Optimization and Persistence

Abstract

Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scenario and managerially preferable to a dramatically different solution that is mathematically optimal. Mathematical programming models can be stated and solved so that they exhibit varying degrees of persistence with respect to previous values of variables, constraints, or even exogenous considerations. We use case studies to highlight how modeling with persistence has improved managerial acceptance and describe how to incorporate persistence as an intrinsic feature of any optimization model.

Analyzing the Vulnerability of Critical Infrastructure to Attack and Planning Defenses

“…Because we assume that AD0 is feasible even when asset k has been interdicted and has no capacity, it must be possible to set a cost on asset k's capacity that makes it too costly to use: p k is just that cost. This is the standard approach to formulating an "elastic model"; see Brown et al [8] for more discussion.…”

Optimizing Schedules for Maritime Humanitarian Cooperative Engagements from a United States Navy Sea Base

“…The revised plan also adheres to a "persistence" specification made by the commander that missions carried out at the at-sea location starting July 2 had to remain within the prescheduled time windows because of their multinational character. The concept of optimization with persistence (Brown et al 1997) is used, for example, in the recent work by Fagerholt et al (2009), who reschedule and reroute ships ensuring that, given the new information available, their solutions are near optimal and close to a prespecified baseline plan. In GFSMP, we do not implement persistence based on relative penalties for deviations with respect to a baseline plan.…”

The Kellogg Company Optimizes Production, Inventory, and Distribution

“…Fixing model variables is one method of enforcing solution persistence [Brown, Dell, and Wood 1997]. That is, we require that the solution of KPS covering, say, weeks t through t ‫ם‬ 29, persist to some degree with respect to last week's solution covering weeks t ‫מ‬ 1 through t ‫ם‬ 28.…”

“…An added benefit is that the tactical KPS is easier to solve than the operational version, and this is important when running a large number of what-if scenarios. (Brown, Dell, and Wood [1997] give more details. )…”