A state-of-art survey of static scheduling research involving due dates

Mixed-Integer Programming Models for Flowshop Scheduling Problems Minimizing the Total Earliness and Tardiness

“…Constraints (13)(14)(15) impose the rules for the starting time of each job on each machine; while, as mentioned above, equality (12) gives the completion time of each job on the last machine as a function of its start time and its processing time. Constraint (13) says that between the starting times of consecutive jobs on a machine, there must be enough time for the first (of the two jobs) to be processed.…”

“…Constraint (14) indicates that between the starting times of a job on two consecutive machines, there must enough time for the job to be processed on the first machine. Constraint (15) simply says that the starting time of the first job on the first machine must be non-negative, i.e., the insertion of idle time at the beginning of the schedule is allowed. The remaining constraints were already explained before.…”

“…In the numerical experiments, we considered instances with (n, m) ∈ {(5, 3), (10, 3), (10, 7), (10, 10), (15,3), (15, 7), (15,10), (20, 3)}.…”

Due Date Management Policies

“…Our focus in this survey is on DDM, where a DDM policy consists of a due date setting policy and a sequencing policy. In contrast to most of the scheduling literature [49] [78] [88], where due dates are either ignored or assumed to be set exogenously (e.g., by the sales department, without knowing the actual production schedule), we focus on the case where due dates are set endogenously. Most of the research reviewed here does not consider inventory decisions and hence is applicable to MTO systems.…”

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

“…These costs include: penalty clauses in the contract, if applicable; loss of goodwill resulting in an increased probability of losing the customer for some or all future jobs; and a damaged reputation which will turn other customers away (Sen and Gupta 1984). The difficulty level of this problem can be assessed by means of a particular case whose solution is undoubtedly complex, namely, the deterministic problem when all jobs are available at the same time with one machine is NP-hard for the criterion of minimizing total tardiness (Du and Leung 1990).…”