Knowledge that Transforms

Most serial bond issues are sold competitively on an NIC (net interest cost) basis. The municipality awards the issue to the bidder submitting the lowest NIC. Although it is often acknowledged that NIC is a defective measure of the interest cost and sometimes a costly one to the issuer, an alternative measure, the TIC (true interest cost, effective interest cost, interest cost according to the Canadian method, or the internal rate of return) is often regarded as too computationally difficult to employ. State and local governments are becoming increasingly aware of the internal rate of return or TIC as a measure of interest expense. The use of TIC as a method of awarding bond issues to underwriters is growing very rapidly. This paper contains a simple computer algorithm for calculating optimal bids on a TIC basis.

Most marketing planning models have carry-over effects in which one period's decisions influence the results obtained in future periods. In this paper it is shown that failure to allow for the carry-over effect beyond the planning horizon can result in underallocation of resources and in biases in the timing pattern of resource expenditure. For a wide class of market planning models, a procedure is developed to take into account this long-term effect. The distortion and the procedure are illustrated in an example.

This paper extends the field of heuristic algorithms for resource constrained scheduling problems in three important areas. First, an algorithm is introduced where the role of the heuristic scheduling urgency factor is expanded from one of solely determining the order in which activities are considered for scheduling at a given instant, to one of determining the combination of activities to be scheduled at this instant. Second, a new hybrid scheduling urgency factor capitalizing on the fact that this algorithm is sensitive to the absolute value rather than relative sequence of the urgency factors is introduced. Finally, a systematic approach to the evaluation of such algorithms is introduced. This includes the identification of relevant problem attributes and the adoption of evaluative concepts such as computational efficiency and analytic and systems effectiveness.

A model is developed that integrates capital investment decisions with output and pricing decisions for a situation of growing demand. Conditions are derived for the model that permit application of a general approach for determining the optimal sequence and timing of investments in a continuous-time framework. The behavior of optimal pricing and output decisions is characterized analytically. Specific results are given for a quadratic cost and revenue case, and an example illustrates the form of a solution. Possible extensions of the model are also discussed.

A fire department, in order to balance equitably its resources throughout a city, must consider several often conflicting objectives. This paper describes an allocation method that avoids the difficulty of choosing an objective in advance by allowing the decision-maker to enumerate a range of criteria by varying a trade-off parameter. The method uses travel time to fires as a measure of system performance and generates allocations satisfying criteria ranging from the minimization of city-wide travel time to the equalization of average travel times in different regions. A comparison of the allocations generated by the model to the current allocation of fire companies in New York City shows that one value of the trade-off parameter produces results that correspond closely to the current allocation policy. An example of how the model can be used as a policy tool is given.

This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e., maximization of quotients subject to constraints. In Part I a duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector, Craven-Mond, Jagannathan, Sharma-Swarup, et al. Basic duality theorems of linear, quadratic and convex programming are extended. In Part II Dinkelbach's algorithm solving fractional programs is considered. The rate of convergence as well as a priori and a posteriori error estimates are determined. In view of these results the stopping rule of the algorithm is changed. Also the starting rule is modified using duality as introduced in Part I. Furthermore a second algorithm is proposed. In contrast to Dinkelbach's procedure the rate of convergence is still controllable. Error estimates are obtained too.

This note identifies instances where nonlinearities may occur in the application of goal programming. An illustration is presented and implications discussed.

The problem of allocating customers of different types to various channels of a service system is considered. Service times are assumed to be independent identically distributed random variables whose distribution functions depend on the type of customers as well as the service channel. The total loading time of each channel consists of the sum of service times of all customers which were allocated to it and is thus a random variable also. If the loading time of a given channel exceeds (falls short) its nominal capacity, an overtime (idle time) penalty is incurred. Penalties are assumed to be proportional to the time lapse involved. There is also a revenue gain which is proportional to the number of customers served. The objective is to find the optimal allocation of customers to channels, x ij , such that the expected net gain, revenue minus losses, is maximized. It is shown that the distribution function of a loading time depends on the choice of the x ij and hence that, in general, no claims can be made with respect to desirable convexity properties of the objective function. It is further shown that if the service times are assumed to be normally distributed, then the objective function depends also on the means and the variances of the loading times. The mathematical properties of the program are utilized to ascertain that the solution obtained via a suggested algorithm is global. The nonlinear program is reduced to a (possibly iterative) solution of a linear program by using previous results obtained by the first author.

This paper concerns the analysis of two basic planning problems inherent in the building inspection operations of municipal fire prevention bureas. These problems are (1) how often to inspect each type occupancy in each area of the city, and (2) how to divide the city into “area-of-responsibility” districts, with one district for each inspector. The problems are interrelated and are represented in one model. Formulation of the model is based on the operations of the Atlanta, Georgia, Fire Prevention Bureau. The model constitutes a “controllable” analogue to the political redistricting problem. A solution procedure is presented which is a modification of the Hess and Weaver redistricting algorithm. Application of the model and solution procedure to Atlanta is given. Preliminary results indicate an improvement in districting over current practices.

Conventional PERT procedures frequently introduce undesirable and often indeterminant biases into the derived time statistics of large-scale complex projects. An alternative scheduling procedure BPERT is developed, employing an activity-based time estimation loss structure and a cost-minimization criterion. Bayesian point estimates are formulated for beta-distributed activity duration times minimizing the potential losses of misestimation. Viewed as certainty equivalents, these time estimates are then aggregated to yield a single project completion time. “Crashing” is introduced, and us implications for BPERT examined. An illustrative example contrasts PERT and BPERT.