Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Naval policy and national strategy in France, 1933–1937

This article argues that French naval policy‐makers were slow to adjust to the changed strategic landscape of the 1930s. During the 1920s France did not face a serious land or air threat. Defence policy‐makers were therefore able to devote a large portion of the defence budget to rebuilding French maritime power. But when the Depression and the rise of Nazi Germany overturned the strategic situation in Europe, policy‐makers adjusted by giving priority to land and air rearmament and by placing ever greater emphasis on securing an alliance with Great Britain. The French naval establishment resisted this trend unsuccessfully. The frustration of naval planning increased the resentment and mistrust of both the Third Republic and Great Britain that characterised naval attitudes before and particularly during the Second World War.     

Waiting times for M/G/1 queues with service-time or delay-dependent server vacations

This article shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one-at-a-time or exhaustive server vacations, depending on either service times or accrued workload. For the first type of dependence, each vacation time is a function of the immediately preceding service time or of whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. For the second type of dependence, the vacation time assigned to an arrival to follow its service is a function of the level of virtual wait reached. By this device, we can model situations in which vacations may be shortened whenever virtual delays have gotten excessive. The method of analysis employs level-crossing theory, and examples are given for various cases of service and vacation-time distributions. A closing discussion relates the new model class to standard M/G/1 queues where the service time is a sum of variables having complex dependencies. © 1992 John Wiley & Sons, Inc.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Case Study Commentary and Analysis: The Moral Sword of Damocles

Case summary, by James Cook (Case Study Editor):

In the final issue of the 2015 volume of the Journal of Military Ethics, we published a case study entitled “Coining an Ethical Dilemma: The Impunity of Afghanistan’s Indigenous Security Forces”, written by Paul Lushenko. The study detailed two extra-judicial killings (EJKs) by Afghan National Police (ANP) personnel in an area stabilized and overseen by a US-led Combined Task Force (CTF). To deter further EJKs following the first incident, the CTF’s commander reported the incidents up his chain of command and used the limited tools at his disposal to influence local indigenous officials directly. Apparently, the ANP unit took no notice. In his commentary on the case study, Paul Robinson considered moral compromise in war more generally. Coalition troops in Afghanistan, for instance, have encountered not just EJKs but also sexual abuse of minors, killing of non-combatants, kidnapping, torture, and widespread corruption. What should the soldier on the ground do if indigenous personnel violate Laws of Armed Conflict (LOAC) with impunity? Refusing to serve will not right or prevent moral wrongs, while staying on to fight the good but futile fight will mire the soldier in moral compromise. “?… [S]oldiers faced with this dilemma have no good options. The systemic failings surrounding them mean that it is probable that nothing they do will help”. In a concluding note, I suggested that while an individual soldier may indeed have no good options, as Paul Robinson suggests, that soldier’s military and nation at large are obliged to do what they can. At least, they must keep to the moral high ground so as not to give indigenous security forces an excuse to misbehave, and determine the nature of crimes such as EJKs: are they outlaw acts or in fact endorsed by the indigenous culture and perhaps even government? Below Colonel Dave Barnes, himself a veteran of Operation Enduring Freedom, analyzes Paul Lushenko’s case study at “?…?the local, tactical level: If a commander is in this situation – where her unit witnesses an EJK or other war crime – what should she do?”     

Utility assessment procedures for polynomial-exponential functions

This article develops a methodology for testing constant exchange risk properties and identifying an appropriate form for a decision maker's utility function. These risk properties characterize six different utility functions which are sums of products of polynomials and exponential functions. Such functional forms are commonly used in decision analysis applications. The practical advantage of this methodology is that these constant exchange risk properties eliminate the usual arbitrariness in the selection of a parametric utility function and often reduce the data requirements for subsequent estimation. The procedure is straightforward to apply. The decision maker need only provide certainty equivalents for two-outcome gambles and determine the more-preferred gamble in paired comparisons. The technical details of the procedure can be handled by interactive computer software.     

Controlling rates in a double queue

A double-ended queue with a Poisson arrival pattern is examined in a situation where the rates depend (in a restricted sense) on both the time and the state of the system. Under some circumstances, the rates can be controlled. This article studies the distribution of the difference in queue sizes for each member of a large class of control strategies and introduces the problem of determining the optimal times at which the control should be in effect in order to maximize certain objective functions.     

Minimum-cost mixtures of area and point defenses assuming simultaneous attack

It is desired to select numbers of area and point interceptors that minimize the cost of such defensive missiles under the condition that the maximum total expected damage produced by an unknown number of attacking missiles A be bounded above by a given function of A. Area coverages may overlap. The attacker is assumed to know the numbers of area and point interceptors and to launch a simultaneous attack (of arbitrary size A) against all targets, which is optimal against the given defenses. The defender is assumed to observe the attack and then allocate his area and point interceptors against attacking missiles so as to minimize the total expected damage. Upper and lower bounds on the minimal cost are obtained by solving integer programming problems.     

Algorithms and heuristics for variable-yield lot sizing

We consider the multiperiod lot-sizing problem in which the production yield (the proportion of usable goods) is variable according to a known probability distribution. We review two economic order quantity (EOQ) models for the stationary demand continuous-time problem and derive an EOQ model when the production yield follows a binomial distribution and backlogging of demand is permitted. A dynamic programming algorithm for an arbitrary sequence of demand requirements is presented. Heuristics based on both the EOQ model and appropriate modification of the underlying perfect-yield lot-sizing policies are discussed, and extensive computational evaluation of these heuristics is presented. Two of these heuristics are then modified to include the notion of supply safety stock. The modified heuristics consistently produce near-optimal lot-sizing policies for problems with stationary and time-varying demands.