An application of approximate dynamic programming in multi-period multi-product advertising budgeting

<p style='text-indent:20px;'>Advertising has always been considered a key part of marketing strategy and played a prominent role in the success or failure of products. This paper investigates a multi-product and multi-period advertising budget allocation, determining the amount of advertising budget for each product through the time horizon. Imperative factors including life cycle stage, <inline-formula><tex-math id="M1">\begin{document}$ BCG $\end{document}</tex-math></inline-formula> matrix class, competitors' reactions, and budget constraints affect the joint chain of decisions for all products to maximize the total profits. To do so, we define a stochastic sequential resource allocation problem and use an approximate dynamic programming (<inline-formula><tex-math id="M2">\begin{document}$ ADP $\end{document}</tex-math></inline-formula>) algorithm to alleviate the huge size of the problem and multi-dimensional uncertainties of the environment. These uncertainties are the reactions of competitors based on the current status of the market and our decisions, as well as the stochastic effectiveness (rewards) of the taken action. We apply an approximate value iteration (<inline-formula><tex-math id="M3">\begin{document}$ AVI $\end{document}</tex-math></inline-formula>) algorithm on a numerical example and compare the results with four different policies to highlight our managerial contributions. In the end, the validity of our proposed approach is assessed against a genetic algorithm. To do so, we simplify the environment by fixing the competitor's reaction and considering a deterministic environment.</p>

Fighting Wildfires under Uncertainty - A Sequential Resource Allocation Approach

Standard disaster response involves using drones (or helicopters) for reconnaissance and using people on the ground to mitigate the damage. In this paper, we look at the problem of wildfires and propose an efficient resource allocation strategy to cope with both dynamically changing environment and uncertainty. In particular, we propose Firefly, a new resource allocation algorithm, that can provably achieve optimal or near optimal solutions with high probability by first efficiently allocating observation drones to collect information to reduce uncertainty, and then allocate the firefighting units to extinguish fire. For the former, Firefly uses a combination of maximum set coverage formulation and a novel utility estimation technique, and it uses a knapsack formulation to calculate the allocation for the latter. We also demonstrate empirically by using a real-world dataset that Firefly achieves up to 80-90% performance of the offline optimal solution, even with a small amount of drones, in most of the cases.

Variables Reduction in Sequential Resource Allocation Problems

This paper presents a general framework to address diverse notoriously difficult problems arising in the area of optimal resource management, exploitation of natural reserves, pension fund valuation, environmental protection, and storage operation. Using some common abstract features of this problem class, we present a technique which provides a significant reduction of decision variables. As an application, we discuss a battery storage control to show how a decision problem, which is practically unsolvable in the original formulation, can be treated by our method.