ABSTRACT
The set of order i = (1, 2, …, i), where i is one of the k product type and profit per unit is Pik. Each order must be processed through set of production unit N = (1, 2, …, n). An order i is said to be early if finishing time t is equal or less than due date d, t−Di ≤ 0 and overdue if t is more than the due date t−Di > 0. A product k consumes capacity CTPnt as eijknt per unit, so the selected orders will occupy total production capacity e qk ikt
i ∑ for ∀t.
Each production order consists of several jobs. The jobs have precedence (i.e., job j + 1 can start only if job j is completed). RTn is the regular working time allowed in a day, which is assumed to be eight hours. The model can be defined as follow:
