Threshold incentives over multiple periods and the sales hockey stick phenomenon

In this article, we study threshold‐based sales‐force incentives and their impact on a dealer's optimal effort. A phenomenon, observed in practice, is that the dealer exerts a large effort toward the end of the incentive period to boost sales and reach the threshold to make additional profits. In the literature, the resulting last‐period sales spike is sometimes called the hockey stick phenomenon (HSP). In this article, we show that the manufacturer's choice of the incentive parameters and the underlying demand uncertainty affect the dealer's optimal effort choice. This results in the sales HSP over multiple time periods even when there is a cost associated with waiting. We then show that, by linking the threshold to a correlated market signal, the HSP can be regulated. We also characterize the variance of the total sales across all the periods and demonstrate conditions under the sales variance can be reduced. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Book reviews

Third World Military Expenditure: Determinants and Implications. By Robert McKinlay. Frances Pinter, London (1989)

The UK Defence Industrial Base: Development and Future Policy Options. By Trevor Taylor and Keith Hayward. Brassey's, London, for Royal United Services Institute (1989), ISBN 0-08-036713-5, £22.50

Mutiny. By Lawrence James. Buchan & Enright, London (1987), ISBN 0-907675-70-0, £12.95; Scapegoat! Famous Courts Martial. By John Harris. Severn House, London (1988), ISBN 0-7278-2103-2, £12.95; In Glass Houses. By Robert Boyes. Military Provost Staff Corps Association, Colchester (1986), ISBN 0-9513467-0-9, £6.50 (paperback)

The Nuclear Weapons World: Who, How and Where. Edited by Patrick Burke. Frances Pinter, London (1988), ISBN 086187-705-5, £50.00

Merchants of Treason—America's Secrets for Sale. By Thomas B. Allen and Norman Polmar. Robert Hale, London (1988), ISBN 0-7090-3543-8, £14.95 ($21.95); Intelligence and Intelligence Policy in a Democratic Society. Edited by Stephen J. Cimbala. Transnational Publishers, Dobbs Ferry, NY (1987), ISBN 0-941320-44-8, $37.50; Catching Spies—Principles and Practices of Counterespionage. By H. H. A. Cooper and Lawrence J. Redlinger. Paladin Press, Boulder, CO (1988), ISBN 0-87364-466-2, $24.95

The BattleshipRoyal Sovereignand Her Sister Ships. By Peter C. Smith. William Kimber, Wellingborough (1988), ISBN 0-7183-0704-6, £12.95; Air Power at Sea, 1945 to Today. By John Winton. Sidgwick & Jackson, London (1987), £9.95     

Book reviews

British Military History: a Supplement to Robin Higham's Guide to the Sources.. Edited by Gerald Jordan. Garland, New York (1988), xii + 586 pp., $75.00

Red Duster at War. By John Slader. William Kimber, London (1988), 352 pp., £15.50

Armed Services and Society. By Martin Edmonds. Leicester University Press, Leicester (1988), 226 pp., £25.00     

Qmp/USP: A modern alternative to MIL-STD-105D

The Quality Measurement Plan (QMP) and the Universal Sampling Plan (USP) are the data analysis and sampling plans for the AT&T Technologies quality audit. This article describes QMP/USP, an acceptance sampling plan based on QMP and USP principles. QMPIUSP is a complete acceptance sampling system. It combines the elements of classical rectification inspection plans with those of MIL-STD-IOSD. There is no switching between plans, no tables of numbers to look through, and no discontinue state. QMP/USP is a computerized, self-contained system that features:

• Acceptance decisions based on the QMP Bayes empirical Bayes analysis of current and past sampling result
• Sample size selection based on USP, i.e., lot size, AQL, a cost ratio, the QMP analysis, and a budget constraint
• Guaranteed AOQ
• A complete statistical analysis of the quality process.

In this article, we describe the operation of QMP/USP and compare its performance with that of MIL-STD-IOSD. The comparison is made under many different quality environments with many metrics. Our results show that QMP/USP and MIL/STD/IOSD perform similarly for the environments where quality could be described as “in control”; and that QMPlUSP is superior in the environments where quality is “out of control”.     

Closure properties of the relevation transform*

Sufficient conditions under which the relevation of two probability distributions is (i) NBU, (ii) IFRA, (iii) IFR are derived. The result for case (iii) corrects an error in a previous article by Baxter.     

One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.