Some order relations in closed networks of queues with multiserver stations

Consider a closed network of queues of the “product-form” type, where each station has s servers (s ≥ 1 is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.     

Probabilistic partial set covering problems

In this article, we consider a situation in which a group of facilities need to be constructed in order to serve a given set of customers. However, the facilities cannot guarantee an absolute coverage to any of the customers. Hence, we formulate this problem as one of maximizing the total service reliability of the system subject to a budgetary constraint. For this problem, we develop and test suitable branch-and-bound algorithms and study the effect of problem parameters on solution difficulty. Some generalizations of this problem are also mentioned as possible extensions.     

A nested benders decomposition approach for telecommunication network planning

Despite its ability to result in more effective network plans, the telecommunication network planning problem with signal‐to‐interference ratio constraints gained less attention than the power‐based one because of its complexity. In this article, we provide an exact solution method for this class of problems that combines combinatorial Benders decomposition, classical Benders decomposition, and valid cuts in a nested way. Combinatorial Benders decomposition is first applied, leading to a binary master problem and a mixed integer subproblem. The subproblem is then decomposed using classical Benders decomposition. The algorithm is enhanced using valid cuts that are generated at the classical Benders subproblem and are added to the combinatorial Benders master problem. The valid cuts proved efficient in reducing the number of times the combinatorial Benders master problem is solved and in reducing the overall computational time. More than 120 instances of the W‐CDMA network planning problem ranging from 20 demand points and 10 base stations to 140 demand points and 30 base stations are solved to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Inventory policies for a make‐to‐order system with a perishable component and fixed ordering cost

We consider a make‐to‐order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s_n,S,S) policy is optimal. Under this policy, S along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s_n,S) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Detection of a Markovian target with optimization of the search efforts under generalized linear constraints

This paper deals with search for a target following a Markovian movement or a conditionally deterministic motion. The problem is to allocate the search efforts, when search resources renew with generalized linear constraints. The model obtained is extended to resource mixing management. New optimality equations of de Guenin's style are obtained. Practically, the problem is solved by using an algorithm derived from the FAB method. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 117–142, 2002; DOI 10.1002/nav.10009     

Inventory control under substitutable demand: A stochastic game application

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018     

A branch‐and‐cut algorithm for the quay crane scheduling problem in a container terminal

The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch‐and‐cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

We consider an integrated usage and maintenance optimization problem for a k‐out‐of‐n system pertaining to a moving asset. The k‐out‐of‐n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircraft, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 418–434, 2017     

Degeneracy in inventory models

In order‐quantity reorder‐point formulations for inventory items where backordering is allowed, some of the more common ways to prevent excessive stockouts in an optimal solution are to impose either a cost per unit short, a cost per stockout occasion, or a target fill rate. We show that these popular formulations, both exact and approximate, can become “degenerate” even with quite plausible parameters. By degeneracy we mean any situation in which the formulation either cannot be solved, leads to nonsensical “optimal” solutions, or becomes equivalent to something substantially simpler. We explain the reasons for the degeneracies, yielding new insight into these models, and we provide practical advice for inventory managers. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 686–705, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10037     

Warranty reserves for nonstationary sales processes

Estimation of warranty costs, in the event of product failure within the warranty period, is of importance to the manufacturer. Costs associated with replacement or repair of the product are usually drawn from a warranty reserve fund created by the manufacturer. Considering a stochastic sales process, first and second moments (and thereby the variance) are derived for the manufacturer's total discounted warranty cost of a single sale for single‐component items under four different warranty policies from a manufacturer's point of view. These servicing strategies represent a renewable free‐replacement, nonrenewable free‐replacement, renewable pro‐rata, and a nonrenewable minimal‐repair warranty plans. The results are extended to determine the mean and variance of total discounted warranty costs for the total sales over the life cycle of the product. Furthermore, using a normal approximation, warranty reserves necessary for a certain protection level, so that reserves are not completely depleted, are found. Results and their managerial implications are studied through an extensive example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 499–513, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10023