Algorithms for scheduling incompatible job families on single batching machine with limited capacity

•We introduce the problem of scheduling job families on single batching machine.•We present a mixed integer program and their computational complexity.•Polynomial time algorithms are proposed for the problem.•Time complexity and worst case performance of the algorithms are analyzed. Motivated by applications in food processing and semiconductor manufacturing industries, we consider the scheduling problem of a batching machine with jobs of multiple families. The machine has a limited capacity to accommodate jobs. The jobs are in arbitrary sizes and multiple families. Jobs from different families cannot be processed in a batch. We show the problems of minimizing makespan and total batch completion time are both NP-hard in the strong sense. We present a mixed integer programming model for the problems. Then we propose two polynomial time heuristics based on longest processing time first rule and first fit rule. For the special case where a larger job also has a longer processing time, the heuristic for minimizing makespan is optimal. For the general case, we show the performance guarantee of the methods for the two objectives respectively.