An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

Intelligent design guidance

This paper presents results from an investigation regarding the use of the Design Structure Matrix (DSM) as a means to guide a designer through the calculation of numerical relationships within the early design system Designer. Characteristics, relationships and goals are used within Designer to enable the evaluation and approximation of the design model and are represented within the system as a digraph. Despite being a useful representation of the interactions within the design model, the digraph does not aid the designer in identifying a sequence of activities that need to be performed in order to evaluate the model. The DSM system was used to represent the characteristics and the dependencies obtained through the relationships. The sequence of characteristics within the DSM was optimised and used to produce a design process to guide the designer in model evaluation. The objective of the optimisation was to minimise the amount of iteration within the design process. The process enabled a designer who is unfamiliar with the model to evaluate it and satisfy the design goals and requirements. Both the DSM system and the Designer system are generic in nature andmay be applied to any design problem