ and a time complexity of $$O(n\log n + nm^2/\epsilon )$$ O ( n log n + n m 2 / ϵ ) , where $$\epsilon >0$$ ϵ > 0 can be any small given constant.