A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane

We present a stochastic programming model for informing the deployment of temporary flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.Comment: 35 pages, 12 figure

Two-stage models for flood mitigation of electrical substations

We compare stochastic programming and robust optimization decision models for informing the deployment of temporary flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce novel adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of a blackout indicator variable and relaxed model of power generation. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas the choice of power flow model is of little to no consequence

Integrated inventory and transportation mode selection: A service parts logistics system

We present an optimization-based model to gain insights into the integrated inventory and transportation problem for a single-echelon, multi-facility service parts logistics system with time-based service level constraints. As an optimization goal we minimize the relevant inventory and transportation costs while ensuring that service constraints are met. The model builds on stochastic base-stock inventory model and integrates it with transportation options and service responsiveness that can be achieved using alternate modes (namely slow, medium and fast). The results obtained through different networks show that significant benefits can be obtained from transportation mode and inventory integration.Inventory management Transportation mode selection Service parts logistics Integer programming

An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels

We consider a model to allocate stock levels at warehouses in a service parts logistics network. The network is a two-echelon distribution system with one central warehouse with infinite capacity and a number of local warehouses, each facing Poisson demands from geographically dispersed customers. Each local warehouse uses a potentially different base stock policy. The warehouses are collectively required to satisfy time-based service targets: Certain percentages of overall demand need to be satisfied from facilities within specified time windows. These service levels not only depend on the distance between customers and the warehouses, but also depend on the part availabilities at the warehouses. Moreover, the warehouses share their inventory as a way to increase achieved service levels, i.e., when a local warehouse is out of stock, demand is satisfied with an emergency shipment from another close-by warehouse. Observing that the problem of finding minimum-cost stock levels is an integer non-linear program, we develop an implicit enumeration-based method which adapts an existing inventory sharing model from the literature, prioritizes the warehouses for emergency shipments, and makes use of a lower bound. The results show that the proposed inventory sharing strategy results in considerable cost reduction when compared to the no-sharing case and the method is quite efficient for the considered test problems.Inventory allocation Service parts logistics Time-based service levels

On Combinatorial Auction and Lagrangean Relaxation for Distributed Resource Scheduling

Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new method based on a distributed and locally autonomous decision structure using the notion of combinatorial auction. In combinatorial auction the bidders demand a combination of dependent objects with a single bid. We show that not only can we use this auction mechanism to handle complex resource scheduling problems, but there exist strong links between combinatorial auction and Lagrangean-based decomposition. Exploring some of these properties, we characterize combinatorial auction using auction protocols and payment functions. This study is a #rst step toward developing a distributed scheduling framework that maintains system-wide performance while accommodating local preferences and objectives. We provide some insights to this framework by demonstrating four di#erent versions of the auction mechanism using job shop scheduling proble..