Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

A Markovian model for process setup and improvement

We examine the setup and improvement policies for a production process with multiple performance states. Assume that the production process deteriorates randomly over time, following a Markovian process with known transition probabilities. In order to reduce the production cost incurred because of process deterioration, the process is inspected at the end of each period. Then one of three actions may be taken: do nothing, perform routine process setup, or perform routine setup and process improvement. The routine setup operation returns the process to its best performance state, whereas the process improvement action may reduce future production and setup costs and improve the process-state transition probabilities. A discounted Markovian model is formulated to find the strategy that minimizes the total cost of operating the production process. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 383–400, 1997     

Stochastic regret minimization for revenue management problems with nonstationary demands

We study an admission control model in revenue management with nonstationary and correlated demands over a finite discrete time horizon. The arrival probabilities are updated by current available information, that is, past customer arrivals and some other exogenous information. We develop a regret‐based framework, which measures the difference in revenue between a clairvoyant optimal policy that has access to all realizations of randomness a priori and a given feasible policy which does not have access to this future information. This regret minimization framework better spells out the trade‐offs of each accept/reject decision. We proceed using the lens of approximation algorithms to devise a conceptually simple regret‐parity policy. We show the proposed policy achieves 2‐approximation of the optimal policy in terms of total regret for a two‐class problem, and then extend our results to a multiclass problem with a fairness constraint. Our goal in this article is to make progress toward understanding the marriage between stochastic regret minimization and approximation algorithms in the realm of revenue management and dynamic resource allocation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 433–448, 2016     

Predictability of operational processes over finite horizon

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well‐known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Parameter estimation for the EOQ lot-size model: Minimax and expected value choices

This article provides formulas for estimating the parameters to be used in the basic EOQ lot-size model. The analysis assumes that the true values of these parameters are unknown over known ranges and perhaps nonstationary over time. Two measures of estimator “goodness” are derived from EOQ sensitivity analysis. Formulas are given for computing the minimax choice and the minimum expected value choice for the parameter estimates using both measures of estimator “goodness”. A numerical example is included.     

On the behavior of the batch arrival queue Mx/M/1 during a busy period

The queue size process (^t)⁰≤^t≤^t0 of the batch arrival queue M^X/M/1 is studied under the condition that the duration of its busy period is larger than t⁰. Explicit formulas for the transition probabilities are given and the limiting Markov process for t⁰ → ∞ is investigated. Several properties of this process are considered. Its transition probabilities and moments and the distribution of its minimum are derived and a functional limit theorem for the rescaled process is proved. © 1994 John Wiley & Sons, Inc.     

The single server queue in discrete time-numerical analysis I

This is the first of a sequence of papers dealing with the computational aspects of the transient behavior of queues in discrete time It is shown that for a substantial class of queues of practical interest, a wealth of numerical information may be obtained by relatively unsophisticated methods This approach should prove useful in the analysis of unstable queues which operate over a limited time interval, but is by no means limited to such queues Mathematically the service unit is modeled in terms of a multivariate Markov chain, whose particular structure is used in iterative computation. Many important queue features may then be derived from the n-step transition probabilities of this chain.     

相依目标群状态转移概率矩阵的特性及其应用

本文对相依目标群的状态转移概率矩阵的性质进行了深入的分析,得到了若干重要结论,并在此基础上讨论了相依目标群系统的火力分配模型     

一种基于SVD的非平稳信号重叠分段降噪算法

在分析基于SVD的平稳信号降噪原理的基础上,提出了一种基于SVD的非平稳信号重叠分段降噪算法.非平稳信号通过数据分段可近似处理为多段平稳信号.为降低连续分段降噪误差,进行一定比例的重叠分段,应用基于SVD的平稳信号降噪方法对各分段信号进行降噪,相邻段之间的重叠信号经过多次降噪后求平均得到最终降噪信号.仿真结果表明,该算...     

Optimizing search with positive information feedback

A search model is formulated in which positive information may be obtained, through the detection of trails, as to the target's earlier whereabouts. The corresponding Bayesian update formulas for target location probabilities are derived. The model does not appear to be amenable to rigorous optimization. A moving-horizon rule, and a heuristic simplification thereof, are, however, derived. In two numerical examples it is demonstrated that actively designing for detecting trail information, through use of these moving-horizon rules, has substantial potential advantage over using, for example, myopic rules even if the positive information is adaptively incorporated into location probabilities before applying the latter rules in each time period.     

On the reduction of total‐cost and average‐cost MDPs to discounted MDPs

This article provides conditions under which total‐cost and average‐cost Markov decision processes (MDPs) can be reduced to discounted ones. Results are given for transient total‐cost MDPs with transition rates whose values may be greater than one, as well as for average‐cost MDPs with transition probabilities satisfying the condition that there is a state such that the expected time to reach it is uniformly bounded for all initial states and stationary policies. In particular, these reductions imply sufficient conditions for the validity of optimality equations and the existence of stationary optimal policies for MDPs with undiscounted total cost and average‐cost criteria. When the state and action sets are finite, these reductions lead to linear programming formulations and complexity estimates for MDPs under the aforementioned criteria.© 2017 Wiley Periodicals, Inc. Naval Research Logistics 66:38–56, 2019     

Partially controlled demand and inventory control: An additive model

The primary goal of this paper is to establish properties of the inventory and advertising policy minimizing the expected discounted cost over a finite horizon in a dynamic nonstationary inventory model with random demand which is influenced by the level of goodwill. Under linearization of the cost associated with the maximum inventory and the advertising effect on demand, the model is shown to be equivalent to an inventory model with disposal. Many results of this paper are extended to cover convex ordering cost of inventory and time lag in delivery of stocks.     

A generalized assignment model for dynamic supply chain capacity planning

We consider a generalization of the well‐known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single‐period assignment costs and agent‐capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single‐period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation‐based heuristic as well as a branch‐and‐bound algorithm for MultiGAP. Computational experience with the heuristic and branch‐and‐bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high‐quality and in many cases near‐optimal solutions. The branch‐and‐bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Fluctuations of the optimal advertising and inventory policy: A qualitative analysis

This paper discusses the properties of the inventory and advertising policy minimizing the expected discounted cost over a finite horizon in a dynamic nonstationary inventory model with random demand which is influenced by the level of promotion or goodwill. Attention is focused on the relation between the fluctuations over time of the optimal policies and the variations over time of the factors involved, i.e., demand distributions and various costs. The optimal policies are proved to be monotone in the various factors. Also, three types of fluctuations over time of the optimal policies are discussed according to which factor varies over time. For example, if over a finite interval, the random demand increases (stochastically) from one period to the next, reaches a maximum and then decreases, then the optimal inventory level will do the same. Also the period of maximum of demand never precedes that of maximum inventory. The optimal advertising behaves in the opposite way and its minimum will occur at the same time as the maximum of the inventory. The model has a linear inventory ordering cost and instantaneous delivery of stocks; many results, however, are extended to models with a convex ordering cost or a delivery time lag.     

A dynamic,nonstationary inventory problem for a price/quantity setting firm

A dynamic and nonstationary model is formulated for a firm which attempts to minimize total expected costs over a finite planning horizon. The control variables are price and production. The price p and the demand ζ are linked through the relationship ζ = g(p) + η, where g(p) is the riskless demand curve and η is a random variable. The general model allows for proportional ordering costs, convex holding and stockout costs, downward sloping riskless demand curve, backlogging, partial backlogging, lost sales, partial spoilage of inventory, and two modes of collecting revenue. Sufficient conditions are developed for this problem to have an optimal policy which resembles the single critical number policy known from stochastic inventory theory. It is also shown what set of parameters will satisfy these sufficiency conditions.     

Inspection games with local and global allocation bounds

This article discusses a two‐player noncooperative nonzero‐sum inspection game. There are multiple sites that are subject to potential inspection by the first player (an inspector). The second player (potentially a violator) has to choose a vector of violation probabilities over the sites, so that the sum of these probabilities do not exceed one. An efficient method is introduced to compute all Nash equilibria parametrically in the amount of resource that is available to the inspector. Sensitivity analysis reveals nonmonotonicity of the equilibrium utility of the inspector, considered as a function of the amount of resource that is available to it; a phenomenon which is a variant of the well‐known Braess paradox. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Operations analysis during the underwater search for Scorpions

This paper discusses the operations analysis in the underwater search for the remains of the submarine Scorpion The a priori target location probability distribution for the search was obtained by monte-carlo procedures based upon nine different scenarios concerning the Scorpion loss and associated credibility weights. These scenarios and weights were postulated by others. Scorpion was found within 260 yards of the search grid cell having the largest a priori probability Frequent computations of local effectiveness probabilities (LEPs) were carried out on scene during the search and were used to determine an updated (a posteriori) target location distribution. This distribution formed the basis for recommendation of the current high probability areas for search The sum of LEPs weighted by the a priori target location probabilities is called search effectiveness probability (SEP) and was used as the overall measure of effectiveness for the operation. SEP and LEPs were used previously in the Mediterranean H-bomb search On-scene and stateside operations analysis are discussed and the progress of the search is indicated by values of SEP for various periods during the operation.     

The cyclic separation scheduling problem

This paper deals with the problem of scheduling items (tasks, employees, equipment, etc.) over a finite time horizon so as to minimize total cost expenditures while maintaining a predefined separation between certain items. The problem is cyclic, because the same schedule will be repeated over several consecutive time periods of equal length. Thus, requirements are present to maintain the separation of items not only within the individual time periods considered, but also between items in adjoining periods. A special purpose branch-and-bound algorithm is developed to solve this scheduling problem by taking advantage of its cyclic nature. Computational results are given.     

Discrete compound poisson processes and tables of the geometric poisson distribution

This paper discusses the properties of positive, integer valued compound Poisson processes and compares two members of the family: the geometric Poisson (stuttering Poisson) and the logarithmic Poisson. It is shown that the geometric Poisson process is particularly convenient when the analyst is interested in a simple model for the time between events, as in simulation. On the other hand, the logarithmic Poisson process is more convenient in analytic models in which the state probabilities (probabilities for the number of events in a specified time period) are required. These state probabilities have a negative binomial distribution. The state probabilities of the geometric Poisson process, known as the geometric Poisson distribution, are tabled for 160 sets of parameter values. The values of mean demand range from 0.10 to 10; those for variance to mean ratio from 1.5 to 7. It is observed that the geometric Poisson density is bimodal.