W e consider a cargo booking problem on a single-leg flight with the goal of maximizing expected contribution. Each piece of cargo is endowed with a random volume and a random weight whose precise values are not known until just before the flight's departure. We formulate the problem as a Markov decision process (MDP). Exact solution of the formulation is impractical, because of its high-dimensional state space; therefore, we develop six heuristics. The first four heuristics are based on different value-function approximations derived from two computationally tractable MDPs, each with a one-dimensional state space. The remaining two heuristics are obtained from solving related methematical programming problems. We also compare the heuristics with the first-come, first-served (FCFS) policy. Simulation experiments suggest that the value function approximation derived from separate "volume" and "weight" problems offers the best approach. Comparisons of the expected contribution under the heuristic to an upper bound show that the heuristic is typically close to optimal.

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C arriers (airlines) use medium-term contracts to allot bulk cargo capacity to forwarders who deliver consolidated loads for each flight in the contractual period (season). Carriers also sell capacity to direct-ship customers on each flight. We study capacity contracts between a carrier and a forwarder when certain parameters such as the forwarder's demand, operating cost to the carrier, margin, and reservation profit are its private information. We propose contracts in which the forwarder pays a lump sum in exchange for a guaranteed capacity allotment and receives a refund for each unit of unused capacity according to a pre-announced refund rate. We obtain an upper bound on the informational rent paid by the carrier for a menu of arbitrary allotments and identify conditions under which it can eliminate the informational rent and induce the forwarder to choose the overall optimal capacity allotment (i.e., one that maximizes the combined profits of the carrier and the forwarder).

Consider an agricultural land-water resource allocation problem in which yields are spatial dependent and stochastically correlated. To achieve sustainability, we formulate a multiobjective (MO) optimization problem, in which the decision maker determines the cultivation areas and the supplemental irrigation water levels at different locations, with social, economic, and environmental goals in mind. For the social goal, we minimize the root mean squared difference of incomes among locations. For the economic goal, we minimize the production risk. We show that minimizing production risk is equivalent to maximizing the service level, when demand is normally distributed. For the environmental goal, we minimize the resource utilization. Assume that the yield vector at different locations follows a multivariate normal distribution. We formulate the MO optimization problem using a weight global criterion method, and we provide a sufficient condition for convex quadratic programming. We demonstrate the applicability of our proposed framework in the case study of sugarcane production in Thailand. To capture yield response to water, we propose several models including linear and nonlinear regressions, and we obtain the closed-form expression for the linear and probit yield response models. The numerical experiment reveals that our solution significantly improves the social and economic goals, compared to the current policy. Finally, we illustrate how to apply our model to quantify the monetary value from reducing yield variability, which could be resulted from smart irrigation or precision agriculture.

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