Browsing by Subject "Bilevel programming"

Now showing 1 - 4 of 4

Open Access
A bilevel uncapacitated location/pricing problem with Hotelling access costs in one-dimensional space
(International Conference on Information Systems, Logistics and Supply Chain, 2016) Arbib, C.; Pınar, Mustafa Ç.; Tonelli, M.
We formulate a spatial pricing problem as bilevel non-capacitated location: a leader first decides which facilities to open and sets service prices taking competing offers into account; then, customers make individual decisions minimizing individual costs that include access charges in the spirit of Hotelling. Both leader and customers are assumed to be risk-neutral. For non-metric costs (i.e., when access costs do not satisfy the triangle inequality), the problem is NP-hard even if facilities can be opened at no fixed cost. We describe an algorithm for solving the Euclidean 1-dimensional case (i.e., with access cost defined by the Euclidean norm on a line) with fixed opening costs and a single competing facility.
Open Access
Designing intervention strategy for public-interest goods
(2016-09) Demirci, Ece Zeliha
Public-interest goods, which are also referred as goods with positive externalities, create benefits to individual consumers as well as non-paying third parties. Some significant examples include health related products such as vaccines and products with less carbon emissions. When positive externalities exist, the good may be under-produced or under-supplied due to incorrect pricing policies or failing to value external benefits and that is why a need for intervention arises. A central authority such as government or social planner intervenes into the system of these goods so that their adoption levels are increased towards socially desirable levels. The central authority seeks to design and finance an intervention strategy that will impact the decisions of the channel in line with the good of the society, specified as social welfare. A key issue in designing an intervention mechanism is choosing the intervention tools to incorporate. The intervention tools can target the supply or demand of the good. One option for the intervention tool is investment in demand-increasing strategies, which affects the level of stochastic demand in the market. Second option is investment in strategies that will improve supply of the good. Alternatives for this option include registering rebates or subsidies and investment in yield-improving strategies when production process faces imperfect yield. As several real life cases indicate, central authority operates under a limited budget in this environment. Thus, we introduce and analyze social welfare maximization models with the emphasis on optimal budget allocation. We model the lower level problem, which represents the channel as a newsvendor problem. We then utilize bilevel programming for modeling the environment incorporating the role of central authority. After obtaining single level equivalent formulations of the problems, we analyze and solve them as non-linear programs. Our first problem is to analyze an intervention strategy, which uses only subsidy issued per unit order quantity. We explore the subsidy design problem for single retailer and n retailers cases. We show that all of the budget will be used under mild conditions and present structural results. Also, we analyze subsidy design problem for two echelon setting, where the central authority gives subsidy both to retailer and manufacturer. We consider centralized and manufacturer-driven problems and present numerical results. In the remaining part of the thesis, we focus on joint intervention mechanisms in which two intervention tools are applied simultaneously. First, we study a joint mechanism composed of demand-increasing strategy and rebate. We present two models and associated structural properties. First model aims to find optimal budget and allocation of it among intervention tools. We deduce that rebate amount may be independent of investment made in demand-increasing strategies and improvement pattern of demand. Second model decides on the optimal allocation of a given budget between intervention tools. We show that central authority will allocate all budget under mild conditions. Furthermore, we use real-life data and information of California electric vehicle market in order to verify the proposed models and show benefits of taking such an approach. We also explore the application of the joint mechanism under a given budget for exponentially distributed demand family and fully characterize the optimal solution. The analysis of the solution reveals that designing an intervention scheme without considering an explicit budget constraint will result in budget deficit and excess money transfers to the retailer. As the second modeling environment we consider a joint mechanism consisting of demand-increasing strategy and yield-improving strategy in a setting where yield uncertainty exists. We introduce lognormal demand and yield models that take into account the investments made for improving them. We test the suggested model with a case study relying on the available estimates of US influenza market. The results indicate that addressing both demand and yield issues by the proposed mechanism will increase vaccination percentages remarkably.
Open Access
Radio Communications Interdiction Problem under deterministic and probabilistic jamming
(Elsevier, 2019) Tanergüçlü, Türker; Karaşan, Oya Ekin; Akgün, I.; Karaşan, Ezhan
The Radio Communications Interdiction Problem (RCIP) seeks to identify the locations of transmitters on the battlefield that will lead to a robust radio communications network by anticipating the effects of intentional radio jamming attacks used by an adversary during electronic warfare. RCIP is a sequential game defined between two opponents that target each other’s military units in a conventional warfare. First, a defender locates a limited number of transmitters on the defender’s side of the battlefield to optimize the relay of information among its units. After observing the locations of radio transmitters, an attacker locates a limited number of radio jammers on the attacker’s side to disrupt the communication network of the defender. We formulate RCIP as a binary bilevel (max–min) programming problem, present the equivalent single level formulation, and propose an exact solution method using a decomposition scheme. We enhance the performance of the algorithm by utilizing dominance relations, preprocessing, and initial starting heuristics. To reflect a more realistic jamming representation, we also introduce the probabilistic version of RCIP where a jamming probability is associated at each receiver site as a function of the prevalent jamming to signal ratios leading to an expected coverage of receivers as an objective function. We approximate the nonlinearity in the jamming probability function using a piecewise linear convex function and solve this version by adapting the decomposition algorithm constructed for RCIP. Our extensive computational results on realistic scenarios show the efficacy of the solution approaches and provide valuable tactical insights.
Open Access
Solving the hazmat transport network design problem
(Pergamon Press, 2008) Erkut, E.; Gzara, F.
In this paper, we consider the problem of network design for hazardous material transportation where the government designates a network, and the carriers choose the routes on the network. We model the problem as a bilevel network flow formulation and analyze the bilevel design problem by comparing it to three other decision scenarios. The bilevel model is difficult to solve and may be ill-posed. We propose a heuristic solution method that always finds a stable solution. The heuristic exploits the network flow structure at both levels to overcome the difficulty and instability of the bilevel integer programming model. Testing on real data shows that the linearization of the bilevel model fails to find stable solutions and that the heuristic finds lower risk networks in less time. Further testing on random instances shows that the heuristically designed networks achieve significant risk reduction over single-level models. The risk is very close to the least risk possible. However, this reduction in risk comes with a significant increase in cost. We extend the bilevel model to account for the cost/risk trade-off by including cost in the first-level objective. The biobjective-bilevel model is a rich decision-support tool that allows for the generation of many good solutions to the design problem.