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This paper analyses the search-based advertising problem from an advertiser’s view point, and proposes optimal bid prices for a set of keywords targeted for the advertising campaign. The advertiser...

Since highway improvement project selection requires screening thousands of road segments with respect to crashes for further analysis and final project selection, we provide a two-step project selection methodology and describe an application case to demonstrate its advantages. In the first step of the proposed methodology, we will use odds against observing a given crash count, injury count, run-off road count and so on as measures of risk and a multi-criteria pre-selection technique with the objective to decrease the number of prospective improvement locations. In the second step, the final project selection is accomplished based on a composite efficiency measure of estimated cost, benefit and hazard assessment (odds) under budget constraints. To demonstrate the two-step methodology, we will analyze 4 years of accident data at 23 000 locations where the final projects are selected out of several hundred of potential locations.

Competitive facility location models consider two main strategies for increasing the market share captured by a chain subject to a budget constraint. One strategy is the improvement of existing facilities. The second strategy is the construction of new facilities. In this paper we analyse these two strategies as well as the joint strategy which is a combination of the two. All three strategies are formulated as a unified model. The best solution to an individual strategy is a feasible solution to the joint one. Therefore, the joint strategy must yield solutions that are at least as good as the solutions to each of the individual strategies. Based on the results of extensive experiments, we conclude that the increase in market share captured by a chain when the joint strategy is employed can be significantly higher than increases obtained by individual strategies. A branch and bound procedure and a tabu search heuristic are constructed for the solution of the unified model. Both algorithms performed very well on a set of test problems with up to 900 demand points. A total of 62% of the test problems were optimally solved by the branch and bound procedure.

In this paper, we consider the location of a new obnoxious facility that serves only a certain proportion of the demand. Each demand point can be bought by the developer at a given price. An expropriation budget is given. Demand points closest to the facility are expropriated within the given budget. The objective is to maximize the distance to the closest point not expropriated. The problem is formulated and polynomial algorithms are proposed for its solution both on the plane and on a network.

This paper deals with a multi-item newsvendor problem subject to a budget constraint on the total value of the replenishment quantities. Fixed costs for non-zero replenishments have been explicitly considered. Dynamic programming procedures are presented for two situations: (i) where the end item demand distributions are assumed known (illustrated for the case of normally distributed demand) and (ii) a distribution free approach where only the first two moments of the distributions are assumed known. In addition, simple and efficient heuristic algorithms have been developed. Computational experiments show that the performance of the heuristics are excellent based on a set of test problems.

Existing customer preference based product design models do not consider product prices and consumer budgets. These models assume that a purchase is based only on the satisfaction obtained from the product, irrespective of the product price and customer budget. However, when products are expensive relative to buyers' budgets, the effect of prices and budgets must be considered in addition to customer satisfaction. Most current models, moreover, assume that a low preference for one product characteristic is compensated by high preference for another, which may not hold for unacceptable levels of characteristics. For such products, we incorporate prices, budget constraints, and minimum acceptable thresholds in our model. To solve the model we develop a highly accurate, robust and efficient Beam Search (BS) based heuristic that identifies optimal or near optimal product lines. The heuristic is tested on 300 simulated problems and an application. It is also compared to a Genetic Algorithms (GA) based heuristic. We found that our heuristic worked better than the GA heuristic in identifying optimal and near optimal solutions quickly. We also give detailed examples that illustrate the heuristic and demonstrate a pricing analysis application of the model.

The object of this paper is to show how to maximize the expected response of an advertising campaign, subject to a budget constraint. Four response functions are considered with closed-form solutions given for the resulting expected responses. These expected responses use only univariate marginal distributions and pairwise duplications, so they can be rapidly calculated compared with the usual cumbersome calculation based on the full frequency distribution. A simple heuristic solution to the formulated non-linear integer programming problem is given, resulting in big savings in computation time over the branch-and-bound technique, for example.

Multi-level inventory problems provide the opportunity for operations researchers to assert simultaneous control over entire distribution and production systems. A backorders minimization problem is considered for a particular multi-level inventory structure for which several finished goods with normally distributed demand are produced from a common component. Complete centralization of all inventory at the component level versus complete decentralization of all inventory to the finished-good level has previously been studied. Inventory may be stored at either level in this approach. A general, non-linear mathematical formulation with the objective of minimizing total penalty costs for expected backorders and a budget constraint upon holding costs is considered to determine amounts to stock at each point. Necessary conditions for optimality are derived and are shown to resemble closely the classical newsboy result for which a proper trade-off must be achieved between the consequences of too much and too little inventory.

A model is developed for planning the acquisition and disposal of equipment in a transport fleet. It deals specifically with the composition over time of a commercial airline fleet but is generally applicable to any problem of fleet planning under conditions of technological change with budgetary constraints on interrelated projects and dealing with items which deteriorate with use. A number of previous models are examined, each of which deals separately with a different element of the problem, and by analysis of the theoretical background to some of these a realistic but still viable model is developed. The size and composition over time of a fleet is considered as a set of interrelated capital investment projects subject to demand, availability, budgetary and technological constraints. A simple numerical illustration is formulated and solved and the solution discussed.

This paper considers an optimal control problem for the dynamics of the Nerlove-Arrow advertising model, the optimal control being the rate of advertising expenditure required to maximize the present value of net profit streams (or, sales) over a finite horizon subject to a budget constraint. The maximum available advertising budget is given in present-value terms. It is shown that a singular level of advertising exists and that it is smaller than the singular or optimal stationary level obtained by Nerlove and Arrow. Along with the forms of the optimal control in all possible cases, two simple computational algorithms are also provided to obtain the optimal path including the end-game situation as a result of the finite horizon. Closed-form solutions are worked out for simple examples illustrating the use of the algorithm. An analogy with a car with a given amount of fuel (budget) concludes the paper.

A 0-1 integer linear programme for the selection and scheduling of US National Aeronautics and Space Administration (NASA) missions over a long planning horizon is presented. This model was formulated to allow a higher-level user-interaction with an advanced missions database currently being developed. The model implicitly considers the multi-objective nature of the problem, which results from the desire to maximize benefits in several categories as well as from the desire to minimize cost. In addition, the model allows the planner much flexibility in the selection process. This is accomplished by allowing the planner the ability to specify long- or short-term budget constraints, precursor/follow-on mission requirements, or any number of other idiosyncratic constraints which might be of importance in the decision process. Small example problems are solved in order to illustrate the approach, and areas for further research are discussed.

A strategic planning approach is used to compute the value of sample information in a project-selection problem for a risk-neutral decision-maker. Under this setting, a three-stage procedure is developed, and the decisions of purchasing information and selecting projects are derived for different cases. An exact solution is computed for the case with no budget constraints. Formulations, exact procedures and heuristics are suggested for other cases. In addition, upper bounds are derived for the amount of money that the decision-maker will be willing to pay in each case.