Humanitarian response to hurricane disasters: Coordinating flood‐risk mitigation with fundraising and relief operations

To alleviate flooding, caused by hurricanes, governments build structural barriers called levees. In addition, relief providers such as the nongovernmental organizations and charities raise funds, and procure and deliver supplies (food, water, and medicines) for humanitarian relief. The strategy for managing disasters must, therefore, weigh the costs and benefits of building levees as well as procuring and delivering supplies. We use a three‐stage decision making framework to study how the investment in levee capacity can be integrated with supply procurements, fundraising, and rapid response. One of our major findings is that a large fundraising cost discourages postdisaster funding, implying relatively large investments in levee and prepositioned supplies. That notwithstanding, a large social value (of saving life) can tilt the balance in favor of postdisaster funding. If the levee capacity increases, funding for predisaster procurement is reduced without affecting postdisaster funding. For a sufficiently large increase in capacity, however, postdisaster response becomes superfluous. We also find that hurricane uncertainty motivates levees with large capacity. In contrast, levee‐failures motivate levees with small capacity.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

An approach to postoptimality and sensitivity analysis of zero-one goal programs

In this article we present a methodology for postoptimality and sensitivity analysis of zero-one goal programs based on the set of k-best solutions. A method for generating the set of k-best solutions using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problem are discussed. Rules for determining the range of parameter changes that still allows a member of the k-best set to be optimal are developed. An investigation of a sufficient condition for postoptimality analysis is also presented.     

An optimal ordering policy for situations with uncertainty in supply

A one-period inventory model where supply is a random variable with mean proportional to the quantity ordered has been considered. Under new better than used in expectation assumption on the supply variable, a strategy which maximizes a minimum profit has been suggested. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been proposed and almost sure convergence of this estimate to its true value with increasing sample size has been established.     

Between a rock and a hard place: Europe in a post-INF world

The end of the 1987 Intermediate-range Nuclear Forces (INF) Treaty has the potential to plunge Europe and NATO into deep crisis. Russia’s continued violation coupled with the Donald J. Trump administration’s desire to balance against Moscow and Beijing could force a new missile debate on Europeans. Even though Washington is trying to assuage its allies, the specter of another round of INF missile deployments to Europe is not unrealistic. Meanwhile, NATO’s European members face a dilemma. Some want NATO to resolutely push back against Russia. Others want to avoid a new deployment debate, at almost all costs. The Kremlin will use these cleavages to weaken NATO. If not carefully handled, NATO’s response to the Russian missile buildup could lead to domestic turmoil in a number of European states and render the alliance ineffective for a prolonged period. Europeans need to act now and voice their preferences in the military and diplomatic domains. A number of different military options are available, below the level of deploying new INF missiles in Europe. However, Europeans need to consider trade-offs regarding crisis and arms-race stability. At the same time, it will be up to European capitals to conceptualize a new arms-control framework for the post-INF world, one that takes into account today’s geopolitical realities and the entanglement of modern conventional and nuclear forces. Given the Trump administration’s loathing of arms control, concepts of mutual restraint may well have to wait for the next US administration. In any case, that should not stop Europeans from taking on more responsibility for their own security.     

A bivariate optimal replacement policy for a cold standby repairable system with repair priority

In this article, an optimal replacement policy for a cold standby repairable system consisting of two dissimilar components with repair priority is studied. Assume that both Components 1 and 2, after repair, are not as good as new, and the main component (Component 1) has repair priority. Both the sequence of working times and that of the components'repair times are generated by geometric processes. We consider a bivariate replacement policy (T,N) in which the system is replaced when either cumulative working time of Component 1 reaches T, or the number of failures of Component 1 reaches N, whichever occurs first. The problem is to determine the optimal replacement policy (T,N)* such that the long run average loss per unit time (or simply the average loss rate) of the system is minimized. An explicit expression of this rate is derived, and then optimal policy (T,N)* can be numerically determined through a two‐dimensional‐search procedure. A numerical example is given to illustrate the model's applicability and procedure, and to illustrate some properties of the optimal solution. We also show that if replacements are made solely on the basis of the number of failures N, or solely on the basis of the cumulative working time T, the former class of policies performs better than the latter, albeit only under some mild conditions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A note on “resource flexibility with responsive pricing”

We revisit the capacity investment decision problem studied in the article “Resource Flexibility with Responsive Pricing” by Chod and Rudi [Operations Research 53, (2005) 532–548]. A monopolist firm producing two dependent (substitutable or complementary) products needs to determine the capacity of one flexible resource under demand risk so as to maximize its expected profit. Product demands are linear functions of the prices of both products, and the market potentials are random and correlated. We perform a comparative statics analysis on how demand variability and correlation impact the optimal capacity and the resulting expected profit. In particular, C&R study this problem under the following assumptions/approximations: (i) demand intercepts follow a bivariate Normal distribution; (ii) demand uncertainty is of an additive form; (iii) and under approximate expressions for the optimal capacity and optimal expected profit. We revisit Propositions 2, 3, 4, 5, and 10 of C&R without these assumptions and approximations, and show that these results continue to hold (i) for the exact expressions for the optimal expected profit and optimal capacity, and (ii) under any arbitrary continuous distribution of demand intercepts. However, we also show that the additive demand uncertainty is a critical assumption for the C&R results to hold. In particular, we provide a case of multiplicative uncertainty under which the C&R results (Propositions 2 and 3) fail. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010