Probabilistic solution and bounds for serial inventory systems with discounted and average costs

We consider the infinite horizon serial inventory system with both average cost and discounted cost criteria. The optimal echelon base‐stock levels are obtained in terms of only probability distributions of leadtime demands. This analysis yields a novel approach for developing bounds and heuristics for optimal inventory control polices. In addition to deriving the known bounds in literature, we develop several new upper bounds for both average cost and discounted cost models. Numerical studies show that the bounds and heuristic are very close to optimal.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Approximation algorithms for capacitated stochastic inventory systems with setup costs

We develop the first approximation algorithm with worst‐case performance guarantee for capacitated stochastic periodic‐review inventory systems with setup costs. The structure of the optimal control policy for such systems is extremely complicated, and indeed, only some partial characterization is available. Thus, finding provably near‐optimal control policies has been an open challenge. In this article, we construct computationally efficient approximate optimal policies for these systems whose demands can be nonstationary and/or correlated over time, and show that these policies have a worst‐case performance guarantee of 4. We demonstrate through extensive numerical studies that the policies empirically perform well, and they are significantly better than the theoretical worst‐case guarantees. We also extend the analyses and results to the case with batch ordering constraints, where the order size has to be an integer multiple of a base load. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 304–319, 2014     

准静态受遮蔽的Rician衰落信道中空时格码的性能上界

针对准静态受遮蔽的 Rician 衰落信道,在收端已知信道状态信息的条件下,文中分析了空时格码的性能.推导了码字差相关阵为对角阵的空时格码系统的成对差错概率的确切表达式,得到了相应空时格码在准静态受遮蔽的 Rician 衰落信道中的性能上界。仿真结果表明,在遮蔽不太严重的信道中,文中得到的 union 界与相应编码系统的实际性能有很好的近似度。     

Newsvendor bounds and heuristics for serial supply chains with regular and expedited shipping

We study an infinite‐horizon, N‐stage, serial production/inventory system with two transportation modes between stages: regular shipping and expedited shipping. The optimal inventory policy for this system is a top–down echelon base‐stock policy, which can be computed through minimizing 2N nested convex functions recursively (Lawson and Porteus, Oper Res 48 (2000), 878–893). In this article, we first present some structural properties and comparative statics for the parameters of the optimal inventory policies, we then derive simple, newsvendor‐type lower and upper bounds for the optimal control parameters. These results are used to develop near optimal heuristic solutions for the echelon base‐stock policies. Numerical studies show that the heuristic performs well. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Sharp bounds for the reliability of systems and mixtures with ordered components

In this article, we study how to derive bounds for the reliability and the expected lifetime of a coherent system with heterogeneous ordered components. These bounds can be used to compare the performance of the systems obtained by permuting the components at a given system structure, that is, to study where we should place the different components at a system structure to get the most reliable system. Moreover, a similar procedure is applied to get bounds for mixtures and for the generalized proportional hazard rate model when the baseline populations are ordered. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 108–116, 2017     

Minimizing makespan in a multimode multiprocessor shop scheduling problem

We study the problem of multimode scheduling tasks on dedicated processors, with the objective of minimizing the maximum completion time. Each task can be undertaken in one among a set of predefined alternative modes, where each mode specifies a required set of dedicated processors and a processing time. At any time each processor can be used by a single task at most. General precedence constraints exist among tasks, and task preemption is not allowed. The problem consists of assigning a mode and a starting time to each task, respecting processor and precedence constraints, to minimize the time required to complete all tasks. The problem is NP-hard in several particular cases. In previous works, we studied algorithms in which a solution was obtained by means of an iterative procedure that combines mode assignment and sequencing phases separately. In this paper, we present some new heuristics where the decision on the mode assignment is taken on the basis of a partial schedule. Then, for each task, the mode selection and the starting time are chosen simultaneously considering the current processor usage. Different lower bounds are derived from a mathematical formulation of the problem and from a graph representation of a particular relaxed version of the problem. Heuristic solutions and lower bounds are evaluated on randomly generated test problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 893–911, 1999     

On a class of multiple failure mode systems

The primary objective of this work is to introduce and perform a detailed study of a class of multistate reliability structures in which no ordering in the levels of components' performances is necessary. In particular, the present paper develops the basic theory (exact reliability formulae, reliability bounds, asymptotic results) that will make it feasible to investigate systems whose components are allowed to experience m ≥ 2 kinds of failure (failure modes), and their breakdown is described by different families of cut sets in each mode. For illustration purposes, two classical (binary) systems are extended to analogous multiple failure mode structures, and their reliability performance (bounds and asymptotic behavior) is investigated by numerical experimentation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 167–185, 2002; DOI 10.1002/nav.10007     

Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems

Assemble‐to‐order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order‐based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein–Chen approximation as well as its error‐bound for order‐based fill rate for a multiproduct multicomponent ATO system with random leadtimes to replenish components. This approximation gives an expression for order‐based fill rate in terms of component‐based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement in order‐based fill rates when the base‐stock level for any component changes. Numerical studies demonstrate that the approximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base‐stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r,s)‐out‐of‐(m,n):F system

A 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system consists of m × n components, and fails if and only if k or more components fail in an r × s submatrix. This system can be treated as a reliability model for TFT liquid crystal displays, wireless communication networks, etc. Although an effective method has been developed for evaluating the exact system reliability of small or medium‐sized systems, that method needs extremely high computing time and memory capacity when applied to larger systems. Therefore, developing upper and lower bounds and accurate approximations for system reliability is useful for large systems. In this paper, first, we propose new upper and lower bounds for the reliability of a 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system. Secondly, we propose two limit theorems for that system. With these theorems we can obtain accurate approximations for system reliabilities when the system is large and component reliabilities are close to one. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

A heuristic for maximizing the number of on‐time jobs on two uniform parallel machines

We consider the problem of maximizing the number of on‐time jobs on two uniform parallel machines. We show that a straightforward extension of an algorithm developed for the simpler two identical parallel machines problem yields a heuristic with a worst‐case ratio bound of at least . We then show that the infusion of a “look ahead” feature into the aforementioned algorithm results in a heuristic with the tight worst‐case ratio bound of , which, to our knowledge, is the tightest worst‐case ratio bound available for the problem. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006