IMA Journal of Management Mathematics - current issue

Advertising in a segmented market: comparison of media choices

Grosset, L., Viscolani, B. — 2008-06-20

Segmentation is a core strategy in modern marketing but, to the best of our knowledge, it is not considered in most dynamic advertising models. In this paper, we aim to fill such a gap by presenting a dynamic advertising model which includes market segmentation. First, we model goodwill evolution in a segmented market under the assumption that the decision maker may independently choose the advertising intensity directed at each different segment. Then, we assume that the decision maker must use a single medium, which reaches several segments with different effectiveness. We obtain the explicit solutions of the relevant optimal control problems. These results permit us to compare the two different contexts and to obtain a preference index for advertising media.

A survey of effective heuristics and their application to a variety of knapsack problems

Wilbaut, C., Hanafi, S., Salhi, S. — 2008-06-20

We present a family of knapsack problems (KPs) while highlighting their particular applications. Though most of the problems are derived from the classical KP, the differences arise in the addition or modification of the constraints or in the way the objective function is defined. Appropriate techniques that were found to be successful in solving these problems are briefly reviewed. Hybrid methods that combine the strengths of different methods such as exact and heuristics are also briefly discussed. Some research avenues that we believe to be useful and challenging are also pointed out.

Length of service and age characteristics in proportionality Markov manpower systems

Nilakantan, K., Raghavendra, B. G. — 2008-06-20

In this paper are analysed the length of service and age characteristics of members in a hierarchical organization under the influence of ‘proportionality’ policies. Proportionality policies are those that restrict the recruitment to every level of the hierarchy to be in strict proportion to the promotions into that level. The characteristics of the length of service in grade as well as those of the length of service in organization under these conditions have been derived. The characteristics of the chronological age of the members in the organization have also been derived. The analyses will be of relevance to organizations which outsource a part of their work, the outsourced workforce being notionally viewed as recruits to the system.

A utility model for multi-category baskets

Nadarajah, S. — 2008-06-20

An exact expression for the consumer's utility has not been known when a multi-category basket is assumed. This technical note derives an exact and explicit expression. consumer's utility; Gumbel distribution; multi-category basket; sums of random variables.

Forecasting aggregate time series with intermittent subaggregate components: top-down versus bottom-up forecasting

Viswanathan, S., Widiarta, H., Piplani, R. — 2008-06-20

In this paper, we evaluate the performance of top-down (TD) and bottom-up (BU) forecasting strategies in estimating the aggregate data series when the subaggregate time series components are intermittent. The findings of our simulation-based study are as follows. When the variability of the inter-order intervals of the subaggregate time series is low, BU forecasting that is carried out using Croston's method outperformed TD for estimating the aggregate data series. However, when the inter-order intervals and the demand sizes of the subaggregate components are highly variable and the aggregate data series is composed of many subaggregate components, TD forecasting outperformed BU. Finally, for forecasting the aggregate demand using TD forecasting, the simple exponential smoothing technique outperformed Croston's method in a majority of the cases.

Robust stochastic programming with uncertain probabilities

Thiele, A. — 2008-06-20

Stochastic programming has traditionally assumed the exact knowledge of the underlying scenario probabilities. In practice, however, such probabilities are difficult to estimate accurately and the optimal decision variables may be quite sensitive to the assumed distributions. This motivates the use of minimax stochastic models, where the decision maker minimizes the maximum expected cost over the set of possible probability distributions. We use ideas from the field of robust optimization to reformulate the minimax stochastic programming problem when probabilities belong to a polyhedral uncertainty set as a single convex problem, and show that it can be solved efficiently using the traditional techniques developed to address sequential decision making under uncertainty. In the two-stage setting, we describe how the Benders decomposition algorithm can be modified to solve the robust formulation. In the case of multiple stages, we build upon the recursive equations of dynamic programming to formulate an approach as tractable as the multi-stage stochastic problem where the probabilities are known exactly. Key contributions of this work are the following: (i) we show that the minimax approach is equivalent to the nominal stochastic programming problem with a penalty term, which measures the cost volatility due to the ambiguity on the probability estimates, and (ii) we provide deeper insights into the connection between the value of the recourse function in a given scenario and the worst-case probability associated with that outcome. The robust approach also allows the decision maker to adjust the parameters defining the uncertainty set in order to better capture his own trade-off between ambiguity and performance.