Netform Modeling and Applications

Abstract

Many real-world applications have profited from netform innovations in both modeling and solution strategies. Practical experience shoves that advances in netform modeling and solution strategies overcome many of the difficulties in conceptual design and problem solving of previous approaches to system optimization. Moreover, they provide the type of technologies required of truly useful decision-planning tools, technologies that facilitate modeling, solution, and implementation. The ultimate test and worth of computer-based planning models, however, depends on their use by practitioners. In this tutorial, we show how certain algebraic models can be viewed graphically using netform modeling and describe several large practical problems we have solved. Some of our insights can make it easier for practitioners to take advantage of these technologies.

Using error bounds to compare aggregated generalized transportation models

“…We can treat this case as an intermediate one between the TP, where the gains are the same for all arcs, and a general form of the GTP, where the gains vary from arc to arc. Interpreting the GTP as the machine loading problem (see, e.g., Ahuja, Magnanti, and Orlin (1993), and Glover, Klingman, and Phillips (1990)), producing one unit of product j on machine i consumes d i j hours of the machine's time. If p i is interpreted as a production "velocity" of the machine i, and t j is a "length" of the product j measured in suitable units, then the assumption d i j = p i t j holds.…”

“…For the second interpretation, the multipliers are used to transform one type of item into another (manufacturing, machine loading and scheduling, currency exchanges, etc.). For a more detailed discussion on the GTP and its applications see Ahuja, Magnanti, and Orlin (1993) and Glover, Klingman, and Phillips (1990). In contrast to the TP, much less work has been done in aggregation for the GTP.…”

New constructs for the description of combinatorial optimization problems in algebraic modeling languages

“…These systems dispense with any constraint expression language, employing instead a collection of standard symbols -such as the netforms of Glover, Klingman and Philips [15,16] [28,25,26,27], and Kendrick's PTS [30,31] can thus offer intuitive graphical interfaces for the solution of combinatorial optimization problems on networks.…”

Lot sizing with inventory gains

“…The latter interpretation has applications in manufacturing, production, energy conversion, blending, manpower planning and currency exchange problems (Glover, Hultz, Klingman and Stultz, 1978;Glover, Klingman and Phillips, 1990;Ahuja, Magnanti and Orlin, 1993). A diverse range of signicant practical appplications have been modelled as generalized networks, or as one of their discrete variants which include integer generalized networks and xed charge generalized networks.…”

“…These models and related specialized solution techniques are well documented in the literature. See, for example, Glover et al (1978), Aronson (1989), Glover et al (1990), and Ahuja et al (1993), and the references cited therein.…”