No abstract

This paper considers an overbooking problem with multiple reservation and inventory classes, in which the multiple inventory classes may be used as substitutes to satisfy the demand of a given reservation class (perhaps at a cost). The problem is to jointly determine overbooking levels for the reservation classes, taking into account the substitution options. Such problems arise in a variety of revenue management contexts, including multicabin aircraft, back-to-back scheduled flights on the same leg, hotels with multiple room types, and mixed-vehicle car rental fleets. We model this problem as a two-period optimization problem. In the first period, reservations are accepted given only probabilistic knowledge of cancellations. In the second period, cancellations are realized and surviving customers are assigned to the various inventory classes to maximize the net benefit of assignments (e.g., minimize penalties). For this formulation, we show that the expected revenue function is submodular in the overbooking levels, which implies the natural property that the optimal overbooking level in one reservation class decreases with the number of reservations held in the other reservation classes. We then propose a stochastic gradient algorithm to find the joint optimal overbooking levels. We compare the decisions of the model to those produced by more naive heuristics on some examples motivated by airline applications. The results show that accounting for substitution when setting overbooking levels has a small, but still significant, impact on revenues and costs.

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In this paper, we consider the classical multifare, single-resource (leg) problem in revenue management for the case where demand information is limited. Our approach employs a competitive analysis, which guarantees a certain performance level under all possible demand scenarios. The only information required about the demand for each fare class is lower and upper bounds. We consider both competitive ratio and absolute regret performance criteria. For both performance criteria, we derive the best possible static policies, which employ booking limits that remain constant throughout the booking horizon. The optimal policies have the form of nested booking limits. Dynamic policies, which employ booking limits that may be adjusted at any time based on the history of bookings, are also obtained. We provide extensive computational experiments and compare our methods to existing ones. The results of the experiments demonstrate the effectiveness of these new robust methods.revenue management, robust optimization, competitive analysis

We consider a discrete-time supply chain for perishable goods having separate demand streams for items of different ages. For a good that has two periods of lifetime, we build a model that generalizes and/or subsumes many of the models in the literature and study the effectiveness of two intuitive heuristic (base-stock) replenishment policies combined with different substitution rules. For each replenishment policy, we identify sufficient conditions on cost parameters for a substitution rule to be economically superior to others under our base-stock replenishment policies. Our analysis shows that the replenishment policy almost universally advocated in the perishable inventory literature may lead to pathological behavior when used with issuance rules that pool inventory (via substitution) to satisfy multiple, age-differentiated demand streams. Furthermore, we find that system behavior is typically more predictable, and potentially less costly, under a policy long-discarded in the literature that ignores the inventory of aged items, ordering a constant amount each period. Thus the benefit of pooling inventory for substitutable, perishable products depends critically on the replenishment policy used.inventory management, perishable goods, substitution, heuristics