When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

The solution to an open problem for a caching game

In a caching game introduced by Alpern et al. (Alpern et al., Lecture notes in computer science (2010) 220–233) a Hider who can dig to a total fixed depth normalized to 1 buries a fixed number of objects among n discrete locations. A Searcher who can dig to a total depth of h searches the locations with the aim of finding all of the hidden objects. If he does so, he wins, otherwise the Hider wins. This zero‐sum game is complicated to analyze even for small values of its parameters, and for the case of 2 hidden objects has been completely solved only when the game is played in up to 3 locations. For some values of h the solution of the game with 2 objects hidden in 4 locations is known, but the solution in the remaining cases was an open question recently highlighted by Fokkink et al. (Fokkink et al., Search theory: A game theoretic perspective (2014) 85–104). Here we solve the remaining cases of the game with 2 objects hidden in 4 locations. We also give some more general results for the game, in particular using a geometrical argument to show that when there are 2 objects hidden in n locations and n→∞, the value of the game is asymptotically equal to h/n for h≥n/2. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 23–31, 2016     

Network design for time‐constrained delivery

To meet customer demand, delivery companies are offering an increasing number of time‐definite services. In this article, we examine the strategic design of delivery networks which can efficiently provide these services. Because of the high cost of direct connections, we focus on tree‐structured networks. As it may not be possible to identify a tree‐structured network that satisfies all of the delivery guarantees, we allow these guarantees to be violated but seek to minimize the sum of the violations. We establish the complexity of the problem and exploit an empirically identified solution structure to create new neighborhoods which improve solution values over more general neighborhood structures. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

The value of losing control: Competition in markets for complements

When selling complementary products, manufacturers can often benefit from considering the resulting cross‐market interdependencies. Although using independent retailers makes it difficult to internalize these positive externalities, the ensuing double marginalization can mitigate within‐market competition. We use standard game theoretic analysis to determine optimal distribution channel strategies (through independent retailers or integrated) for competing manufacturers who participate in markets for complements. Our results suggest that a firm's optimal channel choice is highly dependent on its competitive positioning. A firm with a competitive advantage in terms of product characteristics (customer preferences) or production capabilities (cost) might benefit from selling through company‐controlled stores, allowing coordinated pricing across the two markets, whereas a less competitive firm might be better off using independent channel intermediaries to mitigate price competition. We consider two scenarios depending on whether the two firms make their distribution channel decisions sequentially or simultaneously. Although firms are unlikely to make such decisions at exactly the same instant, the simultaneous model also serves as a proxy for the scenario where firms decide sequentially, but where they cannot observe each other's strategic channel choices. For the sequential case, we find that the sequence of entry can have tremendous impact on the two firms'profits; whereas in some cases, the first mover can achieve substantially higher profits, we find that when the two markets are of sufficiently different size and only loosely related, a firm with a competitive advantage might be better off as a follower. Interestingly, our results suggest that, when the markets are of rather similar size, both firms are better off if they enter the industry sequentially. In those cases, the first entrant has incentive to reveal its planned channel strategies, and the follower has incentive to seek out and consider this information. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Strategic capacity decision‐making in a stochastic manufacturing environment using real‐time approximate dynamic programming

In this study, we illustrate a real‐time approximate dynamic programming (RTADP) method for solving multistage capacity decision problems in a stochastic manufacturing environment, by using an exemplary three‐stage manufacturing system with recycle. The system is a moderate size queuing network, which experiences stochastic variations in demand and product yield. The dynamic capacity decision problem is formulated as a Markov decision process (MDP). The proposed RTADP method starts with a set of heuristics and learns a superior quality solution by interacting with the stochastic system via simulation. The curse‐of‐dimensionality associated with DP methods is alleviated by the adoption of several notions including “evolving set of relevant states,” for which the value function table is built and updated, “adaptive action set” for keeping track of attractive action candidates, and “nonparametric k nearest neighbor averager” for value function approximation. The performance of the learned solution is evaluated against (1) an “ideal” solution derived using a mixed integer programming (MIP) formulation, which assumes full knowledge of future realized values of the stochastic variables (2) a myopic heuristic solution, and (3) a sample path based rolling horizon MIP solution. The policy learned through the RTADP method turned out to be superior to polices of 2 and 3. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Integrated capacity,demand, and production planning with subcontracting and overtime options

Models for integrated production and demand planning decisions can serve to improve a producer's ability to effectively match demand requirements with production capabilities. In contexts with price‐sensitive demands, economies of scale in production, and multiple capacity options, such integrated planning problems can quickly become complex. To address these complexities, this paper provides profit‐maximizing production planning models for determining optimal demand and internal production capacity levels under price‐sensitive deterministic demands, with subcontracting and overtime options. The models determine a producer's optimal price, production, inventory, subcontracting, overtime, and internal capacity levels, while accounting for production economies of scale and capacity costs through concave cost functions. We use polyhedral properties and dynamic programming techniques to provide polynomial‐time solution approaches for obtaining an optimal solution for this class of problems when the internal capacity level is time‐invariant. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Designing safety space in a supply chain to handle system‐wide disruptions

In some supply chains serious disruptions are system wide. This happens during periods of severe weather, as when storms cause shuttle tankers serving oil platforms in the North Sea to stop movements of crude oil, barges are frozen in the Mississippi, or all airplanes are grounded after a blizzard. Other notable instances of system‐wide disruption happened after the attack on the World Trade Center when all aircraft were grounded and the natural gas and crude‐oil pipelines were tangled by hurricanes in 2005. We model a situation where shutting down supply facilities is very difficult and expensive because of excessive inventory buildup from an inability to move out the production. We present a planning model that balances the cost of spare capacity versus shutting down production when planning for disruptions. The model uses an assignment model embedded in a simulation. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Provocation,war and restraint under the nuclear shadow: The Kargil conflict 1999

ABSTRACT

The Kargil conflict was a limited war between India and Pakistan fought along the Kashmir Line of Control during the spring/summer of 1999. Named for the principal town in the combat zone on the Indian side, it was the first open warfare between India and Pakistan as declared nuclear weapons states and included the first combat employment of the Indian Air Force since 1971. Despite its intensity, it was also characterised by considerable restraint on both sides. The potential for conventional escalation, however, was high and the possibility of nuclear confrontation could not be excluded. It had significant long-term ramifications for both countries and constitutes an important part of the backdrop to their relations today.     

Changing the paradigm: Simulation,now a method of first resort

Decades ago, simulation was famously characterized as a “method of last resort,” to which analysts should turn only “when all else fails.” In those intervening decades, the technologies supporting simulation—computing hardware, simulation‐modeling paradigms, simulation software, design‐and‐analysis methods—have all advanced dramatically. We offer an updated view that simulation is now a very appealing option for modeling and analysis. When applied properly, simulation can provide fully as much insight, with as much precision as desired, as can exact analytical methods that are based on more restrictive assumptions. The fundamental advantage of simulation is that it can tolerate far less restrictive modeling assumptions, leading to an underlying model that is more reflective of reality and thus more valid, leading to better decisions. Published 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 293–303, 2015