Solving scheduling problems with earliness and tardiness penalties using priority rules and linear programming

Most research papers in production scheduling are concerned with the optimisation of a single criterion. However, the study of the performance of schedules often involves more than a single aspect and therefore needs a multi‐objective treatment. For example, in just in time philosophy, it is very common to consider two conflicting criteria namely earliness and tardiness. Both of these criteria are obtained from processing times which can be in certain cases fixed or obtained from an interval. This scheduling problem can be solved by a wide range of different approaches including both exact and heuristic methods. In this paper, we try to find the most appropriate method that can minimise the two criteria simultaneously for a practical case in the chemical industry. A zero one integer linear programme was developed and implemented through the software LINDO which allowed us to solve our practical problem and compare its solution to those of some priority rules. The goal of this paper is to develop different methods that can find a schedule which minimises the sum of earliness and tardiness penalties.