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THE SPECIALIST WITH A UNIVERSAL MIND
ANDREW VAZSONYI, Feature Editor, McLaren School of Business, University of San Francisco
How to Get a Free Lunch
by Andrew Vazsonyi, University of San Francisco
Milton Friedman had a profound impact on our outlook for decision making. We all believe that you cannot get something for nothing. However, there are many examples where we do improve our situation, and in fact get something for nothing.
Randolph Hall of the University of California at Berkeley, in his excellent book on queueing methods (Hall 1991) develops the concept that the new philosophy for queueing systems design is not one of trade-off values, but trade-up values. ``That is, instead of buying more of an outdated system, the new way is to replace the system with something that is more flexible at meeting customer needs.'' I find the concept useful not only in queueing systems but in a much broader context.
Consider first linear programming and an interior solution in the solution space. If this is a cost minimization problem, the cost can be lowered without violating the constraints. The system can be a trade-up. And in many real-life problems, this is what management does. However, a solution on the boundary cannot be a trade-up, only a trade-off. Shadow prices tell us how much benefit we can get at the expense of relaxing constraints. It turns out that many practical solutions to problems deal with interior solutions, although management may not know it.
In multiattribute decision theory, the distinction is made between dominated and undominated solutions. Solution A is said to be dominated by B if A is worse (or at least not better) than B, on every one of the attributes. A solution is undominated if there is no solution that dominates it. Undominated solutions are on the boundary of the solution space and are also called Pareto efficient solutions. Moving from one efficient solution always involves a trade-off; moving from inefficient solutions may involve trade-up. The theory of multiattribute decision making is primarily interested in how to move from inefficient solutions to efficient solutions, in sub-optimization. In real-life, managers may be interested to move from an inefficient solution to a better inefficient solution, that is, to satisfice, or to trade-up.
WHAT-IF analysis is the principal technique to study trade-ups. Managers search scenarios using computers in an interactive mode. Spreadsheets are one of the most popular tools to manage scenarios. WHAT-IF diagrams and ratios are commonly used to facilitate traveling in the solution space.
The most powerful mathematical tool for trade-up is calculus, by evaluating ordinary and partial differential quotients. These predict the slopes of changes in values, when parameters or decision variables are changed slightly. The method of steepest descent is the basis of most search techniques. Tornado diagrams are popular graphical tools in decision analysis, but could be used in practically any field of decision sciences. Spider diagrams (showing value changes as functions of deviations from base case parameters and decision variables) are rarely used tools, although they could be applied in many contexts.
Hall has several practical examples from queueing processes where the trade-up heuristic helped find better solutions. For example, consider the idle time of workers due to uncertainties. The trade-off syndrome would balance the cost of workers waiting against machines waiting. But better scheduling of workers will reduce both costs. Hall reports that in a major West Coast Savings and Loan company there were large ``random'' fluctuations in demand. However, the fluctuations were not ``random'' at all but caused by predictable eventsþpaydays, holidays, and the hour of the day. Better forecasting brought high-quality service.
One of our favorite topics when teaching inventory control is the economic order quantity formula. It shows the optimum trade-off between setup and run costs. But the Japanese discarded the trade-off syndrome, and using a trade-up heuristic found ways to reduce setup times from many hours to a few minutes.
In fact, the Theory of Constraints of production and operations management, introduced by Eliyahu M. Goldratt, is based on trade-up. Material requirements planning, MRP, balances the cost of uncertainty in workloads against inventory costs. But the Japanese declared inventory to be a waste, installed tight control systems, eliminated inventory, and increased production. The theory of constraints focuses on root causes and applies the trade-up philosophy.
Trade-off analysis is a most important technique of decision sciences, but blind adherence can turn it into a syndrome trying to improve obsolete systems. On the other hand, stressing the trade-up heuristic encourages creativity and the discovery of new approaches to problem solving.
Hall, R.W., Queueing Methods, For Services and Manufacturing, Prentice Hall, 1991. ______, ``From trade-offs to trade-ups, the new face of `Queuing Theory,''' APIX: The Performance Advantage, July 1992, pp. 32-33.
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