Showing papers in "Naval Research Logistics in 1992"
TL;DR: In this paper, the leader's objective function is converted into a parameterized constraint, and then the resulting problem is solved to find a point in the feasible reagion, which leads to a global optimum.
Abstract: The bilevel programming problem (BLPP) is an example of a two-stage, noncooperative game in which the first player can influence but not control the actions of the second. This article addresses the linear formulation and presents a new algorithm for solving the zero-one case. We begin by converting the leader's objective function into a parameterized constraint, and then attempt to solve the resultant problem. This produces a candidate solution that is used to find a point in the BLPP feasible reagion. Incremental improvements are sought, which ultimately lead to a global optimum. An example is presented to highlight the computations and to demonstrate some basic characteristics of the solution. Computational experience indicates that the algorithm is capable of solving problems with up to 50 variables in a reasonable amount of time.
146 citations
TL;DR: In this article, a branch-and-bound algorithm for minimizing total tardiness with unequal release dates has been proposed, where each job has to be scheduled on a machine able to perform only one job at a time and no preemptive job is allowed.
Abstract: This article deals with the scheduling problem for minimizing total tardiness with unequal release dates. A set of jobs have to be scheduled on a machine able to perform only one job at a time. No preemptive job is allowed. This problem has been proven to be NP-hard. We prove some dominance properties, and provide a lower bound polynomially computed for this problem. On the basis of our previous results, we propose a branch-and-bound algorithm to solve the problem. This algorithm was tested on hard problems involving 30 jobs and also on relatively easy problems with up to 230 jobs. Detailed computational results are given.
126 citations
TL;DR: In this paper, the authors developed approximations to estimate the expected backorders in a multiechelon system in which lateral supply actions between bases are allowed when a backorder occurs.
Abstract: We develop approximations to estimate the expected backorders in a multiechelon system in which lateral supply actions between bases are allowed when a backorder occurs. These approximations are easy to compute, and the average absolute error over a wide range of parameter values is less than 4% when items are depot repairable, even when bases are dissimilar. With lateral supply, backorder reductions of 30-50% are not uncommon, and a 72% reduction was observed in two cases. Lateral supply becomes more important with low demand rates. A similar approach was unsuccessful for base-repairable items. However, lateral supply has a beneficial effect only when the lateral supply time is very short, 1/4 or less of the average base repair time. Even in such cases lateral supply is unlikely to be important in an actual application, because base management can expedite repair of critical items.
97 citations
TL;DR: In this paper, the basis structure of the linear relaxation of the generalized assignment problem is examined and a simple heuristic that uses only generalized network optimization codes is presented, where the violated inequalities are found directly from the relaxation basis.
Abstract: We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where the violated inequalities are found directly from the relaxation basis. An improvement heuristic with the same flavor is also presented.
95 citations
92 citations
TL;DR: This work proposes a new dual-based solution procedure for TUFLP that can be used as a heuristic or incorporated into branch-and-bound procedures to obtain optimal solutions to T UFLP.
Abstract: The two-echelon uncapacitated facility location problem (TUFLP) is a generalization of the uncapacitated facility location problem (UFLP) and multiactivity facility location problem (MAFLP). In TUFLP there are two echelons of facilities through which products may flow in route to final customers. The objective is to determine the least-cost number and locations of facilities at each echelon in the system, the flow of product between facilities, and the assignment of customers to supplying facilities. We propose a new dual-based solution procedure for TUFLP that can be used as a heuristic or incorporated into branch-and-bound procedures to obtain optimal solutions to TUFLP. The algorithm is an extension of the dual ascent and adjustment procedures developed by Erlenkotter for UFLP. We report computational experience gained by solving over 420 test problems. The largest problems solved have 25 possible facility locations at each echelon and 35 customer zones, implying 650 integer variables and 21,875 continuous variables.
89 citations
TL;DR: In this article, the authors introduced a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure, which is proven to be NP-hard.
Abstract: This article introduces a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure This quadratic minimum spanning tree problem is proven to be NP-hard A technique for generating lower bounds for this problem is discussed and incorporated into branch-and-bound schemes for obtaining exact solutions Two heuristic algorithms are also developed Computational experience with both exact and heuristic algorithms is reported
85 citations
TL;DR: Heuristics for the problems of minimizing maximum lateness with dynamic arrivals and minimizing number of tardy jobs are presented and special problem structure is exploited to derive worst-case error bounds.
Abstract: We examine a class of single-machine scheduling problems with sequence-dependent setup times that arise in the context of semiconductor test operations. We present heuristics for the problems of minimizing maximum lateness with dynamic arrivals and minimizing number of tardy jobs. We exploit special problem structure to derive worst-case error bounds. The special problem structure also enables us to derive dynamic programming procedures for the problems where all jobs are available simultaneously.
83 citations
TL;DR: In this paper, the authors give a full analysis of a component-replacement model in which preventive replacements are only possible at maintenance opportunities, and conditions for the existence of a unique average optimal control limit policy are established and an equation characterizing the optimal policy and minimal average costs is derived.
Abstract: textThis article gives a full analysis of a component-replacement model in which preventive replacements are only possible at maintenance opportunities. These oppertunities arise according to a Poisson process, independently of failures of the component. Conditions for the existence of a unique average optimal control limit policy are established and an equation characterizing the optimal policy and minimal average costs is derived. An important result is that the optimal policy can be described as a so-called one-opportunity-look-ahead policy. Such policies play an important role as heuristic in more gernal models. It is shown that there is a correspondence with the will-known age-replacement model, which can be considered as an extreme case of the model. Finally, some numerical results are given.
69 citations
TL;DR: An approximate cost function and service level constraint is formulated, a greedy heuristic algorithm is presented for solving the resulting approximate constrained optimization problem, and experimental results showing that the heuristics developed have good cost performance relative to optimal are presented.
Abstract: Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (siSi) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.
64 citations
TL;DR: A mathematical-programming-based approach to solve the classification problem in discriminant analysis which explicitly considers the classification gap and appears to be more robust than other classification techniques with respect to outlier-contaminated data conditions.
Abstract: This article proposes a mathematical-programming-based approach to solve the classification problem in discriminant analysis which explicitly considers the classification gap. The procedure consists of two distinct phases and initially treats the classification gap as a fuzzy set in which the classification rule is not yet established. The nature of the classification gap is examined and a variety of methods are discussed which can be applied to identify the most appropriate classification rule over the fuzzy set. The proposed methodology has several potential advantages. First, it offers a more refined approach to the classification problem, facilitating careful analysis of the fuzzy region where the classification decision may not be obvious. Secondly, the two-phase approach enables the analysis of larger data sets when using computer-intensive procedures such as mixed-integer programming. Finally, because of the restricted choice of separating hyperplanes in phase 2, the approach appears to be more robust than other classification techniques with respect to outlier-contaminated data conditions. The robustness issue and computational advantage of our proposed methodology are illustrated using a limited simulation experiment.
TL;DR: In this paper, the authors studied (nQ, r) inventory policies, under which the order quantity is restricted to be an integer multiple of a base lot size, and the decision variables are decision variables.
Abstract: This article studies (nQ, r) inventory policies, under which the order quantity is restricted to be an integer multiple of a base lot size Q. Both Q and r are decision variables. Assuming the one-period expected holding and backorder cost function is unimodal, we develop an efficient algorithm to compute the optimal Q and r. The algorithm is facilitated by simple observations about the cost function and by tight upper bounds on the optimal Q. The total number of elementary operations required by the algorithm is linear in these upper bounds. By using the algorithm, we compare the performance of the optimal (nQ, r) policy with that of the optimal (s, S) policy through a numerical study, and our results show that the difference between them is small. Further analysis of the model shows that the cost performance of an (nQ, r) policy is insensitive to the choice of Q. These results establish that (nQ, r) models are potentially useful in many settings where quantized ordering is beneficial.
TL;DR: This article presents a branching algorithm with effective dominance rules to obtain the optimal schedule for replacements to minimize the total cost for a given planning period.
Abstract: The problem of imperfect preventive maintenance (pm) and replacement schedule for a system which works below a specified failure rate is studied. For a given planning period, the optimal schedule for replacements to minimize the total cost is obtained. This article presents a branching algorithm with effective dominance rules to obtain the optimal schedule. Numerical illustration and computational experience are also presented.
TL;DR: In this article, a branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme, which substantially dominate several other upper bounds that are derived using standard techniques as problem size increases.
Abstract: This article is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.
TL;DR: This article presents a label-correcting procedure for determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it and develops two pruning techniques, which are able to speed up the label-Correcting procedure by many orders of magnitude.
Abstract: In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest-path problems. We present a label-correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label-correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label-correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time. © 1992 John Wiley & Sons, Inc.
TL;DR: In this article, the problem of scheduling m items, facing constant demand rates, on a single facility to minimize the long-run average holding, backorder, and setup costs is considered.
Abstract: We are concerned with the problem of scheduling m items, facing constant demand rates, on a single facility to minimize the long-run average holding, backorder, and setup costs. The inventory holding and backlogging costs are charged at a linear time weighted rate. We develop a lower bound on the cost of all feasible schedules and extend recent developments in the economic lot scheduling problem, via time-varying lot sizes, to find optimal or near-optimal cyclic schedules. The resulting schedules are used elsewhere as target schedules when demands are random. © 1992 John Wiley & Sons, Inc.
TL;DR: In this article, the effect of increasing component commonality in an assemble-to-order system was investigated, and it was shown that the optimal holding cost for a given service level is concave in the level of commonality.
Abstract: We investigate the effect of increasing component commonality in an assemble-to-order system. Numerical investigation of two end products that share up to three components, and whose demands are identically distributed according to either the exponential or the geometric distribution, shows that increasing component commonality results in increasing marginal returns when the criteria are aggregate service level and aggregate stock requirement. For arbitrary end-product demands and general service measures, it is shown that the optimal holding cost for a given service level is concave in the level of commonality. © 1992 John Wiley & Sons, Inc.
TL;DR: This work uses a parametric analysis to establish sufficient conditions for the optimality of control limit policies and generalizes several existing results for optimal replacement models in the literature.
Abstract: We study a class of replacement models for systems subject to deterioration. The objective is to determine an optimal replacement policy that minimizes the average operating costs of the system. We use a parametric analysis to establish sufficient conditions for the optimality of control limit policies. This work generalizes several existing results for optimal replacement models in the literature. © 1992 John Wiley & Sons, Inc.
TL;DR: In this paper, the exact steady-state customer-delay distribution for both the warehouse and the retailer locations is derived for a two-echelon inventory system where the exogenous demands occur only at the retailers locations, and the demand rates are functions of an underlying continuous-time Markov chain.
Abstract: We consider a two-echelon inventory system where the exogenous demands occur only at the retailer locations, and the demand rates are functions of an underlying continuous-time Markov chain. This underlying process may represent, for example, general economic conditions, the number of active users in the system, et cetera. Each retailer location follows a base-stock policy that is independent of the process. However, the warehouse (central depot) follows a state-dependent base-stock policy. We develop a procedure to compute the exact steady-state customer-delay distribution for both the warehouse and the retailer locations.
TL;DR: In this article, control-variate selection criteria that minimize mean-square confidence region volume were proposed for multiresponse simulations requiring point and confidence region estimators of the mean response.
Abstract: For multiresponse simulations requiring point and confidence-region estimators of the mean response, we propose control-variate selection criteria that minimize mean-square confidence-region volume in two situations: (a) Only the mean control vector is known, and standard linear control-variate estimation procedures are used. (b) Covariances among controls are also known and are incorporated into new linear control-variate estimation procedures. An example illustrates the performance of these selection criteria.
TL;DR: In this article, necessary and sufficient conditions are specified for a general theory of additive measurement that presumes very little set-theoretic structure and is illustrated for numerical representations in extensive, conjoint, difference, threshold, expected utility, probability, ambiguity, and subset measurement.
Abstract: Necessary and sufficient conditions are specified for a general theory of additive measurement that presumes very little set-theoretic structure. The theory is illustrated for numerical representations in extensive, conjoint, difference, threshold, expected utility, probability, ambiguity, and subset measurement. © 1992 John Wiley & Sons, Inc.
TL;DR: Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels and on the degree of dependence of the components based on a two-component parallel system with possibly dependent component lifetimes.
Abstract: We consider the following replacement model in reliability theory. A technical system with random lifetime is replaced upon failure. Preventive replacements can be carried out before failure. The time for such a replacement depends on the observation of a random state parameter and is therefore in general a random time. Different costs for preventive and failure replacements are introduced which may depend on the age of the working system. The optimization criterion followed here to find an optimal replacement time is to minimize the total expected discounted costs. The optimal replacement policy depends on the observation of the state of the system. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Several examples based on a two-component parallel system with possibly dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components. © 1992 John Wiley & Sons, Inc.
TL;DR: In this paper, it was shown that the deterministic non-preemptive scheduling problem with earliness and tardiness penalties can be solved in polynomial time for certain forms of an objective function provided that a certain optimization problem is solved.
Abstract: We show that the deterministic nonpreemptive scheduling problem with earliness and tardiness penalties can be solved in polynomial time for certain forms of an objective function provided that a certain optimization problem can be solved. We give instances where this problem has a solution and show that this generalizes several results from the literature. These results do not require symmetric penalization and the penalty functions need only be lower semicontinuous.
TL;DR: In this article, a new approach for inference from accelerated life tests is presented based on a dynamic general linear model setup which arises naturally from the accelerated life testing problem and uses linear Bayesian methods for inference.
Abstract: : We present a new approach for inference from accelerated life tests. Our approach is based on a dynamic general linear model setup which arises naturally from the accelerated life testing problem and uses linear Bayesian methods for inference. The advantage of the procedure is that it does not require large number of items to be tested and that it can deal with both censored and uncensored data. Furthermore, the approach produces closed form inference results. We illustrate the use of our approach with some actual accelerated life test data. (AN)
TL;DR: The steady-state workload at an arbitrary time is considered for several single-server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times.
Abstract: The steady-state workload at an arbitrary time is considered for several single-server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.