This post uses the retail industry as a sketchpad to illustrate some simple but useful conflict resolution ideas employed within optimization methods in practice.
Least Infeasible Answers
Retailers have to address a myriad of business rules while optimizing merchandising, pricing, shelving, replenishing, and assortment planning decisions. Operations Researchers build mathematical models that translate these rules into a combination of soft constraints (goals, objectives, Key Performance Indicators (KPI)) that have to be maximally satisfied, and hard constraints that must be absolutely satisfied.
Conflicting hard rules can prevent the optimization application from returning a recommendation. The retailer would like to know which among their long list of rules is/are the root cause of this conflict so that they can address them appropriately and re-evaluate. Commercial solvers like CPLEX (and GUROBI, among others) can perform an infeasibility analysis to provide useful information pertaining to IIS (Irreducibly Inconsistent Sets), and based on optimizing a user-parameterized penalty function, can also find a minimally infeasible answer. These are non-trivial problems. (Try explaining to a senior pilot why a more junior pilot was assigned that plum schedule filled with all those long Hawaii layovers!) JW Chinneck has an entire book dealing with such issues.
The liberal-arts degree armed retail store manager (RSM) has a business to operate and sales targets to achieve. Many a RSM care little for iterative conflict refinement and resolution and have even lesser patience to set up paramterized penalty functions. He/She often desires that the analytics software product automatically flag problematic rules and always return the "best possible" answer(s) and be done with it. 'Null' or 'Try, try again' is not an option. A positive user experience combined with the ability to "help me earn a bonus or you are toast" is correlated with continued patronage. In such situations, the decision analytics plumbing must be designed in such that it can, with little to no external guidance, produce practically useful diagnostics that pinpoints infeasibility and generate 'best fit' solutions that are readily business-comprehensible to the average user. After all, the business application interface and functionality is not primarily meant to be a analytics-tutorial warp drive thingy.
Actions Express Priorities - Mohandas Gandhi
A store manager may have a high-level goal in mind such as: find a minimally business disruptive resolution of conflicting business rules. Toward this, several retailers employ prioritized business rules that result in a special haystack structure that invariably makes the conflict identification and resolution process more transparent and easy to manage. What would this decision problem structure look like? Borrowing computer-ware terminology (for example), it would be akin to an ordered collection of hard constraints, soft constraints, and firm constraints. Patented methods that gainfully exploit related ideas have been used to build retail optimization products that turned out to be successful in the global marketplace. On the other hand, the efficacy of such resolution methods can be context-specific and is not necessarily designed to yield universally scalable solutions. If your job is to solve only your company's or industry's specific problems and not that of all current and future corporations in the galaxy and beyond, such methods can be handy.