Journal of Industrial & Management Optimization
April 2013 , Volume 9 , Issue 2
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In order to study deregulated electricity spot markets, various models have been proposed. Most of them correspond to a, so-called, multi-leader-follower game in which an Independent System Operator (ISO) plays a central role. Our aim in this paper is to consider quadratic bid functions together with the transmission losses in the multi-leader-follower game. Under some reasonable assumptions we deduce qualitative properties for the ISO's problem. In the two islands type market, the explicit formulae for the optimal solutions of the ISO's problem are obtained and we show the existence of an equilibrium.
Group-buying price is a new pricing mechanism originated from Internet bidding. It has been proved that, with this pricing mechanism, buyers' cooperation in a B2C environment is beneficial for both the seller and buyers. The contribution of this paper is two-fold. First, we formally prove that, when buyers' valuation on the product is transparent and known information, the optimal form of buyers' cooperation is to organize only one ``bidding ring'' with all buyers. Second, we study how cooperation with all buyers can be organized if each buyer's valuation of the product is private information not known to others. We find that there may not exist a feasible compensation mechanism such that all buyers will report their true values in the cooperative coalition. Given that buyers may hide some information and report a lower value, we show that it is still possible to organize the cooperation if the number of buyers with higher values is large enough.
The purpose of the paper is to develop globally convergent algorithms for solving the popular stationarity systems for mathematical programs with complementarity constraints (MPCC) directly. Since the popular stationarity systems for MPCC contain some unknown index sets, we first present some nonsmooth reformulations for the stationarity systems by removing the unknown index sets and then we propose a Levenberg-Marquardt type method to solve them. Under some regularity conditions, we show that the proposed method is globally and superlinearly convergent. We further report some preliminary numerical results.
In many real-life scheduling environments, the jobs deteriorate at a certain rate while waiting to be processed. This paper addresses some single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a linear deterioration. The p-s-d delivery time of a job is proportional to the job's waiting time. It is assumed that the deterioration process is reflected in the job processing times being an increasing function of their starting times. We consider the following objectives: the makespan, total completion time, total weighted completion time, maximum lateness, and total absolute differences in completion times. We seek the optimal schedules for the problems to minimize the makespan and total completion time. Despite that the computational complexities of the problems to minimize the total weighted completion time and maximum lateness remain open, we present heuristics and analyze their worst-case performance ratios, and show that some special cases of the problems are polynomially solvable. We also show that the optimal schedule for the problem to minimize the total absolute differences in completion times is $V$-shaped with respect to the normal job processing times.
Transport systems play a crucial role for sustainable development, and hence, sustainable urban transportation has recently become a major research area. Most of the existing studies propose evaluation methods that use simulation tools to assess the sustainability of different transportation policies. Although there are some recent studies, considering the sustainability dimension and the resulting policies through mathematical programming models is still an open research area. In this study, we focus on controlling the gas emissions for the environmental sustainability and propose several mathematical programming models that incorporate the measurements of gas emissions over a traffic network. We define emission functions in terms of the traffic flow so that the accumulated emission amounts can be modeled accurately, particularly in case of congestion. Using these emission functions, we introduce alternate objective functions and develop optimization models under various policies which are based on the well-known toll pricing and capacity enhancement. The proposed models both reflect the route choice decisions of the network users and the decisions of the transportation managers that aim at making the transport systems more sustainable through the policies of interest. We conduct a computational study on a well-known testing network and present numerical results to evaluate the proposed alternate models. We conclude that simultaneously applying the toll pricing and capacity enhancement policies is in general more effective in serving the travel demand and reducing the emission amounts compared to implementing these policies individually.
In this paper we propose a penalty method combined with a finite difference scheme for the Hamilton-Jacobi-Bellman (HJB) equation arising in pricing American options under proportional transaction costs. In this method, the HJB equation is approximated by a nonlinear partial differential equation with penalty terms. We prove that the viscosity solution to the penalty equation converges to that of the original HJB equation when the penalty parameter tends to positive infinity. We then present an upwind finite difference scheme for solving the penalty equation and show that the approximate solution from the scheme converges to the viscosity solution of the penalty equation. A numerical algorithm for solving the discretized nonlinear system is proposed and analyzed. Numerical results are presented to demonstrate the accuracy of the method.
A penalty-free method is introduced for solving nonlinear programming with nonlinear equality constraints. This method does not use any penalty function, nor a filter. It uses trust region technique to compute trial steps. By comparing the measures of feasibility and optimality, the algorithm either tries to reduce the value of objective function by solving a normal subproblem and a tangential subproblem or tries to improve feasibility by solving a normal subproblem only. In order to guarantee global convergence, the measure of constraint violation in each iteration is required not to exceed a progressively decreasing limit. Under usual assumptions, we prove that the given algorithm is globally convergent to first order stationary points. Preliminary numerical results on CUTEr problems are reported.
This paper extends the model in Riesner (2007) to a Markov modulated Lévy process. The parameters of the Lévy process switch over time according to the different states of an economy, which is described by a finite-state continuous time Markov chain. Employing the local risk minimization method, we find an optimal hedging strategy for a general payment process. Finally, we give an example for single unit-linked insurance contracts with guarantee to display the specific locally risk-minimizing hedging strategy.
Modigliani and Miller's argument of the irrelevance of the debt-equity ratio to the value of the firm implies that capital structure has no impact on the value of the firm (irrelevance result). In the existing work, the proof or disproof of the Modigliani and Miller theorem is based critically on some specific assumptions, not general enough to be always valid in practical finance, and including especially a constant interest rate for borrowing. This paper develops another optimal financing model, whose assumptions differ from those in previous models for the Modigliani and Miller theorem. If the borrowing rate increases with the amount borrowed, there is a unique optimal ratio of debt to equity, determining the optimal capital structure. Therefore the debt-equity ratio does affect the value of the firm, and hence the need for good corporate financial management to maximize the value of the firm, by choosing the optimal debt. Some important issues of sensitivity are also analysed. The proposed model should apply to more real situations, and therefore makes an original contribution to finance.
Recently, due to rapid economic development in emerging nations, the world's raw material prices have been rising. In today's unrestricted information environment, suppliers typically announce impending supply price increases at specific times. This allows retailers to replenish their stock at the present price, before the price increase takes effect. The supplier, however, will generally offer only limited quantities prior to the price increase, so as to avoid excessive orders. The retail price will usually reflect any supply price increases, as market demand is dependent on retail price. This paper considers deteriorating items and investigates (1) the possible effects of a supply price increase on retail pricing, and (2) ordering policies under the conditions that special order quantities are limited and demand is dependent on retail price. The purpose of this paper is to determine the optimal special order quantity and retail price to maximize profit. Our theoretical analysis examines the necessary and sufficient conditions for an optimal solution, and an algorithm is established to obtain the optimal solution. Furthermore, several numerical examples are given to illustrate the developed model and the solution procedure. Finally, a sensitivity analysis is conducted on the optimal solutions with respect to major parameters.
In this paper, one introduces the second-order weak composed contingent epiderivative of set-valued maps, and discusses some of its properties. Then, by virtue of the second-order weak composed contingent epiderivative, necessary optimality conditions and sufficient optimality conditions are obtained for set-valued optimization problems. As consequences, recent existing results are derived. Several examples are provided to show the main results obtained.
This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of auxiliary time-delay systems. On this basis, the parameter identification problem can be solved using existing gradient-based optimization techniques. We conclude the paper with two numerical simulations.
This paper discusses an optimal portfolio selection problem in a continuous-time economy, where the price dynamics of a risky asset are governed by a continuous-time self-exciting threshold model. This model provides a way to describe the effect of regime switching on price dynamics via the self-exciting threshold principle. Its main advantage is to incorporate the regime switching effect without introducing an additional source of uncertainty. A martingale approach is used to discuss the problem. Analytical solutions are derived in some special cases. Numerical examples are given to illustrate the regime-switching effect described by the proposed model.
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