This paper presents a specialized algorithm for the transshipment along a single road problem. The problem is a specially structured network flow problem. For larger problems, the specialized algorithm is in excess of a hundred times faster than the primal simplex method on a graph.
{"title":"An efficient algorithm for the transshipment along a single road problem","authors":"A. Ali","doi":"10.1002/NAV.3800330411","DOIUrl":"https://doi.org/10.1002/NAV.3800330411","url":null,"abstract":"This paper presents a specialized algorithm for the transshipment along a single road problem. The problem is a specially structured network flow problem. For larger problems, the specialized algorithm is in excess of a hundred times faster than the primal simplex method on a graph.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128508227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article proposes a modified preventive maintenance (PM) policy which may be done only at scheduled times nT (n = 1,2, …): The PM is done at the next such time if and only if the total number of failures exceeds a specified number k. The optimal number k* to minimize the expected cost rate is discussed. Further, four alternative similar PM models are considered, when the system fails due to a certain number of faults, uses, shocks, and unit failures.
{"title":"Modified discrete preventive maintenance policies","authors":"T. Nakagawa","doi":"10.1002/NAV.3800330413","DOIUrl":"https://doi.org/10.1002/NAV.3800330413","url":null,"abstract":"This article proposes a modified preventive maintenance (PM) policy which may be done only at scheduled times nT (n = 1,2, …): The PM is done at the next such time if and only if the total number of failures exceeds a specified number k. The optimal number k* to minimize the expected cost rate is discussed. Further, four alternative similar PM models are considered, when the system fails due to a certain number of faults, uses, shocks, and unit failures.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127795181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic models are developed for a weapon system which attacks at a certain rate, but withdraws when attacked (guerrilla warfare). The models yield as output the distributions and mean values in closed form of the survival period and number of attacks made. As input are, for the weapon system, attack rate or amount of ammunition and time horizon, and, for the opponent, kill rate and probability of killing the weapon system, given the opponent has been attacked (strike back performance of the opponent). One model allows, however, for strike back also by the weapon system, when attacked by the opponent. This model is then used to determine, when the weapon system should strike back. The models are based on the Poisson and the binomial processes. Consistency among the models is shown and an example is provided.
{"title":"Survival and effectiveness of a weapon system against a superior force (guerrilla warfare)","authors":"N. Bache","doi":"10.1002/NAV.3800330408","DOIUrl":"https://doi.org/10.1002/NAV.3800330408","url":null,"abstract":"Stochastic models are developed for a weapon system which attacks at a certain rate, but withdraws when attacked (guerrilla warfare). The models yield as output the distributions and mean values in closed form of the survival period and number of attacks made. As input are, for the weapon system, attack rate or amount of ammunition and time horizon, and, for the opponent, kill rate and probability of killing the weapon system, given the opponent has been attacked (strike back performance of the opponent). One model allows, however, for strike back also by the weapon system, when attacked by the opponent. This model is then used to determine, when the weapon system should strike back. The models are based on the Poisson and the binomial processes. Consistency among the models is shown and an example is provided.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122495615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A capacity expansion model with multiple facility types is examined, where different facility types represent different quality levels. Applications for the model can be found in communications networks and production facilities. The model assumes a finite number of discrete time periods. The facilities are expanded over time. Capacity of a high‐quality facility can be converted to satisfy demand for a lower‐quality facility. The costs considered include capacity expansion costs and excess capacity holding costs. All cost functions are nondecreasing and concave. An algorithm that finds optimal expansion policies requires extensive computations and is practical only for small scale problems. Here, we develop a heuristic that employs so‐called distributed expansion policies. It also attempts to decompose the problem into several smaller problems solved independently. The heuristic is computationally efficient. Further, it has consistently found near‐optimal solutions.
{"title":"A heuristic for capacity expansion planning with multiple facility types","authors":"H. Luss","doi":"10.1002/NAV.3800330412","DOIUrl":"https://doi.org/10.1002/NAV.3800330412","url":null,"abstract":"A capacity expansion model with multiple facility types is examined, where different facility types represent different quality levels. Applications for the model can be found in communications networks and production facilities. The model assumes a finite number of discrete time periods. The facilities are expanded over time. Capacity of a high‐quality facility can be converted to satisfy demand for a lower‐quality facility. The costs considered include capacity expansion costs and excess capacity holding costs. All cost functions are nondecreasing and concave. An algorithm that finds optimal expansion policies requires extensive computations and is practical only for small scale problems. Here, we develop a heuristic that employs so‐called distributed expansion policies. It also attempts to decompose the problem into several smaller problems solved independently. The heuristic is computationally efficient. Further, it has consistently found near‐optimal solutions.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134143098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.
{"title":"The procurement problem: An integer programming problem well suited to a solution using duality","authors":"E. Gunn, A. Kusiak","doi":"10.1002/NAV.3800330407","DOIUrl":"https://doi.org/10.1002/NAV.3800330407","url":null,"abstract":"A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122263661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Degeneracy in linear programming models has been analyzed for its impacts on algorithmic properties. A complementary analysis here is on what the solutions mean. The framework presented is couched in marginal sensitivity analysis, introducing concepts of “compatible bases” and “transition graphs”.
{"title":"An analysis of degeneracy","authors":"H. J. Greenberg","doi":"10.1002/NAV.3800330409","DOIUrl":"https://doi.org/10.1002/NAV.3800330409","url":null,"abstract":"Degeneracy in linear programming models has been analyzed for its impacts on algorithmic properties. A complementary analysis here is on what the solutions mean. The framework presented is couched in marginal sensitivity analysis, introducing concepts of “compatible bases” and “transition graphs”.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130899379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a framework in which warranty policies for non‐repairable items can be evaluated according to risk preferences of both buyers and sellers. In particular, a warranty price schedule is established such that sellers are indifferent among the policies. Given this schedule, a buyer's response is expressed by selecting the price‐warranty combination that minimizes disutility. Within this framework, a warranty can be viewed as an instrumet of risk management that can induce more sales and greater profitability. For given utility functions, analytical results for the development of a price schedule are developed. Numerical results illustrate the substitution effects between warranty terms, prices, and risk parameters.
{"title":"Warranty design under buyer and seller risk aversion","authors":"P. Ritchken, C. Tapiero","doi":"10.1002/NAV.3800330410","DOIUrl":"https://doi.org/10.1002/NAV.3800330410","url":null,"abstract":"This paper provides a framework in which warranty policies for non‐repairable items can be evaluated according to risk preferences of both buyers and sellers. In particular, a warranty price schedule is established such that sellers are indifferent among the policies. Given this schedule, a buyer's response is expressed by selecting the price‐warranty combination that minimizes disutility. Within this framework, a warranty can be viewed as an instrumet of risk management that can induce more sales and greater profitability. For given utility functions, analytical results for the development of a price schedule are developed. Numerical results illustrate the substitution effects between warranty terms, prices, and risk parameters.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"256 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122877900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider a fleet of vehicles comprised of K1 identical tankers and K2 identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K2 nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K1 refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.
{"title":"Optimal refueling sequence for a mixed fleet with limited refuelings","authors":"A. Melkman, H. Stern, A. Mehrez","doi":"10.1002/NAV.3800330418","DOIUrl":"https://doi.org/10.1002/NAV.3800330418","url":null,"abstract":"Consider a fleet of vehicles comprised of K1 identical tankers and K2 identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K2 nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K1 refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133149752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On presente une methode branch and bound pour resoudre le probleme de la minimisation d'une fonction concave separable sur un ensemble polyedral convexe ou les variables sont contraintes a etre entieres. On donne des resultats de calcul
提出了一种分支定界方法，解决了变量约束为整数的凸多面体上可分离凹函数的最小化问题。给出了计算结果
{"title":"A branch and bound algorithm for solving a class of nonlinear integer programming problems","authors":"A. Cabot, S. Erenguc","doi":"10.1002/NAV.3800330403","DOIUrl":"https://doi.org/10.1002/NAV.3800330403","url":null,"abstract":"On presente une methode branch and bound pour resoudre le probleme de la minimisation d'une fonction concave separable sur un ensemble polyedral convexe ou les variables sont contraintes a etre entieres. On donne des resultats de calcul","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132117403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.
{"title":"Optimal replacement for fault‐tolerant systems","authors":"H. M. Taylor, Beatriz E. Rodriguez","doi":"10.1002/NAV.3800330417","DOIUrl":"https://doi.org/10.1002/NAV.3800330417","url":null,"abstract":"We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115108934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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