Pub Date : 2019-12-18DOI: 10.17535/CRORR.2020.0001
Mohsine Jennane, L. E. Fadil, E. Kalmoun
We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the relationship between local quasi weak efficient solutions and vector critical points.
{"title":"On local quasi efficient solutions for nonsmooth vector optimization problems","authors":"Mohsine Jennane, L. E. Fadil, E. Kalmoun","doi":"10.17535/CRORR.2020.0001","DOIUrl":"https://doi.org/10.17535/CRORR.2020.0001","url":null,"abstract":"We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the relationship between local quasi weak efficient solutions and vector critical points.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/CRORR.2020.0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47136930","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0017
Pavan Kumar
In this manuscript, a model is proposed for the inventory planning problem with items which deteriorate linearly with respect to time. The concept of salvage value for deteriorated items is considered and incorporated in this model. The solution procedure of proposed optimization model is illustrated by a couple of numerical examples. A convexity check of the average total cost function is performed by plotting a two dimensional graph. The sensitivity test of the proposed model is performed to study the effect of changing the least as well as the most sensitive parameters in the proposed optimization model. Some graphical representations are constructed to discuss the outcomes and results so obtained for a choice of various parameters
{"title":"An inventory planning problem for time-varying linear demand and parabolic holding cost with salvage value","authors":"Pavan Kumar","doi":"10.17535/crorr.2019.0017","DOIUrl":"https://doi.org/10.17535/crorr.2019.0017","url":null,"abstract":"In this manuscript, a model is proposed for the inventory planning problem with items which deteriorate linearly with respect to time. The concept of salvage value for deteriorated items is considered and incorporated in this model. The solution procedure of proposed optimization model is illustrated by a couple of numerical examples. A convexity check of the average total cost function is performed by plotting a two dimensional graph. The sensitivity test of the proposed model is performed to study the effect of changing the least as well as the most sensitive parameters in the proposed optimization model. Some graphical representations are constructed to discuss the outcomes and results so obtained for a choice of various parameters","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"187-199"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44283965","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0025
Vishnu Pratap Singh, Debjani Chakraborty
A bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of leader and follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time it is inconvenient to find the veracious relationship between the objective functions of leader, follower and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower, is composed by a block of fuzzy if-then rules. In order to analyze the model, A dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of leader as well as follower. Thus a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. To solve the final problem, we use the lingo software to find the optimal of objective function of follower first and using its solution we optimize the objective function of leader. A numerical example has been solved to signify the computational procedure.
{"title":"Bi-level optimization based on fuzzy if-then rule","authors":"Vishnu Pratap Singh, Debjani Chakraborty","doi":"10.17535/crorr.2019.0025","DOIUrl":"https://doi.org/10.17535/crorr.2019.0025","url":null,"abstract":"A bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of leader and follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time it is inconvenient to find the veracious relationship between the objective functions of leader, follower and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower, is composed by a block of fuzzy if-then rules. In order to analyze the model, A dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of leader as well as follower. Thus a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. To solve the final problem, we use the lingo software to find the optimal of objective function of follower first and using its solution we optimize the objective function of leader. A numerical example has been solved to signify the computational procedure.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"315-328"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44482229","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0019
Lahcene Yahiaoui, A. Bouchentouf, M. Kadi
This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.
{"title":"Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers","authors":"Lahcene Yahiaoui, A. Bouchentouf, M. Kadi","doi":"10.17535/crorr.2019.0019","DOIUrl":"https://doi.org/10.17535/crorr.2019.0019","url":null,"abstract":"This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"211-226"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45197214","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0018
E. Garajová, M. Hladík, M. Rada
Interval programming provides one of the modern approaches to modeling optimization problems under uncertainty. Traditionally, the best and the worst optimal values determining the optimal value range are considered as the main solution concept for interval programs. In this paper, we present the concept of semi-strong values as a generalization of the best and the worst optimal values. Semi-strong values extend the recently introduced notion of semi-strong optimal solutions, allowing the model to cover a wider range of applications. We propose conditions for testing values that are strong with respect to the objective vector, right-hand-side vector or the constraint matrix for interval linear programs in the general form.
{"title":"The best, the worst and the semi-strong: optimal values in interval linear programming","authors":"E. Garajová, M. Hladík, M. Rada","doi":"10.17535/crorr.2019.0018","DOIUrl":"https://doi.org/10.17535/crorr.2019.0018","url":null,"abstract":"Interval programming provides one of the modern approaches to modeling optimization problems under uncertainty. Traditionally, the best and the worst optimal values determining the optimal value range are considered as the main solution concept for interval programs. In this paper, we present the concept of semi-strong values as a generalization of the best and the worst optimal values. Semi-strong values extend the recently introduced notion of semi-strong optimal solutions, allowing the model to cover a wider range of applications. We propose conditions for testing values that are strong with respect to the objective vector, right-hand-side vector or the constraint matrix for interval linear programs in the general form.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"319 12","pages":"201-209"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41258876","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0021
Mohamed Saidane
This paper is concerned with the statistical modeling of the latent dependence and comovement structures of multivariate financial data using a new approach based on mixed factorial hidden Markov models, and their applications in Value-at-Risk (VaR) valuation. This approach combines hidden Markov Models (HMM) with mixed latent factor models. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a mixture of factor analyzers observation process. This new switching specification provides an alternative, compact, model to handle intra-frame correlation and unobserved heterogeneity in financial data. For maximum likelihood estimation we have proposed an iterative approach based on the Expectation-Maximisation (EM) algorithm. Using a set of historical data, from the Tunisian foreign exchange market, the model parameters are estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR of the Tunisian public debt portfolio. Through a backtesting procedure, we found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions and can avoid serious violations when a financial crisis occurs.
{"title":"Forecasting portfolio-Value-at-Risk with mixed factorial hidden Markov models","authors":"Mohamed Saidane","doi":"10.17535/crorr.2019.0021","DOIUrl":"https://doi.org/10.17535/crorr.2019.0021","url":null,"abstract":"This paper is concerned with the statistical modeling of the latent dependence and comovement structures of multivariate financial data using a new approach based on mixed factorial hidden Markov models, and their applications in Value-at-Risk (VaR) valuation. This approach combines hidden Markov Models (HMM) with mixed latent factor models. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a mixture of factor analyzers observation process. This new switching specification provides an alternative, compact, model to handle intra-frame correlation and unobserved heterogeneity in financial data. For maximum likelihood estimation we have proposed an iterative approach based on the Expectation-Maximisation (EM) algorithm. Using a set of historical data, from the Tunisian foreign exchange market, the model parameters are estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR of the Tunisian public debt portfolio. Through a backtesting procedure, we found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions and can avoid serious violations when a financial crisis occurs.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"241-255"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41539563","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0024
M. Rahal, Ziadi Abdelkader, Ellaia Rachid
This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $mathbb{R}^{n}$ and H"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=ell _{i}(t),1leq ileq n$ of $alpha $-dense curve $ell_{alpha }$ in the compact $D$, for $t$ in an interval $mathbb{I}$ of $mathbb{R}$, which allows to convert the initial problem to a one dimensional H"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $alpha $ of the curve $ell _{alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $alpha $ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.
{"title":"Generating $alpha $-dense curves in non-convex sets to solve a class of non-smooth constrained global optimization","authors":"M. Rahal, Ziadi Abdelkader, Ellaia Rachid","doi":"10.17535/crorr.2019.0024","DOIUrl":"https://doi.org/10.17535/crorr.2019.0024","url":null,"abstract":"This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $mathbb{R}^{n}$ and H\"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=ell _{i}(t),1leq ileq n$ of $alpha $-dense curve $ell_{alpha }$ in the compact $D$, for $t$ in an interval $mathbb{I}$ of $mathbb{R}$, which allows to convert the initial problem to a one dimensional H\"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $alpha $ of the curve $ell _{alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $alpha $ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"289-314"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48135464","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0026
N. Gadhi, L. Lafhim
In this paper we investigate a bilevel optimization problem by using the optimistic approach. Under a non smooth generalized Guignard constraint qualification, due the optimal value reformulation, the necessary optimality conditions in terms of convexificators and Karush-Kuhn-Tucker (KKT) multipliers are given.
{"title":"Optimality conditions for a bilevel optimization problem in terms of KKT multipliers and convexificators","authors":"N. Gadhi, L. Lafhim","doi":"10.17535/crorr.2019.0026","DOIUrl":"https://doi.org/10.17535/crorr.2019.0026","url":null,"abstract":"In this paper we investigate a bilevel optimization problem by using the optimistic approach. Under a non smooth generalized Guignard constraint qualification, due the optimal value reformulation, the necessary optimality conditions in terms of convexificators and Karush-Kuhn-Tucker (KKT) multipliers are given.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"329-335"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42180653","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0020
I. Derpich, N. Muñoz, Andrea Espinoza
This paper presents a linear programming model used for decision making in the mining process of copper concentration from sulphide minerals. The developed model enables the decision maker to select the types of ore to be used in the mix to maximize the metallurgical recovery and the copper grade at the end of the process. The model is of the mixture model of minerals with added economic variables such as processing costs, electric power and others. The process has four sub-processes that are crushing the ore, crushing the crushed ore, flotation of the ground ore to obtain copper concentrate and drying, in which the water is extracted. The model uses a set of variables whose size varies according to the number of lots of minerals and the number of planning days considered. The model may be considered a considerable problem when a long period of time is planned, but has only been implemented with 3.000 variables and 2.000 constraints. The developed model is being implemented in the National mining company, which buys ore from small producers to produce copper concentrate and then melt and refine it to obtain high grade copper. The generated model produces savings of the order of thousand dollars per day, when compared to the current methods of allocating minerals, which represents millions of dollars per year. It also produces a benefit due to the fact that lower operating costs are obtained, with estimate savings of the order of 5% of the current cost.
{"title":"Improving the productivity of the copper mining process in the Chilean copper industry","authors":"I. Derpich, N. Muñoz, Andrea Espinoza","doi":"10.17535/crorr.2019.0020","DOIUrl":"https://doi.org/10.17535/crorr.2019.0020","url":null,"abstract":"This paper presents a linear programming model used for decision making in the mining process of copper concentration from sulphide minerals. The developed model enables the decision maker to select the types of ore to be used in the mix to maximize the metallurgical recovery and the copper grade at the end of the process. The model is of the mixture model of minerals with added economic variables such as processing costs, electric power and others. The process has four sub-processes that are crushing the ore, crushing the crushed ore, flotation of the ground ore to obtain copper concentrate and drying, in which the water is extracted. The model uses a set of variables whose size varies according to the number of lots of minerals and the number of planning days considered. The model may be considered a considerable problem when a long period of time is planned, but has only been implemented with 3.000 variables and 2.000 constraints. The developed model is being implemented in the National mining company, which buys ore from small producers to produce copper concentrate and then melt and refine it to obtain high grade copper. The generated model produces savings of the order of thousand dollars per day, when compared to the current methods of allocating minerals, which represents millions of dollars per year. It also produces a benefit due to the fact that lower operating costs are obtained, with estimate savings of the order of 5% of the current cost.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"227-240"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45248923","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}
Pub Date : 2019-12-13DOI: 10.17535/crorr.2019.0027
H. Khalifa
This paper deals with fully fuzzy linear programming (FFLP) problem in which all parameters and variables are characterized by L-R fuzzy numbers. By a proposed approach, the FFLP problem is converted into the triple objective functions, and hence a single objective using the weighting method. Through this approach the problem is not transformed into the crisp linear programming problem (LPP) that is enable for obtaining fuzzy optimal solution and the corresponding fuzzy optimal solution which is more realistic to the real world problems. Then a numerical example is taken to the utility and clarify the practically and the efficiency of the approach.
{"title":"Utilizing a new approach for solving fully fuzzy linear programming problems","authors":"H. Khalifa","doi":"10.17535/crorr.2019.0027","DOIUrl":"https://doi.org/10.17535/crorr.2019.0027","url":null,"abstract":"This paper deals with fully fuzzy linear programming (FFLP) problem in which all parameters and variables are characterized by L-R fuzzy numbers. By a proposed approach, the FFLP problem is converted into the triple objective functions, and hence a single objective using the weighting method. Through this approach the problem is not transformed into the crisp linear programming problem (LPP) that is enable for obtaining fuzzy optimal solution and the corresponding fuzzy optimal solution which is more realistic to the real world problems. Then a numerical example is taken to the utility and clarify the practically and the efficiency of the approach.","PeriodicalId":44065,"journal":{"name":"Croatian Operational Research Review","volume":"1 1","pages":"337-344"},"PeriodicalIF":0.7,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.17535/crorr.2019.0027","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44816719","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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