We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches, and is asymptotically optimal under fluid scaling. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach outperform available alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.

The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP , we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called κSDCP , and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the κSDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.

C onsider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm strives to maximize its total expected revenues over a finite horizon, either by choosing a dynamic pricing strategy for each product or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these wellstudied revenue management problems can be reduced to a common formulation in which the firm controls the aggregate rate at which all products jointly consume resource capacity, highlighting their common structure, and in some cases leading to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In the context of their associated deterministic (fluid) formulations, this reduction leads to a closed-form characterization of the optimal controls, and suggests several natural static and dynamic pricing heuristics. These are analyzed asymptotically and through an extensive numerical study. In the context of the former, we show that "resolving" the fluid heuristic achieves asymptotically optimal performance under fluid scaling.

We consider a family of N items that are produced in, or obtained from, the same production facility. Demands are deterministic for each item and each period within a given horizon of T periods. If in a given period an order is placed, setup costs are incurred. The aggregate order size is constrained by a capacity limit. The objective is to find a lot-sizing strategy that satisfies the demands for all items over the entire horizon without backlogging, and that minimizes the sum of inventory-carrying costs, fixed-order costs, and variable-order costs. All demands, cost parameters, and capacity limits may be time dependent. In the basic joint setup cost (JS) model, the setup cost of an order does not depend on the composition of the order. The joint and item-dependent setup cost (JIS) model allows for item-dependent setup costs in addition to the joint setup costs.We develop and analyze a class of so-called progressive interval heuristics. A progessive interval heuristic solves a JS or JIS problem over a progressively larger time interval, always starting with period 1, but fixing the setup variables of a progressively larger number of periods at their optimal values in earlier iterations. Different variants in this class of heuristics allow for different degrees of flexibility in adjusting continuous variables determined in earlier iterations of the algorithm.For the JS-model and the two basic implementations of the progressive interval heuristics, we show under some mild parameter conditions that the heuristics can be designed to be -optimal for any desired value of > 0 with a running time that is polynomially bounded in the size of the problem. They can also be designed to be simultaneously asymptotically optimal and polynomially bounded.A numerical study covering both the JS and JIS models shows that a progressive interval heuristic generates close-tooptimal solutions with modest computational effort and that it can be effectively used to solve large-scale problems.

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Funding for international humanitarian aid falls far behind demand for disaster response, hampering the operations of international humanitarian organizations (IHOs). One remedy to close this gap is to increase the effectiveness of fundraising activities for IHOs. This remedy means spending as little as possible in fundraising activities but, at the same time, still receiving sufficient donations to implement disaster response programs in response to the needs that arise when disasters occur. We contribute to the literature by theoretically developing and estimating a conceptual framework that links donation behavior to the operations that IHOs aim to pursue; the framework incorporates operational costs communicated in appeals, fundraising efforts, and media attention. We argue that effects are not homogenous across disasters but that IHOs can leverage public attention and disaster and appeal characteristics, such as operational costs, to increase donations. We test the framework on a unique data set for disaster response programs operated by the International Federation of Red Cross and Red Crescent Societies (IFRC), covering 174 disasters to which the IFRC responded between 2010 and 2017.

Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations.Numerically analyzing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the riskneutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.