Increasing the amount of inspection activities and inspecting a large fraction of the
items are two approaches that are used to improve products&#39; quality. In this paper, as in a precedent
article by Jaraiedi, et al.[5], 100&#37; inspection in combination with multiple-criteria decision
(MCD) response is considered. Three different inspection procedures for the multi-stage inspection
are presented. Performance of these three procedures are derived and the Average Outgoing
Quality (AOQ), Average False Rejected (AFR), and Overall Average Fraction Inspected (SAFI)
for all procedures are compared. Two examples are discussed in depth to illustrate numerical
comparisons of these procedures.

Majid  Jaraiedi

Richard S. Segall

Venkatramani  Rajamohan

Multi-class decision procedures for the inspection operation

The equation <mml:math alttext="$x^a  + x^b  + x = x^c  + x^d  + 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>x</mml:mi><mml:mi>a</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mi>b</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mi>c</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mi>d</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> considered in this paper is a particular
equiponderate equation. The number and location of the roots (w.r.t. x &#61; 1) of this equation
are determined in case <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>]</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>[</mml:mo></mml:mrow></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math>. Based on these results, it is shown that any weight
quadruplet, a basic tool in fuzzy preference modelling, admits an interesting expression in terms
of Frank t-norms with reciprocal parameters.

Bernard  de Baets

Hans  de Meyer

On the equiponderate equation <svg style="vertical-align:-0.1638pt" height="16.9625" version="1.1" viewBox="0 0 170.875 16.9625" width="170.875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x1D465" d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37&#xA;q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" /></g><g transform="matrix(.012,-0,0,-.012,9.563,8.537)"><path id="x1D44E" d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387&#xA;q-32 15 -73 15q-52 0 -83 -23q-48 -36 -78 -108.5t-30 -152.5q0 -33 8.5 -50.5t20.5 -17.5q31 0 107 79t99 132q15 40 29 126z" /></g><g transform="matrix(.017,-0,0,-.017,19.988,16.7)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" /></g><g transform="matrix(.017,-0,0,-.017,33.739,16.7)"><use xlink:href="#x1D465"/></g><g transform="matrix(.012,-0,0,-.012,43.238,8.537)"><path id="x1D44F" d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76&#xA;q-31 0 -93.5 -49t-107.5 -110q-12 -37 -17 -70q-9 -65 12 -96.5t59 -31.5q31 0 56 14q53 29 89.5 105t36.5 162z" /></g><g transform="matrix(.017,-0,0,-.017,53.225,16.7)"><use xlink:href="#x2B"/></g><g transform="matrix(.017,-0,0,-.017,66.977,16.7)"><use xlink:href="#x1D465"/></g><g transform="matrix(.017,-0,0,-.017,81.188,16.7)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,95.892,16.7)"><use xlink:href="#x1D465"/></g><g transform="matrix(.012,-0,0,-.012,105.412,8.537)"><path id="x1D450" d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" /></g><g transform="matrix(.017,-0,0,-.017,114.638,16.7)"><use xlink:href="#x2B"/></g><g transform="matrix(.017,-0,0,-.017,128.389,16.7)"><use xlink:href="#x1D465"/></g><g transform="matrix(.012,-0,0,-.012,137.9,8.537)"><path id="x1D451" d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5&#xA;h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" /></g><g transform="matrix(.017,-0,0,-.017,148.9,16.7)"><use xlink:href="#x2B"/></g><g transform="matrix(.017,-0,0,-.017,162.652,16.7)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g></svg> and a representation of weight quadruplets

Consider a series system consisting of n components of k types. Whenever a unit fails,
it is replaced immediately by a new one to keep the system working. Under the assumption that
all the life lengths of the components are independent and exponentially distributed and that the
replacement policies depend only on the present state of the system at each failure, the system
may be represented by a birth and death process. The existence of the optimum replacement
policies are discussed and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B5;</mml:mi></mml:math>-optimal policies axe derived. If the past experience of the system
can also be utilized, the process is not a Markov process. The optimum Bayesian policies are
derived and the properties of the resulting process axe studied. Also, the stochastic processes
are simulated and the probability of absorption, the mean time to absorption and the average
proportion of the retrograde motion are approximated.

Dylan  Shi

On selecting the most reliable components

It is known that a threshold policy (or trunk reservation policy) is optimal for Erlang’s
loss system under certain assumptions. In this paper we examine the robustness of this policy
under departures from the standard assumption of exponential service times (call holding times)
and give examples where the optimal policy has a generalized trunk reservation form.

Brian  Moretta

Ilze  Ziedins

Admission controls for Erlang's loss system with service times distributed as a finite sum of exponential random variables

In the classical decision theory framework, the loss is a function of the decision taken
and the state of nature as represented by a parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math>. Information about <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math> can be obtained
via observation of a random variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math>. In some situations however the loss will depend not
directly on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math> but on the observed value of another random variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> whose distribution depends
on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B8;</mml:mi></mml:math>. This adds an extra layer to the decision problem, and may lead to a wider choice of actions.
In particular there are now two sample sizes to choose, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> and for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math>, leading to a range of
behaviours in the Bayes risk. We illustrate this with a problem arising from the cleanup of sites
contaminated with radioactive waste. We also discuss some computational approaches.

Geoff  Jones

The predictive distribution in decision theory: a
case study

In a fast changing global market, a manager is concerned with cost uncertainties
of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag
between the development and application of the model could cause cost parameters to assume
different values when an optimal assignment is implemented.
 The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties.
 A desirable tool is
to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal
solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the
Hungarian method, respectively. Both methods fail to provide direct information to construct the
needed PS. An added difficulty is that these problems might be highly pivotal degenerate.
 Therefore, the sensitivity results obtained via the available linear programming (LP) software might be
misleading.We propose a unified pivotal solution algorithm for both TP and AP.
 The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed
algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally
practical, being easy to understand,  and providing useful information for managers. The results
empower the manager to assess and monitor various types of cost uncertainties encountered in
real-life situations. Some illustrative numerical examples are also presented.

V. Adlakha

H. Arsham

Managing cost uncertainties in transportation and assignment problems

In Data Envelopment Analysis, when the number of decision making units is small,
the number of units of the dominant or effcient set is relatively large and the average effciency is
generally high. The high average effciency is the result of assuming that the units in the effcient
set are 100&#37; effcient. If this assumption is not valid, this results in an overestimation of the
efficiencies, which will be larger for a smaller number of units. Samples of various sizes are used
to find the related bias in the effciency estimation. The samples are drawn from a large scale
application of DEA to bank branch efficiency. The effects of different assumptions as to returns
to scale and the number of inputs and outputs are investigated.

Mohammad R. Alirezaee

Murray  Howland

Cornelis  van de Panne

Sampling size and efficiency bias in data envelopment analysis

With the passage of the Resource Conservation and Recovery Act (RCRA), and the
subsequent amendments to RCRA, efforts to provide tighter controls on the transportation and
disposal of hazardous waste have been steadily gaining ground. This paper, intended as a decision
support tool for regional planning, incorporates information on the hazardous waste generation,
treatment capacity and the costs of waste treatment alternatives into an optimization problem
of finding the relationship between governing agency and the toxic waste producing firms. As an
example, we consider the problem of regional hazardous waste in the San Francisco Bay Area in
Northern California.

Mahyar A. Amouzegar

Stephen E. Jacobsen

A decision support system for regional hazardous waste management alternatives

The formulas for calculating steady state results for the M/M/k queuing system are
well known. Computational difficulties, however, can arise in using these formulas in situations in
which the ratio of the arrival rate to the service rate is high. In this paper we consider a recursive
approach for calculating steady state results which avoid such computational difficulties. As an
additional benefit, such formulas are far easier to program into a spreadsheet package than the
traditional formulas presented in most management science texts.

Barry Alan Pasternack

Zvi  Drezner

Classroom Note: A note on calculating steady state results for an M/M/k queuing system when the ratio of the arrival rate to the service rate is large

In this paper, RL-diode circuit driven by a sinusoidal voltage is employed to obtain nonlinear experimental data. The BDS test statistic is used to analyse these data. According to
the results of the analysis for the first differenced order data, chaotic structure has been found for
each <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>e</mml:mtext></mml:math>
 values.

R.  Kasap

E.  Kurt

Technical Note: An investigation of chaos in the
RL-diode circuit using the BDS test

Two instances of the traveling salesman problem, on the same node set <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math>
but with different cost matrices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math>
 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>C</mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:math>
, are equivalent iff there exist <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>:</mml:mo><mml:mtext>&#x2009;</mml:mtext><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mtext>&#x2009;</mml:mtext><mml:mi>n</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math> such
that for any <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mi>i</mml:mi><mml:mo>, </mml:mo><mml:mi>j</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo>&#x2260;</mml:mo><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>C</mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math> [7]. One of the well-solved special cases
of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution
scheme for this class of TSP given in [9] to a more general class which is closed with respect to
the above equivalence relation. The cost matrix in our general class is a certain composition of
Kalmanson matrices. This gives a new, non-trivial solvable case of TSP.

Md. Fazle Baki

S. N. Kabadi

A generalization of the convex-hull-and-line traveling salesman problem

Although a large literature exists on the repair and deterioration of machines, the
associated problem of maintenance schedules for deteriorating renewable facilities has been little
studied. These facilities include all those which can be restored to a near-new state by renovation
or rebuilding, so that the market value and performance of the facility depends on the current
state of repair rather than on the time since initial construction. This paper solves the general
deterministic problem of finding the optimal repair strategy for a depreciating renewable facility.
It is shown that the value of the facility should approach the level where a function defined as
the "nett internal return" is greatest. If the facility has a finite life before sale or demolition, an
adjustment to repair strategies should be made as the facility approaches this time, increasing
repairs where this permits a better sale price to be obtained, or discontinuing repairs if they are
not justified by scrap or market value. Solutions for a range of common depreciation functions
and for linear and quadratic repair cost functions are obtained. The optimal life of the facility
is determined at the time when nett "external" marginal return, which includes potential capital
gain or loss and opportunity cost of capital, falls to zero.

Joe  Flood

Optimal investment strategies for renewable facilities

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