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This paper studies the inventory management problem of dual channels operated by one vendor. Demands of dual
channels are inventory-level-dependent.We propose a multi-period stochastic dynamic programming model which
shows that under mild conditions, the myopic inventory policy is optimal for the infinite horizon problem. To
investigate the importance of capturing demand dependency on inventory levels, we consider a heuristic where the
vendor ignores demand dependency on inventory levels, and compare the optimal inventory levels with those
recommended by the heuristic. Through numerical examples, we show that the vendor may order less for dual
channels than those recommended by the heuristic, and the difference between the inventory levels in the two cases
can be so large that the demand dependency on inventory levels cannot be neglected. In the end, we numerically
examine the impact of different ways to treat unmet demand and obtain some managerial insights.
This paper studies the eect of risk-aversion in the competitive
newsvendor game. Multiple newsvendors with risk-averse preferences face a
random demand and the demand is allocated proportionally to their inventory
levels. Each newsvendor aims to maximize his expected utility instead of his
expected prot. Assuming a general form of risk-averse utility function, we
prove that there exists a pure Nash equilibrium in this game, and it is also
unique under certain conditions. We nd that the order quantity of each
newsvendor is decreasing in the degree of risk-aversion and increasing in the
initial wealth. Newsvendors with moderate preferences of risk-aversion make
more prots compared with the risk-neutral situation. We also discuss the joint
eect of risk-aversion and competition. If the eect of risk-aversion is strong
enough to dominate the eect of competition, the total inventory level under
competition will be lower than that under centralized decision-making.
This paper studies the capacity allocation game between duopolistic airlines which could offer callable products. Previous literature has shown that callable products provide a riskless source of additional rev- enue for a monopolistic airline. We examine the impact of the introduction of callable products on the revenues and the booking limits of duopolistic airlines. The analytical results demonstrate that, when there is no spill of low-fare customers, offering callable products is a dominant strategy of both airlines and provides Pareto gains to both airlines. When customers of both fare classes spill, offering callable products is no longer a dominant strategy and may harm the revenues of the airlines. Numerical ex- amples demonstrate that whether the two airlines offer callable products and whether offering callable products is beneficial to the two airlines mainly depends on their loads and capacities. Specifically, when the difference between the loads of the airlines is large, the loads of the airlines play the most important role. When the difference between the loads of the airlines is small, the capacities of the airlines play the most important role. Moreover, numerical examples show that the booking limits of the two airlines in the case with callable products are always higher than those in the case without callable products.
In Nash bargaining problem, due to fairness concerns of players, instead
of maximizing the sum of utilities of all players, an implementable solution should
satisfy some axioms or characterizations. Such a solution can result in the so-called
price of fairness, because of the reduction in the sum of utilities of all players. An
important issue is to quantify the system efficiency loss under axiomatic solutions
through the price of fairness. Based on Perles–Maschler solution of two-player Nash
bargaining problem, this paper deals with the extended Perles–Maschler solution of
multi-player Nash bargaining problem.We give lower bounds of threemeasures of the
system efficiency for this solution, and show that the lower bounds are asymptotically
In this paper, we construct a new suboptimal filter by deriving the Ito's stochastic differential equations of the estimation of higher order central moments satisfy and imposing some conditions to form a closed system. The essentially infinite-dimensional cubic sensor problem has been investigated in detail numerically to illustrate the reasonableness of the imposed conditions, and the numerical experiments support our discussion. A 2-dimensional polynomial filtering problem has also been experimented.