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In this paper, we propose an integer quadratic optimization model to determine the optimal decision for a supplier selection problem. The decision is the optimal product volume that has to be purchased from each supplier so that the total cost is minimum and the constraints are satisfied. The cost function that we used is containing the purchasing cost, transportation cost, penalty cost for product that not satisfy the quality level, penalty cost for product that is late and the holding cost whereas the constraints are consisting of supplier capacity constraint, demand satisfying, supplier assignment, inventory management, and budget constraint. A numerical experiment with generated random data is given to illustrate how the supplier selection problem can be solved by using the proposed mathematical model. From the results, the optimum product volume from each suppliers was determined so that the total cost is minimum.

The design of a system with many locations, each with many items which may fail while in use, is considered. When items fail, they require repair; the particular type of repair being governed by a probability distribution. As repairs may be lengthy, spares are kept on hand to replace failed items. System ineffectiveness is measured by expected weighted shortages over all items and locations, in steady state. This can be reduced by either having more spares or shorter expected repair times. Design consists of a provisioning of the number of spares for each item, by location; and specifying the expected repair times for each type of repair, by item and location. The optimal design minimizes expected shortages within a budget constraint, which covers both (i) procurement of spares and (ii) procurement of equipment and manning levels for the repair facilities. All costs are assumed to be separable so that a Lagrangian approach is fruitful, yielding an implementable algorithm with outputs useful for sensitivity analysis. A numerical example is presented.

In a classical Debreu-economy the opportunities open to an agent do not depend on the transaction date; in a sequence economy they may. Moreover, in a Debreu-economy households may always be interpreted as facing a " present value " budget constraint; in a sequence economy this is not always possible. Roughly speaking I shall be defining an inessential sequence economy as one in which the sequence makes no difference to what we have already deduced about the equilibrium of a Debreu-economy. I shall show that only such economies can be Pareto-efficient relative to a transactions technology and distribution of endowments amongst households. But there are also non-inessential sequence economies. This leads me to money and forward markets in money. I deal with the question: " why do agents hold money? " in a crude way, and comment on other ways, i.e. that of Grandmont and Younes [1, 2]. I show that no sequence economy in equilibrium with borrowing and lending of money can be efficient if such borrowing and lending is costly; I shall comment on the robustness of these conclusions. It will become plain that since the classical dichotomy can only fail to hold for economies with sequences which are not inessential this dichotomy seems to imply that monetary equilibria of this kind are inefficient. I start with a recapitulation of an earlier paper from which this one takes its point of departure although before that I provide the notation to be used which I hope improves on the very bad one in [3]. I then construct a sequence economy and a Debreu-economy without money so as to be able to define inessentiality, about which certain theorems are proved. I then discuss efficiency. Lastly the two economies are modified to allow for money and some of the claims made above are substantiated.

This paper develops a theoretical model in which the individual state is viewed as attempting to maximize revenue collections from residents of other states for some given budget constraint. Implic...

Budget or manpower constraints may force a reduction in data collection activities. However, information may be transferred from continued gauge sites to discontinued gauge sites provided there is ‘sufficient’ correlation between flow sequences. Information defined as the reciprocal of variance (of the parameter estimator for which the gauge has been established) is provided at ungauged sites by regression techniques. A set of gauge sites is chosen to satisfy the budget constraint and to maximize the information content. The information content based on regression is a function of the correlations between flow sequences and is subject to the errors in their estimators. Post optimal analysis gives estimates of correlation error effects on the decision process as to which gauges to continue and which to discontinue.

SUMMARY The aim of this paper has been to explore the variation in the distance between the residence and work locations of industrial workers. This distance has been theoretically and empirically related to the income, number of dependents, marital status, sex, and age of workers whose job site was located in the centre of the city. A multiple regression model has shown the over-all importance of the budget constraint as a factor in the residential location decision relative to the job site. Of the variables included in the analysis, the wage rate of the worker is the strongest determinant of the location decision. Although workers who have the same budget constraint show weak locational relationships with the job site relative to the number of dependents and marital status, as suggested by the model, the only strong difference in spatial location occurs when the budget constraint is allowed to vary. Once workers have the means to increase their over-all utility level, they do trade off journey-to-work disutilities for residential facilities farther from the central city job site. But the social conditions of the worker tend to influence the residence-to-work distance only slightly when considered apart from the influence they may have on the wage rate. The over-all dependence of the journey-to-work distance on these variables in this setting hence was small, reaching an R value of only 0.38.

Publisher Summary This chapter discusses inefficiency and the demand for money in a sequence economy. Transaction costs represent the scarce resources used in transferring goods among agents. Even on spot markets, trade is a resource-using activity. Merely incurring such costs is no evidence of inefficiency. Efficiency will usually require reallocation; reallocation is resource-using. Inefficiency arises when such costs are incurred unnecessarily. The solution of the inefficiency is somehow to sever the temporal link between commodity buying and selling transactions while continuing to fulfill the sequential budget constraint. Money is defined as a commodity of positive price and zero transaction cost that does not directly enter in production or consumption. Rather than engage in costly futures trades to achieve budget balance at each trading date, traders use trade in money to bridge the gap in timing between desired sales and purchases. The assumption of zero money transaction cost is of course extreme but it captures the essential point: a major cost reduction relative to commodity trade.

An attempt is made to explore the production set for educational achievement for both “efficient” and “inefficient” schools. The inefficient or average production relationship is obtained by estimating a reduced-form equation for all schools among a sample drawn from a large Eastern city. The efficient set is derived by using a linear programming approach to yield coefficients for those schools that show the largest student achievement output relative to their resource inputs. A comparison of the two sets of technical coefficients suggests that the relative marginal products are probably different. Because of such differences, the optimal combination of inputs for producing educational achievement relative to a given budget constraint will probably vary between achievement-efficient and inefficient schools, and may even vary from school to school. The result is that the use of such production-function estimates for attempting to improve the efficiency of the educational sector may have far less utility than its advocates imply.

Most inventory formulations seek to minimize the sum of ordering costs, holding costs, and stockout costs: however, management often directs inventory policy by specifying a maximum investment level and/or a purchasing budget constraint. Within these limitations, they expect lower level managers to optimize some level of customer satisfaction, such as minimum stockouts or minimum shortages. The author has developed several cases of these “managerial” inventory formulations and has presented some computational results.

This paper develops an analytic model that evaluates the expected number of aircraft not operationally ready at a random point in time because of supply (NORS). The model was developed for application to the F-111 aircraft for a multilevel problem, where demand on a first-level line replaceable unit (LRU) eventually causes second-level demands for one or more modules that are components of the LRU. The model is for a single base. Since it is evaluative in nature, the inputs include item stock levels as well as item demand rates, average repair times, and resupply times. An optimization model to determine stock levels that minimize the number of NORS aircraft subject to a budget constraint would be preferable to the evaluation model. The paper shows, however, that an optimization model is not mathematically tractable because the criterion function is not separable into independent item calculations. But an example using F-111 data indicates that if the METRIC model [see Opns. Res. 16, 122–141 (1968)] is used to optimize stock levels, the resulting number of aircraft NORS is within 1 percent of the minimum number of aircraft achievable with the same budget. Finally, the well-known formula of Erlang for the M/G/s service system with no queue allowed is generalized to the case where demand rates and repair rates may be a function of the number of units already in repair. This enables us to examine the sensitivity of the optimal allocation of budget across a group of items when expediting may take place. Though expediting improves system performance, the conclusion is that the optimal allocation is virtually the same as the METRIC allocation.

Conventional benefit-cost guidelines are erroneous, owing to their failure to recognize the realities of policy making. From appropriate consideration of budgetary constraints, the interdependence of projects, and the influence of project selection on future budgets the conclusion is that project selection should not follow crude rules of thumb, such as the order of project benefit-cost ratios. By means of a dynamic Lagrangian multiplier model the maximum economic advantage principle for the political context is derived. This principle implies that an optimal project schedule does not require that all marginal benefit-cost ratios be equal. For example, if a project increases the economic desirability of other projects, its own economic value increases. Moreover, a project increasing future budgetary allocations takes on increased economic desirability, since one of the project benefits equals the sum of the increased budgetary allotments, as weighted by the appropriate budgetary shadow premiums.

Many problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maxirnands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.

Presents a simple model whose objective is to utilize existing and ongoing survey data in order to allow the advertising manager to segment the market in an optimum way. Shows how segmenting the market in such a way maximizes the budgetary constraints of the advertising manager.

In application of operations research models in the area of logistics, important constraints are typically encountered in the form of limitations on the funds appropriated. A supply system must be operated within whatever budgeted funds are appropriated by Congress. In the present article, various possible types of budget constraints are discussed as well as their impact on certain types of operations research models. The possible misallocations that can result from the setting of specific budgets designated for particular purposes are discussed. The confusion existing in the literature concerning the type of constraints that are actually encountered versus those that are imposed upon the mathematical models is pointed out as well as the typical inconsistency of budget constraints and steady-state models. The difference between a steady-state budget and a transition-phase budget is clarified.

The author discusses computer oriented mathematical models for the simultaneous selection of the number and location of fire engines and stations. The discussion also considers multiple engine response and distance and budget constraints as well as operational problems, such as closing or relocating existing stations.

Suppose that an investing firm is primarily interested in achieving a specified minimum return critical to its economic survival. Then it seems appropriate to maximize the probability of exceeding the aspiration level. This decision criterion will be applied in the context of several stochastic static investment models with budget constraint. As long as the aspiration level does not exceed the maximum expected return achievable with the given budget, the desired investment strategy must be sought among the efficient solutions in the Markowitz sense. For higher aspiration levels this is no longer true. For the special case of the Markowitz model we show that all investment projects with expected yield not exceeding the aspiration level (of yield) should be rejected. This is a surprising confirmation of a well-known deterministic rule of investment theory and practice in a rather different context.

A system is defined whereby there are N p subsystems in passive redundancy, and each subsystem has N A components in active redundancy. The mean time to failure is derived under the assumption of independent failure time, and this is used as a measure of system effectiveness. A budget constraint limits the number of components and switches which may be used to construct a system. This paper finds the maximum mean time to failure for different values of the budget parameters.

A TECHNIQUE of cost-benefit analysis that attempts to provide a criterion for making public investment decisions must take into account both the social opportunity cost of the funds used in the public programme and society's 'social time preference'. In this paper we present an investment decision algorithm that satisfies this requirement. In addition, the method possesses several other useful properties that have not been included in previous cost-benefit models. The Net Social Benefit (NSB) of a particular project is the value at the time of the decision-making of the net addition to consumption that would result from undertaking the project. The NSB value can be used to decide whether or not a particular project is worth doing, to select among mutually incompatible projects, and to evaluate the desirability of postponing all or part of the expenditure. It is directly applicable in the absence of budgetary constraints and can also be used when a capital or budgetary constraint is imposed. The social opportunity cost (SOC) of funds is allowed for directly. This is done by calculating the current value of all the consumption that is foregone because of the resources which the government transfers from the private sector during the life of the project. The important effects of the direct and indirect reductions of private investment are explicitly recognized.2 Inter-temporal comparisons of social benefits and costs are made by using a social-time-preference (STP) discount rate-a normative 'interest' rate that represents government policy with respect to the relative desirability of consumption at different times. Because all costs and benefits are converted into equivalent increases and decreases of consumption, this STP rate can be applied directly. Of course, the STP

The competitive planning exercise described in this article involves simplifying the real world so as to highlight the basic elements of a planning system and demonstrate their role in a manager's decision. A coherent and practical scheme is developed that takes account of the various elements of planning such as technological forecasting, value and cost assessment, budget constraints, and scheduling under uncertainty.

The purpose of this paper is to explain the relation between multiobjective planning of public investment programs and the use of budget constraints, because this important matter is normally not considered in governmental proposals of new planning methods. The multiobjective approach to planning includes: (1) identification of the several objectives of the public organization for which the plans are being made; (2) for each objective development of metrics of its benefits and costs; and (3) design of alternative programs that emphasize alternative combinations of objectives as a means of showing how governmental and private actions can contribute to objectives. In a formal sense a budget constraint is a limit on the total expenditure that can be made for a project or program; and if the constraint is binding, it affects the design of the project or program.

A pollution damage function is developed, using data from a study on the sensitivity of morbidity to ambient air concentrations of individual pollutants. This function is used in a model which incorporates the costs and technology for pollution abatement in the St. Louis Airshed. A set of air quality standards is determined which minimizes morbidity subject to a given control budget constraint. The results indicate that there should be a greater reduction of the pollutants associated with stationary sources than of those characteristic of the automobile.

Those responsible for the assessment of management training programs must answer the questions: Can the demands for measurement and experimental rigor and practical budgetary constraints be simulta...

Consumers have the freedom to determine the type and quality of the goods/services in accordance with their needs. Food safety, quality problems and the impact of irregularities, as well as the strengths, weaknesses, opportunities and threats in the development of food industry quality system is a shared responsibility as the consumer protection efforts. The method in this research using qualitative methods. The research results showed that consumer protection conducted by government agencies and other institutions in the following way i.e. perform monitoring of food products by giving the number of the PIRT against businessmen who are qualified and have previously received counseling about the food products that may be released, as well as to provide warning and withdrawal of products that contain a positive dye textiles. The efforts made by the North Buton Regency POM Halls namely collaborates with government agencies and Institutions Consumers North Buton Regency to do surveillance, sampling and testing, guidance products. Trade a proven violation reported to the District Health Office of North Buton for follow up. Restricting factors for the Government and Consumers North Buton Regency in coping with a circulation of foods that contain colouring substances in textiles, namely budget constraints to organise activities agenda so that there are no activities were carried out, bureaucratic system which is still so convoluted follow-up to businessmen.

Dynamic programming algorithms are developed for optimal capital allocation subject to budget constraints. We extend the work of Weingartner [Weingartner, H. M. 1966. Capital budgeting of interrelated projects: Survey and synthesis. Management Sci. 12(7, March) 485–516.] and Weingartner and Ness [Weingartner, H. M., D. N. Ness. 1967. Methods for the solution of the multi-dimensional 0/1 knapsack problem. Oper. Res. 15(1, January–February) 83–108.] by including multilevel projects, reinvesting returns, borrowing and lending, capital deferrals, and project interactions. We are able to handle dynamic programming models with several state variables because the optimal returns are monotone non-decreasing step functions. Computational experience with a variety of problems is reported.

A mathematical model has been developed for the purpose of assisting R&D management in their evaluation and selection responsibilities of potential R&D projects. It is composed of (1) a project evaluation module that utilizes the concept of discounted cash flow to reduce the measures of each project to a single economic index (the expected net present value) and (2) a project selection module that utilizes a linear programming algorithm with 0-1 variables to select the set of projects that maximizes the total expected net present value, while satisfying specified budget constraints. The system, having been implemented through a time-sharing computer service, is presently operational and is being used by management as a tool to assist in the R&D decision-making process.

The question of how the well-known Neyman stratified allocation result generalizes when it is formally assumed that there is prior information concerning the unknown stratum means is dealt with here. This prior information is taken to be expressible in the form of a multivariate normal prior distribution. Several methods of assessing prior distributions are discussed. The allocation for stratified sampling is shown to be a special case of a more general allocation problem. A computational algorithm is presented for this more general problem of finding the allocation of sampling effort which minimizes the posterior variance of any given linear combination of unknown normal process means subject to a budget constraint. A feature of the solution is that for limited budgets one may rely solely on his prior information concerning some strata, sampling only in a subset of the strata. Finally, several applications are briefly described including a “non-Bayesian” solution to a particular problem of alloc...

Mansfield's Section 203 has triggered a searching review by DOD of its research. Using the general budget constraints of the past few years as an effective springboard, Mansfield went on to question and then challenge all of the federal government's policies for R & D. The entire post-World War II institutional machinery and rhetoric for R & D are now in some disarray and, thus, are open to imaginative, constructive change. Mission-oriented R & D, still central to progress toward our national goals, must be comprehensively rethought in order to restore the public confidence necessary for adequate support of science and technology.

Quarmby D. A. (1970) Estimating the transport value of a Barrage across Morecambe Bay, Reg. Studies 4, 205–239. The paper describes an attempt to estimate the net transport value of a road built on top of a Morecambe Bay Barrage whose primary purpose would be water supply. The basic method involved a traffic model to simulate vehicle movements on the road network in the area, and an economic evaluation procedure to measure benefits arising from changes in the network. Problems included the strong dependence of benefits to the Barrage road on the possible existence of other projects such as the Arnside Link and the Duddon Estuary crossing (and vice versa), and the budget constraint on road building in the Ministry of Transport which has the effect of raising the criteria for road projects above those normally required for other public sector investments. The effects of tolls were also studied.

IN A RECENT PAPER, QUANDT AND BAUMOL HAVE SUGGESTED THAT THE DEMAND FOR TRAVELLING BY AIR, BUS, AUTO AND RAILROAD MAY BE CONSIDERED AS DETERMINED BY THE SAME DEMAND FUNCTION IF SUCH A FUNCTION IS APPROPRIATELY FORMULATED. THE MODELS BASED ON THIS HYPOTHESIS IN GENERAL SPECIFY THAT THE NUMBER OF TRIPS MAY BE EXPLAINED BY MODAL CHARACTERISTICS OF VARIOUS TRANSPORTATION FACILITIES SUCH AS JOURNEY TIME, MONEY COST AND DEPARTURE FREQUENCY AS WELL AS SOME SOCIO- ECONOMIC CHARACTERISTICS AT THE ORIGIN AND THE DESTINATION SUCH AS POPULATION AND INCOME. THE MAJOR ADVANTAGE OF THESE MODELS, KNOWN AS "THE ABSTRACT MODE MODELS", IS THEIR POTENTIAL FORECASTING ABILITY FOR ANY NEW MODE OF TRANSPORTATION FACILITY. THE PRESENT PAPER PRESENTS A FORMAL DISCUSSION OF THE THEORETICAL FOUNDATION OF SUCH AN ABSTRACT MODE APPROACH. IT HAS BEEN SHOWN THAT THE DEMAND FUNCTION AS SPECIFIED BY THE ABSTRACT MODE MODELS CAN BE DERIVED FROM THE UTILITY FUNCTION IF A CONSUMER IS SUPPOSED TO ACT AS IF HE WERE MAXIMIZING THE UTILITY FUNCTION SUBJECT TO THE USUAL BUDGET CONSTRAINT AND THE ADDITIONAL COMMODITY CONSTRAINTS WHICH DEFINE THE FEASIBLE COMBINATIONS OF MODAL CHARACTERISTICS. THE MAJOR PURPOSE OF THE PRESENT PAPER IS TO EXAMINE HOW THE ABSTRACT MODE MODELS OF THE DEMAND FOR TRAVEL CAN BE APPROPRIATELY FORMULATED. FOR EMPIRICAL ANALYSIS, A LOG-LINEAR FORMULATION AND A NON-LINEAR FORMULATION HAVE BEEN PROPOSED. SEVERAL VERSIONS OF EACH OF THESE TWO MODELS HAVE BEEN ESTIMATED BY UTILIZING THE CROSS- SECTION DATA COLLECTED FOR THE NORTHEAST CORRIDOR OF THE UNITED STATES. THE POSSIBILITY OF IMPROVING THE EFFICIENCY OF THE ESTIMATION THROUGH AN APPLICATION OF THE GENERALIZED LEAST-SQUARES PROCEDURE IS ALSO EXAMINED BY CONSIDERING A MODEL WITH CORRELATED ERROR TERMS. IT HAS BEEN SHOWN THAT, UNDER THIS MORE GENERAL MODEL, THE ORDINARY LEAST-SQUARES ESTIMATES ARE STILL ASYMPTOTICALLY EFFICIENT. THE EMPIRICAL RESULTS PRESENTED ARE BASED ON SUCH A RELATIVELY SIMPLE PROCEDURE. IN GENERAL, BOTH THE LOG-LINEAR MODEL AND THE NON-LINEAR MODEL FORMULATED PROVIDE VERY SATISFACTORY EMPIRICAL RESULTS. /TR/

The general aim of this paper is to determine to what extent micro-economic models of consumer behaviour can contribute to the understanding of the fundamental nature of the travel decisions of individuals in the consumptive sphere. Travel requires consumption of goods (and/or services) and of time. Therefore, the models of this paper take explicitly into account the problem of the allocation of travel time among the various activities which enter into the utility function of the consumer. The consumer is considered as a ‘production unit’ of consumption activities which require two types of inputs: goods (or services) and time. Hence, he maximizes his utility function under two constraints: a budget constraint and a time constraint. A fundamental innovation of the models of this paper is that they make a distinction between the utility of time as an input in the production of a given consumption activity and the (dis)satisfaction which results from the circumstances under which the time required to produce that given activity must be spent. Although the models developed here may provide information on the three main travel decisions of individuals (trip production, trip distribution and modal choice), we shall focus on the information they yield about the nature of modal choice and its determinants. Therefore, an important objective of this paper is to determine the possible contribution of micro-economic theory to our knowledge on the value of travel time savings.

This paper presents a dynamic theory of price, output, working capital and interest for the firm and industry. It yields many of the standard properties of the firm and industry at equilibrium, and in addition, a new microeconomic theory of growth, decay and business cycles. This is achieved by adding a working capital or budget constraint to the conventional atomistic single product firm and assuming a one period input-output lag. The theory leads to a simple but instructive example of a new mathematical system called recursive programming that represents ex ante optimizing while at the same time exhibiting ex post nonoptimality under certain conditions.

Consumer choice theory is normally based on the assumption that the domain of commodity mixes which can be chosen is continuously divisible (dense). The effects on consumer choice behavior recently attributed by Harwitz to indivisibilities are shown to be due to the removal of strong convexity and strict monotonicity from the expressed binary preference properties. A binary preference axiomatic treatment is presented which is applicable in the presence of indivisibilities. Tolerance to indivisibilities in the decision domain is accomplished with three binary preference axioms which are sufficient to assure the existence of a utility function. One axiom is added for the budget constraint and another to cover the expenditure minimization concept of rational behavior. With these five axioms, Samuelson's weak axiom and fundamental theorem of consumer behavior can be extended to be applicable with indivisibilities in the decision domain.

This paper considers a one-period multi-item inventory model where the objective is to minimize a function of item backorders subject to a budget constraint. Two functions are considered: the sum of expected item backorders and an expected joint backorder criterion. A main result is a proof that the joint backorder criterion is convex for arbitrary, twice-differentiable demand distributions. The rest of the paper is devoted to comparing the solutions one obtains with the two criterion functions.

El presente artículo tiene la intención de posicionar la Formación de Investigadores Educativos (FIE) como eje principal para la realización de Investigación Educativa (IE) en Chiapas, puesto que ésta es una de las líneas con menor producción de conocimiento en el campo educativo, lo cual se comprueba con la revisión actual de su estado del arte (2003-2016). Con base en las categorías “prestigio educativo” y “oferta de doctorados formadores en IE”, se analizaron los procesos de cuatro universidades de la entidad (tres privadas y una pública) sobre los que se aleccionan a los futuros investigadores en educación, así como la postura que sus egresados han construido de dichos procesos. Para ello se contó con una muestra voluntaria de 40 estudiantes y 20 egresados y, con base en los resultados obtenidos, se puede concluir que la oferta privada de posgrados responde más a los modelos económicos globales (mercantilización educativa) que al interés por desarrollar capital humano de alto nivel como lo define el discurso político oficial mexicano; mientras que, para el sector público, se preveía un 2017 lleno de recortes presupuestales que tienen como objetivo descentralizar estos niveles formativos al pecunio de los interesados.

The model developed by Floyd (1965) to show the effects of farm price supports on the returns to the factors in farming is based on widely accepted assumptions and could be applied to a wide range of economic problems. However, the model is overdetermined, and Floyd's solutions are incorrect. Floyd attempted to solve his model with nominal prices, thereby introducing "money illusion" in a set of relationships which may be depicted by a two-space isoquant map where the slope of a linear budget constraint is a relative (real) price. I will demonstrate that the model is overdetermined by solving the five-equation system with four of the equations. I then briefly discuss the inconsistencies in Floyd's solutions. My alternative model reduces the elasticities Floyd sought to the reciprocal of the relative factor shares and allows estimates of the long-run supply of farm output using the parameters from Floyd's article.

Dynamic transport planning refers to the analysis of the problem of choice of implementation date of the construction or improvement of transport facilities. This analysis may also include consideration of stage construction or progressive improvements in quality and/or capacity over time, beginning from some relatively low standard. A transport facility is defined as a vehicle (e.g., automobile, airplane) or a supporting facility (e.g., highway, port). There appears at present to be a serious lack of any truly comprehensive evaluation of the essentials of the problem of choice of implementation date. It is the intent of the ensuing presentation to help to rectify that situation by introducing new concepts which structure the timing problem. The concepts are based on a suggested classification of future traffic and definitions of independent and indivisible facilities. In addition, volume of traffic and benefits of a transport facility are recognized to be dependent on calendar time and the facility's age. Presently, no uniform theoretical framework exists for establishing the optimal time for constructing new facilities or improving existing ones. A framework based on the aforementioned concepts is introduced. It distinguishes between the phasing of projects through time in the absence of budget constraints and this phasing in the presence of such restrictions. The specific procedures suggested in this paper for the analysis of the problem of choice of implementation date apply to any individual transport facility and tend to unify the concepts involved in dynamic transport planning. The article concludes with a survey of current approaches to dynamic transport planning and discusses these in the light of the above framework.

It is clear that a demand function derived from an agent’s preference preordering cannot be completely arbitrary . For instance it has to reflect the transitivity of the preference preordering . As our interest is not in individual but in aggregate demand , we are much more interested in characterizing excess demand functions of an economy rather than individual demand functions . One might conjecture that restrictions on individual demand play little or no role after aggregation in a large economy if no particular assumptions are made on the nature of the economy as a whole. If this is so , then the set of equilibria of an economy merely has some general mathematical properties and many finite sets may occur as sets of equilibria . In particular , one would expect that there is no bound for the number of equilibria of an economy . The first attack on this problem was made by Sonnenschein (1972) 1). We are now going to report on the procedure and main results of Sonnenschein (1972) .

Advertising is suspected of being in excess of both its social and commercial optimum level. Profit-maximising businessmen have no reason to carry the activity beyond the point where the last pound spent on advertising brings in exactly one pound more of net revenue. Yet the late Lord Leverhulme’s statement suggests that they do exceed this point. Why should this be? How do businessmen decide on their advertising budget levels? How do they allocate their budget among the various media available? This chapter is concerned with providing answers to these questions.

A surveillance system for a given number of effluents, each with certain contaminants, is considered. An effluent can be sampled to determine whether any of the contaminants exceeds its standard, in which case a violation is said to have been detected. Damage costs are associated only with undetected violations. These costs depend upon pollutant loadings, the nature of the pollutants, and the assimilative capacity of the receiving water. The objective is the following: find the sampling frequencies for each effluent (during a certain monitoring period) such as to minimize the total cost of the undetected violations. This is to be done subject to a certain budget constraint for the monitoring period. The cost of an undetected violation is defined as the expected value of the damage. These expectations are evaluated using the statistical knowledge available prior to the beginning of the monitoring period. The statistics of the contaminants are updated at the end of each monitoring period. It is shown that a very simple optimization procedure, namely, the maximum marginal return method, can be used to obtain the optimal sampling frequencies.

This paper extends the theory of optimal taxation and government production to open economies. Appropriate rules for project evaluation and the determination of consumption, production, and trade taxes under a variety of restrictions (e.g., less than 100 percent profit taxes, government budget constraint, foreign exchange constraint) are derived. Among the results are (a) international prices should be used for evaluating public projects, unless there is a government budgetary constraint or there is a quota (this result does not require that tariff rates be optimally chosen); (b) no tariff should be levied on intermediates and only consumption taxes should be employed if there are 100 percent profit taxes. If profits are not taxed at 100 percent, both consumption and trade taxes should be employed.

Following implementation of optimal regression and interdependence analysis, the authors noted that the general algorithm could also be used to solve the optimal network problem which may be stated simply as follows: given n transportation nodes (cities, stations, or points to be served) and the set of n(n − 1)/2 direct, non-directional links joining all pairs of nodes, select the subset of links that minimizes the sum of shortest path distances between all pairs of nodes, subject to a budget constraint on the total link length. This application extended the original algorithm of Beale et al. (1967) in two ways. First, the size constraint (number of variables) is generalized to a linear constraint (total length of network). Second, the algorithm is applied to a potentially larger tree-search problem outside the field of statistics; however, Beale (1970) also described the application of the algorithm to a plant location problem.

It is Wicksteed who first pointed out the ‘fascinating’ analogy between the laws of satisfaction and those of production.1 A trivial idea by now, the formal identity between consumption and production theory comes from the fact that in both cases the main problem is one of maximizing an ordinary function of several independent variables subject to a budget constraint.

Emergent readers enjoy and benefit from reading age appropriate information books, and there are many books published for this cohort. However, the few studies conducted on access suggest that opportunities to find these books are limited. Early reading instruction usually favours fiction, while school library collections may be limited due to budget constraints. Retail selection is poor, and few awards recognize this genre. Public library access may be compromised due to budget issues, library design, fiction in displays, and parental behaviour. More research to clarify issues regarding access is needed to improve young children’s opportunities to find information books.

THE ACCUMULATION of personal wealth is a process that involves two decision elements: choice of the amount to be saved (investment scale) and choice of assets in which savings are to be held (investment mix). Although each of these has received considerable attention in the literature, they are typically treated separately and statically. Portfolio-selection models, for example, normally assume that the amount to be invested is given; time-preference models, at the same time, usually specify a given and certain investment-opportunity schedule. This implies independence of the distributions of scale and mix outcomes over time. It also suggests that personal utility functions should be described separately with respect to time and risk preferences. Separate treatment of relevant determinants provides a limited description of the wealth-accumulation process. This study attempts to conceptualize and construct an integrated decision model, one which accommodates the scale and mix decisions simultaneously and dynamically. The general model proposed consists of a set of algebraic statements describing the financial and personal environment facing an individual investor. Functional relationships to be specified include consumption preference and expected values of salary, rate of return on investment, taxes and the initial wealth position. Any of these can be defined as randomly distributed. The Monte Carlo method is then employed to trace interim and terminal wealth positions over the life cycle of the investor. Successive iteration generates a distribution of wealth positions for each scale-mix combination at each desired observation point over the life cycle. The generalized model described above is flexible, and it can be applied to a number of relevant questions facing individual investors. To cite one example, the wealth effect of alternative life-insurance programs can be evaluated. Timing considerations can also be accommodated; the minimum level of expenditure required to educate one's children may be used to constrain acceptable interim wealth positions. The estimation of return on human investment is another promising area for experimentation, since the costs and benefits of educational and professional activity can be defined as part of the structure of any particular model. For purposes of this study, a hypothetical investor was defined, and a computer program was designed and operated to test the feasibility of the model. Since the assumed environment is not considered to be excessively unrealistic, model outcomes were also subjected to a sensitivity analysis in an attempt to assess the relative significance of each of the decision variables. Salary patterns and consumption propensities were allowed to vary, and the investor was viewed as attempting to maximize wealth within the living standard imposed by his budget constraint. A two-parameter portfolio set was assumed, and parameters were estimated empirically by employing the Sharpe diagonal model. Federal taxes were computed on the basis of existing regulations. The experimental outcomes have relevance, properly speaking, only for the model's hypothetical investor. Nevertheless, some findings have implications of more general in

T I HE effect of coinsurance on the demand for medical services has been debated for many years. Some assert that it helps control total expenditures by giving consumers a stake in how much medical care is purchased. Others assert that coinsurance is irrelevant to choice, since the physician makes the decisions about using medical services for his patients. Persons attempting to predict expenditures under various national health insurance plans are naturally interested in how coinsurance affects demand for services. The evidence we present in this paper decisively rejects the assertion that coinsurance is irrelevant to choice; coinsurance clearly does affect the demand for services. Moreover, as we shall show, the impact of coinsurance varies across medical services in a systematic fashion depending upon the time price of the service. In a longer,more detailedversion of this paper (Phelps and Newhouse 1973) we have derived expressions relating the responsiveness of demand for medical care services to coinsurance, market prices for medical care, and time costs. In the remainder of this section we sketch the assumptions underlying those derivations. We assume that consumers maximize a utility function in "other goods" (x) and health status (H) subject to a budget constraint. Medical care (h) is a homogeneous commodity that can be purchased in the market at a price of p per unit, and x can be purchased at a price of one per unit. There is a production function for H which uses h and time inputs (t). Denote the opportunity cost for time as w per unit of time, and let T be the amount of productive time available to the person. T To-th, where To is total time available and is fixed. The consumer's level of health is considered random. This induces him to purchase insurance. The insurance contract specifies a coinsurance rate -the consumer pays C per cent and the insurer pays (100-C) per cent of all incurred expenses during the period. We are not concerned here with the selection of C (Phelps 1973), but how the consumer reacts to a random loss, given his insurance policy. Assume that C has been previously chosen, or is imposed; in either event, C is fixed, and the premium (or tax) is prepaid. The total price is then the sum of the money price per unit C p and the time-price w t per unit