Designing rewards-based crowdfunding campaigns for strategic (but distracted) contributors

In rewards-based crowdfunding, entrepreneurs solicit donations from a large number of individual contributors. If total donations exceed a prespecified funding target, the entrepreneur distributes nonmonetary rewards to contributors; otherwise, their donations are refunded. We study how to design such campaigns when contributors choose not just whether to contribute, but also when to contribute. We show that strategic contribution behavior—when contributors intentionally delay until campaign success is likely—can arise from the combination of nonrefundable (potentially very small) hassle costs and the risk of campaign failure, and can explain pledging patterns commonly observed in crowdfunding. Furthermore, such delays do not hurt the entrepreneur if contributors are perfectly rational, but they do if contributors are distracted, that is, if they might fail to return to the campaign after an intentional delay. To mitigate this, we find that an entrepreneur can use a simple menu of rewards with a fixed number of units sold at a low price, and an unlimited number sold at a higher price; this segments contributors over time based on the information they observe upon arrival. We show that, despite its simplicity, such a menu performs well compared to a theoretically optimal menu consisting of an infinite number of different rewards and price levels under many conditions.     

Landmarks in defense literature

Military operations and maritime preponderance by Charles E. Callwell, Edinburgh: William Blackwood & Sons, 1905.     

An Investigation of the Weights of Pattern 1907 Bayonets made in the UK around the First World War Period

The standard issue bayonet of the British Army immediately preceding and during the First World War was the Pattern 1907. This was manufactured at different times and in varying numbers during that period by one official body, the Royal Small Arms Factory at Enfield, and by five private contractors. These bayonets were made according to published official specifications issued by the War Department and based on a ‘pattern example’ provided by the Royal Small Arms Factory. The specifications indicate, inter alia, the quality of metal used in making the bayonets, methods of inspection and proofing, and the required maximum and minimum weight range of the completed bayonet. However, examination of a series of these bayonets in a private collection suggested that their weights varied considerably from the mid-point values of the allowed weight ranges in the original and amended specifications (16.5 oz. and 17 oz., respectively). To establish if this was a common feature among this class of bayonet as opposed to a chance factor, the weights of other surviving Pattern 1907 bayonets were determined and compared to establish the degree of variance from the official specifications as originally set out by the Royal Small Arms Factory. Seventy-six percent of the 142 bayonets surveyed were found to be above the mid-point of the allowed weight range given in the amended manufacturing specifications, with many being at the upper end of the allowed range. This is a statistically unusual result. It is speculated that the target weight may have been deliberately set higher by the individual manufacturers to eliminate the possibility of rejection of any underweight bayonets by the Royal Small Arms Factory inspectors and so a refusal of acceptance and payment for the work.     

The Clausewitzian fallacy of absolute war

Clausewitz was much preoccupied with the apparent contradiction between real and absolute war. Why did war in history so rarely exhibit the extremes of violence and energy implied in the pure concept of war? Clausewitz’s commentators have usually followed him in thinking that this was a genuine problem in need of a solution, but I want to question that view. I will argue that Clausewitz did not have a coherent philosophy of absolute war, and therefore the contradiction he posited between real and absolute war was equally meaningless – as, too, was his effort to resolve it by claiming that some real wars approached or even attained the absolute form of war. The real problem was not the opposition of real and absolute war, but the self-contradictory theory of absolute war.     

An index policy for a stochastic scheduling model with improving/deteriorating jobs

We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 706–721, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10036     

Operational Combat Analysis of the Al Qaeda Network

Contemporary network organizational structures have gradually developed over the last decades of the twentieth century. These new structures are challenging the traditional hierarchical structure form in a number of venues. In conflict and war, they made their potentials unequivocally known on 11 September 2001 via Al Qaeda's strategic suicide bombings against the United States. To better understand the military potentials of networks, an operational combat analysis of the Al Qaeda network was conducted. This analysis, a modification of weapons systems analysis, focused on network speed, along with offensive, defensive and combat multiplier attributes. Such analysis allows for a better understanding of the military capabilities and vulnerabilities of non-state OPFORs (opposing forces) and our own emergent counter-insurgency networks.     

Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems

When solving location problems in practice it is quite common to aggregate demand points into centroids. Solving a location problem with aggregated demand data is computationally easier, but the aggregation process introduces error. We develop theory and algorithms for certain types of centroid aggregations for rectilinear 1‐median problems. The objective is to construct an aggregation that minimizes the maximum aggregation error. We focus on row‐column aggregations, and make use of aggregation results for 1‐median problems on the line to do aggregation for 1‐median problems in the plane. The aggregations developed for the 1‐median problem are then used to construct approximate n‐median problems. We test the theory computationally on n‐median problems (n ≥ 1) using both randomly generated, as well as real, data. Every error measure we consider can be well approximated by some power function in the number of aggregate demand points. Each such function exhibits decreasing returns to scale. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 614–637, 2003.     

Duality in constrained multi‐facility location models

We consider the ??_p‐norm multi‐facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multi‐facility minisum location problem with the ??_pb‐norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 410–421, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10010