Minimization of open orders using interval graphs - Lopes, Isabel Cristina (2010)
In this paper we address an order processing optimization problem known as the Minimization of Open Stacks Problem (MOSP). This problem consists in ﬁnding the best sequence for manufacturing the diﬀerent products required by costumers, in a setting where only one product can be made at a time. The objective is to minimize the maximum number of incomplete orders from costumers that are being processed simultaneously. We present an integer programming model, based on the existence of a perfect elimination order in interval graphs, which ﬁnds an optimal sequence for the costumers orders. Among other economic advantages, manufacturing the products in this optimal sequence reduces the amount of space needed to store incomplete orders.