3.7.175. Pattern sequencing

A constraint allowing for expressing the pattern sequencing problem as one single global constraint. The pattern sequencing problem [FinkVoss99] can be described as follows: given a 0 -1 matrix in which each column j (1jp) corresponds to a product required by the customers and each row i (1ic) corresponds to the order of a particular customer (The entry c ij is equal to 1 if and only if customer i has ordered some quantity of product j.), the objective is to find a permutation of the products such that the maximum number of open orders at any point in the sequence is minimised. Order i is open at point k in the production sequence if there is a product required in order i that appears at or before position k in the sequence and also a product that appears at or after position k in the sequence.