Search

A notion called “excess wealth” was introduced by Shaked and Shanthikumar around 1998 (Probab. Eng. Inf. Sci. 12:1–23, 1998). Subsequent to this, much has been written on it, mostly by Shaked and his colleagues; see Sordo (Insur. Math. Econ. 45(3):466–469, 2009) for a recent review. These works have appeared in the literatures of reliability theory and stochastic orderings. Since the term excess wealth connotes a measure of income inequality—much like its dual, poverty—it should have had an impact in economics and the econometric literature. This, it appears is not the case, at least to the extent that it should be. The purpose of this paper is to investigate the above disconnect by looking at the notion of excess wealth more carefully, but keeping in mind the angle of economics and income. Our conclusion is that an alternative definition of excess wealth better encapsulates what one means by a colloquial use of the term. Our motivation for being attracted to this topic arises from two angles. The first is that the stochastics of diagnostic and threat detection tests, in which we have an interest, has a strong bearing on indices of concentration like the Lorenz Curve, the Gini index, and the entropy. Thus the notion of excess wealth, which conveys a sense of income concentration should also be relevant to diagnostics. The second motivation is to honor Moshe Shaked, a prolific researcher and a friend of the first author, by developing a paper based on an idea that is co-attributed to him.

We describe the formulation and development of a supply-chain optimisation model for Fletcher Challenge Paper Australasia (FCPA). This model, known as Paper Industry Value Optimisation Tool (PIVOT), is a large mixed integer program that finds an optimal allocation of supplier to mill, product to paper machine, and paper machine to customer, while at the same time modelling many of the supply chain details and nuances which are peculiar to FCPA. PIVOT has assisted FCPA in solving a number of strategic and tactical decision problems, and provided significant economic benefits for the company.

This paper investigates the problem of obtaining the best arrangement for cutting stockpatterns in the presence of defective material in the paper, which is a common problem inthe industry. This problem is modeled as a multiple subset sum problem and its structure isexploited in order to obtain a practical solution procedure. The solution methodologyemploys the subset sum problem as a subprocedure. Computational results are reported.

For decades, research on the relationship between environmental sustainability and firm performance focused on determining whether the effect of the former on the latter was positive or negative. That potentially controversial approach had driven mainstream research to ask two focal questions: Does it pay to be green? and Does it cost to be green? Recent papers have explored a curvilinear effect (i.e., U-shaped and inverted U-shaped) by tackling another question: When does it pay to be green? These efforts, however, have either oversimplified the complex linkage between these two things into a linear relationship or confined the complexity within a formatted frame. This paper overcomes these shortfalls by exploring the holistic effect of environmental sustainability on firm performance, contingent upon corporate reputation. In conjunction with direct effect analysis, this paper uniquely explores the synergistic effect of environmental sustainability and corporate reputation on performance. In addition to detecting the nonlinear synergy pattern, we found that the synergy effect is asymmetric. Specifically, the effect is complementary for low-reputation firms but substitutive for high-reputation firms. In addition to its theoretical contributions and pragmatic implications, this paper uniquely presents PROCESS-Neural network as a promising analytic paradigm.

In enterprise project management systems, a program at the tactical level coordinates and manages multiple projects at the operational level. There are close relationships between multiple projects in a program, which are typically manifested as shared resources and precedence relationships. Most research efforts have concentrated on the resource sharing by projects, while the precedence relationships between projects have yet to be comprehensively investigated. In this paper, a bi-objective hierarchical resource-constrained program scheduling problem proposed, where both resource sharing and precedence relationships between projects are considered in a distributed environment. The problem contains two different sub-problems at the operational level and the tactical level, and they are modeled in the same way as two bi-objective multi-mode scheduling problems. Shared resources are allocated from the tactical level to the operational level, and once they are allocated to a project, they can only be re-allocated to other projects once the current project is finished. Subsequently, a two-phase algorithm based on NSGA-III is developed. The algorithm runs at the operational level and the tactical level in turn. According to the Pareto fronts of projects that are submitted from the operational level, the bi-objective program planning at the tactical level is conducted under the constraints of precedence relationships and shared resources. The results of computational simulations demonstrate the satisfactory performance of the improved algorithm. By coordinating the local optimization of projects and the global optimization of the program in a hierarchical framework, the method proposed in this paper provides an effective integrated scheduling method for decision-makers at various levels of a program.

This paper addresses cooperative game theory based bi-objective inventory routing problem, where replenishment plans are assumed as a coalition structure. Particularly, a distribution system is a set of customers that may order a single product from unique wholesalers to satisfy their own demands. When the products are carried from one depot to customers, transportation and inventory costs are incurred and some of the customers have insufficient depot capacity to their order levels. Therefore, in this paper, customers are willing to cooperate for cost saving benefits, where the depots are cooperatively used by each other with additional cost. The cooperative inventory game is established. An application is performed in a furniture roving parts company with the Shapley value cost allocation methods. The main objective of the study is to make a new replenishment plan for the demand of the customers, while meet the demands by sharing each other's depots and inventory routing costs. In addition, an improvement of 1.67% is obtained in vehicle utilization. Moreover, the proposed distribution method makes it possible to satisfy all customers demand for their own period. It helps customers who do not satisfy the demand into the warehouse, the three other most free capacitive customers can take the excess orders into their warehouse which are included in the coalition. As a result, a new effective replenishment plan has been obtained that it is economical to bear the additional costs.

Innovation contests have been an important tool used in product research and development for companies. In the innovation contest literature, most papers assume the homogenous innovation contest model or the all-pay auction model. In this paper, we consider the random trial contest model and study the optimal award scheme. We show that, in this contest model, risk types of contestants play important roles in the award scheme, and the results are independent of the probability density function of the random shock. These generalize the work in literature. In addition, the risk aversion coefficient will decide the allocation manner in a multiple-winner scheme, i.e., a concave allocation manner or a convex allocation manner is optimal.

This paper investigates the selection of third-party logistics providers (3PLs) based on the best prices offered by them. The focus is on outbound logistics where 3PLs must have their own distribution centres for storage and picking activities. They must also have suitable trucks for distribution to different small-scale customers. The motivation for this paper is a case study from Germany in which a furniture company with hundreds of small customers in ten zones is seeking one or more 3PLs to do the distribution. A mathematical programming model was built based on integer programming where demand per order can be expressed using exponential distribution in each customer zone. The main contribution of this paper is that it finds the best 3PLs based on the different pricing methods of the various providers; this means including the location problem indirectly using the new integer programming model. The model takes into consideration three different methods of pricing based on the offers of five 3PLs. These different methods make it difficult for the decision makers to choose the best solution, especially if specific trends in demand are expected in the future for some customer zones. The results show that future increases in demand in terms of the number of orders or order size could affect the optimal solution. The best pricing method with the lowest variability in cost over time is selected.

Location of new stations/stops in public transportation networks has attracted much interest from both the point of views of theory and applications. In this paper we consider a set of pairs of points in the plane demanding traveling between the elements of each pair, and a tree network embedded in the plane representing the transportation system. An alternative mode of transportation competes with the combined plane-network mode so that the modal choice is made by distance (time) comparisons. The aim of the problem dealt with in this paper is to locate a new station/stop so that the traffic through the network would be maximized. Since stops at new stations increases the time of passengers that already used the combined mode, and may persuade them to change the mode, a constraint on the increase of the overall time is imposed. A quadratic in the number of pairs time algorithm is proposed.

International audience; Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this paper, we introduce randomized versions of the Progressive Hedging algorithm able to produce new iterates as soon as a single scenario subproblem is solved. Building on the relation between Progressive Hedging and monotone operators, we leverage recent results on randomized fixed point methods to derive and analyze the proposed methods. Finally, we release the corresponding code as an easy-to-use Julia toolbox and report computational experiments showing the practical interest of randomized algorithms, notably in a parallel context. Throughout the paper, we pay a special attention to presentation, stressing main ideas, avoiding extra-technicalities, in order to make the randomized methods accessible to a broad audience in the Operations Research community.

Wireless local area networks (WLAN) has been in the spotlight as a potential solution to solve the exponentially growing demand of wireless services due to its wide availability and there have been a plenty of research works on WLAN including mathematical modeling and analysis. However, the spatial modeling and analysis of WLAN have received little attention due to the complexity in the dynamics of WLAN. In this paper, we provide spatial modeling and analysis based on stochastic geometry theory to investigate the impact of the spatial distribution on the performance of WLAN. Specifically, this paper is concerned with the correlation between consecutive packet transmissions. Throughout our analysis and simulation study we provide the conditions where the independence assumption on individual transmission results holds, which is widely assumed in most of the previous works on WLAN.

In this paper, a global efficiency criterion is established for a class of multidimensional variational control problems governed by first order PDE&PDI constraints and path-independent curvilinear integral cost functionals. More precisely, a minimal efficiency criterion for a local efficient solution to be its global efficient solution in the considered optimization problem is formulated and proved. Also, the theoretical developments derived in the paper are accompanied by an example of a nonconvex optimization problem.

Artificial intelligence (AI) in the workplace is revolutionising the way businesses operate. AI is being integrated into company operations with the goal of saving money, increasing efficiency, producing insights, and opening up new markets. In order to improve the effect of financial control of enterprise groups, this paper applies artificial intelligence technology to enterprise group management, and based on traditional data mining algorithms, this paper improves the data mining algorithm according to the actual needs of enterprise group management data. Starting from the needs of enterprise group management, this paper uses modern information technology as the support and takes several major elements of financial control system of enterprise groups as the breakthrough point to discuss the solution of financial control of enterprise groups under the network environment, and gives some reference significance optimization procedures. In addition, this paper constructs a financial control platform of enterprise groups and analyzes its data operation process. Finally, this paper verifies and evaluates the system performance through simulation tests. The experimental research results show that the financial control platform of enterprise groups based on artificial intelligence and big data constructed in this paper has good practical effects.

In order to study the financial management of the Guangdong-Hong Kong-Macao Greater Bay Area, this paper builds a financial analysis model based on the LS-SVM algorithm and analyzes the implementation process of the LS-SVM algorithm and its modeling process. Moreover, this paper conducts research on CUDA-based GPU high-performance computing methods, designs and implements the LS-SVM algorithm on the CUDA-based GPU platform, and compares and analyzes the performance before and after optimization. In addition, this paper combines the improved algorithm to construct the financial analysis model and verifies the effect of the method proposed in this paper through actual data analysis. The research results prove the effectiveness of this method. The Hausman test achieves the probability of 0.1005 and 9.60182558 chi-square statistics.

In order to explore the reliable smart pension model, this paper improves the data mining algorithm and constructs an intelligent algorithm suitable for data mining of the pension model. Moreover, this paper combines modern information technology to construct functional modules of the smart pension model, and combines with Maslow’s demand theory to construct the functional structure of the pension model system. In addition, starting from the actual situation, this paper combines the actual needs of the pension model to obtain the pension needs through data mining, and updates the system in real time, which is convenient to adapt to the needs of the transformation of the pension model. Finally, this paper combines experiments to evaluate and analyze the system to provide a theoretical reference for the establishment of the follow-up community pension model. Through experimental research, we can see that the smart pension platform based on data mining constructed in this paper has good results, and the system can meet the needs of a variety of pension modes.

In order to build an intelligent financial management model, based on computer information technology, this paper studies the traditional model intelligent model of financial time series, and solves the problem of insufficient correlation of financial data characteristics. Aiming at the complex and changeable financial time series, this paper has a basic understanding of financial time series data and extracts two new data features. Moreover, this paper preprocesses the financial raw data, and then combines the extracted data features to generate a new combination of data features, which improves the correlation with the data. In addition, this paper combines the financial management process to construct a financial management model system that can be used for financial data processing and risk processing and analyzes the performance of the financial management model constructed in this paper. From the research point of view, it can be seen that the financial management model constructed in this paper has a certain practical effect.

This paper investigates the uncertain stochastic resource allocation problem in which the results of a given allocation of resources are described as probabilities and these probabilities are considered to be uncertain from practical aspects. Here uncertainties are introduced by assuming that these probabilities depend on random parameters which are impacted by various factors. The redundancy allocation problem (RAP) and the multi-stage weapon-target assignment (MWTA) problem are special cases of stochastic resource allocation problems. Bi-objective models for the uncertain RAP and MWTA problem in which the conditional value-at-risk measure is used to control the risk brought by uncertainties are presented in this paper. The bi-objective formulation covers the objectives of minimizing the risk of failure of completing activities and the resulting cost of resources. With the aim of determining referenced Pareto fronts, a linearized formulation and an approximated linear formulation are put forward for RAPs and MWTA problems based on problem-specific characteristics, respectively. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (i.e., MOEA/D-AWA and DMOEA- $$\varepsilon \hbox {C}$$ ) are used to solve the formulated bi-objective problem. In view of differences between MOEA/D-AWA and DMOEA- $$\varepsilon \hbox {C}$$ , two matching schemes inspired by DMOEA- $$\varepsilon \hbox {C}$$ are proposed and embedded in MOEA/D-AWA. Numerical experiments have been performed on a set of uncertain RAP and MWTA instances. Experimental results demonstrate that DMOEA- $$\varepsilon \hbox {C}$$ outperforms MOEA/D-AWA on the majority of test instances and the superiority of DMOEA- $$\varepsilon \hbox {C}$$ can be ascribed to the $$\varepsilon $$ -constraint framework.

International audience; This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.

Decision support for Supplier Selection and Order Allocation (SSOA) is an important application area of multiple criteria decision making (MCDM) problems. In Amid et al. (Int J Prod Econ 131(1):139–145, 2011) proposed and developed a weighted maximin model to ensure the weight-consistent solution for SSOA in an MCDM problem under an uncertain environment. Essentially, this model is based on a weight-consistent constraint and a maximin aggregation operator. This paper reanalyzes the weighted maximin model in terms of the weight-consistent constraint, and then proposes a general weight-consistent model for SSOA in MCDM problems under uncertainty. In this paper, two existing models are reviewed and compared with the proposed model. Three datasets with different ranges of fuzzy demand and full factorial patterns of criteria weights are used to test the performances of the related models. The results showed that the proposed model always generates a weight-consistent Pareto-optimal solution in all cases, while the other existing models do not.

This paper develops the performability and cost–benefit models for a two-stage intervened decision system with majority voting rule and binary input and output. The decision process of the system contains two stages: an inspection stage (stage 1) and a result submission stage (stage 2). During the first stage, each decision unit in the system will have multiple states and a supervisor will come to visit each unit and check its state for at most twice. The supervisor will conduct the first visit to each unit for certain. However, the behavior of the second visit to each unit will be determined by its state during the first visit. In addition, each decision unit may be removed from the system given certain states during each visit. Therefore the structure of system may change during the decision process. The units which are not removed during the first stage can submit the result at any time during the second stage. However, the performance of each remaining unit will be determined by the ending state of the first stage. Moreover, in order to improve the efficiency of the decision process, a check point is added to the second stage. The performability and cost–benefit models for this dynamic system are developed by considering the distribution of states at the end of the first stage. A three-step method will be proposed for model optimization. Some numerical examples for the three-step method will be presented. The proposed intervened decision system in this paper can be applied in many contexts such as financial investment, paper submission review and proposal evaluation, credit evaluation and loan application and product release and recall.

Nowadays financial products are extremely complex and the decision to choose among them could represent a stressful event for individuals. Information related to the risk/return profile of an investment instrument and the way it is represented (framing effect) are crucial in determining the outcome of individuals’ decisions. In this paper we consider two schemes that can be employed to represent the random performances of risky financial products, namely the what if and probabilistic scenarios frames. This paper aims at measuring the impact of the two above mentioned schemes on investors’ decision accuracy and peripheral nervous system activity. In particular, the goal is twofold: (1) to investigate the behavioural and physiological indexes elicited in the decision-making process of investors who have to choose on the basis of the two different schemes; (2) to investigate on the effect of time pressure when probabilistic scenarios or what if frames are used. The first point is investigated by means of a decision making task, while the second one by means of a perceptual one.

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

The story of linear programming is one with all the elements of a grand historical drama. The original idea of testing if a polyhedron is non-empty by using a variable elimination to project down one dimension at a time until a tautology emerges dates back to a paper by Fourier in 1823. This gets re-invented in the 1930s by Motzkin. The real interest in linear programming happens during World War II when mathematicians ponder best ways of utilising resources at a time when they are constrained. The problem of optimising a linear function over a set of linear inequalities becomes the focus of the effort. Dantzig’s Simplex Method is announced and the Rand Corporation becomes a hot bed of computational mathematics. The range of applications of this modelling approach grows and the powerful machinery of numerical analysis and numerical linear algebra becomes a major driver for the advancement of computing machines. In the 1970s, constructs of theoretical computer science indicate that linear programming may in fact define the frontier of tractable problems that can be solved effectively on large instances. This raised a series of questions and answers: Is the Simplex Method a polynomial-time method and if not can we construct novel polynomial time methods, etc. And that is how the Ellipsoid Method from the Soviet Union and the Interior Point Method from Bell Labs make their way into this story as the heroics of Khachiyan and Karmarkar. We have called this paper a primer on linear programming since it only gives the reader a quick narrative of the grand historical drama. Hopefully it motivates a young reader to delve deeper and add another chapter.

Searching for minimal path vectors (MPVs) is an important topic in solving network related problems, especially for the evaluation of network reliability. One of the popular approaches, namely the three-stage method (TSM), is influenced deeply on the efficiency of searching for minimal path vectors in multi-state networks (MSN). TSM consists of three stages, i.e., searching for all minimal path sets, searching for all MPVs, and calculating union probability on MPVs. After reviewing previous works in the literaure, this paper proposes a more efficient method based on cyclic check on the candidates of MPVs, which can do an efficient searching for MPVs in MSNs and even reduce the three-step approach to two-step approach. Benchmarking with the well-known algorithms are made in this paper, and more complicated networks are also examined for verification of the proposed method.

This paper provides results in the area of the analytical derivation of the efficient set of a mean-variance portfolio selection problem that has more than three criteria. By “analytical” we mean derived by formula as opposed to being computed by algorithm. By “more than three criteria”, we mean that beyond the mean and variance of regular portfolio selection, the problems addressed have two or more additional linear objectives. The additional objectives might include sustainability, dividend yield, liquidity, and R&D as extra objectives like these are being seen with greater frequency. While not all multiple criteria portfolio selection problems lend themselves to an analytical derivation, a certain class does and the problems in this class are covered by the mathematics of this paper.

We study the classical problem introduced by R. Isaacs and S. Gal of minimizing the time to find a hidden point H on a network Q moving from a known starting point. Rather than adopting the traditional continuous unit speed path paradigm, we use the dynamic “expanding search” paradigm recently introduced by the authors. Here the regions S(t) that have been searched by time t are increasing from the starting point and have total length t. Roughly speaking the search follows a sequence of arcs $$a_i$$ such that each one starts at some point of an earlier one. This type of search is often carried out by real life search teams in the hunt for missing persons, escaped convicts, terrorists or lost airplanes. The paper which introduced this type of search solved the adversarial problem (where H is hidden to maximize the time to be found) for the cases where Q is a tree or is 2-arc-connected. This paper’s main contribution is to give two strategy classes which can be used on any network and have expected search times which are within a factor close to 1 of the value of the game (minimax search time). These strategies classes are respectively optimal for trees and 2-arc-connected networks. We also solve the game for circle-and-spike networks, which can be considered as the simplest class of networks for which a solution was previously unknown.

In this paper, we study an inventory system for products where demand depends on time and price. Shortages are allowed and are fully backordered. We suppose that the demand rate is the product of a power time pattern and a three-parametric exponential price function. The objective is to determine the economic lot size, the optimal shortage level and the best selling price to maximize the total profit per unit time. We present an efficient procedure to determine the optimal solution of the inventory problem for all possible scenarios. This procedure is illustrated with several numerical examples. A sensitivity analysis of the optimal inventory policy with respect to the parameters of the demand rate function is also given. Finally, the main contributions of this paper are highlighted and future research directions are introduced.

Understanding customers’ decision and behavior is the crux of marketing. Despite the broad applications of weighted sum approaches, like conjoint analysis, sophisticated methodological approaches are under-researched in this field. Conversely, multi-criteria decision making’s (MCDM) objective is to focus on and forecast these decisions. Based on the Choquet integral, this paper presents an effective and precise calculation method to understand real customers’ decision making and to overcome the weighted sum method’s limitations. We compare the weighted sum approach with stable and instable Choquet integral methods in three experimental studies. Our results indicate that the weighted sum approach is valuable in pure order-related applications. In quantitative comparisons, both the stable and instable Choquet integral approaches match the decision makers’ preferences more closely than the weighted sum approach. The paper demonstrates that well-developed traditional approaches have their merits and can still be applied in the right context.

A major problem in communication networks is how to efficiently define the routing paths and to allocate bandwidths in order to satisfy a given collection of transmission requests. In this paper, we study this routing problem by modeling it as a bi-objective single path multicommodity flow problem (SMCFP). Two conflicting objective functions are simultaneously optimized: the delay and reliability of the generated paths. To tackle the complexity of this problem (NP-hard), most of the existing studies proposed approximate methods and metaheuristics as solution approaches. In this paper, we propose to adapt the augmented $$\epsilon $$ -constraint method in order to solve small sized instances of the bi-SMCFP. For large scale problems, we develop three metaheuristics: a multiobjective multi-operator genetic algorithm, an adaptive multiobjective variable neighborhood search and new hybrid method combining the $$\epsilon $$ -constraint with the evolutionary metaheuristic. The idea of the hybridization schema is to first use the metaheuristic to generate a good approximation of the Pareto front, then to enhance the quality of the solutions using the $$\epsilon $$ -constraint method to push them toward the exact Pareto front. An intelligent decomposition scheme is used to reduce the size of the search space before applying the exact method. Computational results demonstrate the efficiency of the proposed hybrid algorithm using instances derived from real network topology and other randomly generated instances.

In this paper, we propose a critical event tabu search meta-heuristic for the general integer multidimensional knapsack problem (GMDKP). Variations of GMDKP have enormous applications, and often occur as a sub-problem of more general combinatorial problems. For the special case of binary multidimensional knapsack problems (BMDKP) there are variety of heuristics, mostly sophisticated meta-heuristics, which provides good solutions to the problem. However, to date there is no method that can provide reasonable solutions to realistic size GMDKP. To the best of our knowledge there are only three heuristics published in the literature for GMDKP, and all three are simple greedy heuristics. There is no meta-heuristic available that effectively provides good solutions for large-scale GMDKP. One successful meta-heuristic that has proven to be highly effective in solving combinatorial optimization is a variation of tabu search known as the critical event tabu search (CETS). CETS was originally proposed for the BMDKP with considerable success afterwards. In CETS, clever use of surrogate programming is embedded as choice rules to obtain high quality solutions. The main purpose of this paper is to design the meta-heuristic CETS for the GMDKP using variety of different surrogate choice rules. Extensive computational experiment for large-scale problems are presented. Our procedures open the door for further applications of meta-heuristics to general integer programs.

This paper presents an extension of our earlier paper on the 1-out-of-N repairable cold standby system (i.e., Barron IIE Trans 47:1139–1151, 2015). Specifically, we consider an R-out-of-N repairable system where the lifetimes of the units follow phase-type distribution. The system is functioning if at least R out of its N components work. Each working component is subject to failure. There are fixed, unit repair, and replacement costs associated with the maintenance facility, which is carried out after a fixed lead time $$\tau $$ . A penalty cost is incurred when the number of good components decreases to $$R-1$$ . We assume that the repair takes no time and repaired units are as good as new. By applying renewal theory and matrix-geometric methods, we derive the expected discounted costs under three classes of group maintenance policies: m-failure, T-age, and ( $$m,T,\tau $$ ), which is a refinement of the classical (m, T) policy. Illustrative examples, a comparative study and insights are provided.

Facility layout problem is an NP-hard problem where two basic approaches have commonly been used to optimize layouts i.e. qualitative and quantitative. Qualitative aspect provide layout based on maximizing of closeness rating while quantitative involve minimization of material handling cost. Previous work undertaken by scholars in which they have studied or focussed on optimizing product flow to optimize both objectives either considering constant or varying demand across all period. Here, the facility layout problem is addressed from the point of demand based disaster for disaster relief operations. Therefore, the paper first presents mathematical formulation for multi objective stochastic dynamic facility layout problem (MO-SDFLP) where the product demand is varying over multiple periods for multiple products. Huge demand variations in multiple products across multiple periods may cause disaster as it can impact heavily the supply chain. Hence, the layout problem considered here mainly focus on considering product demand variations to capture disaster for disaster relief operations. MO-SDFLP being NH-hard is solved using simulated annealing (SA) and chaotic simulated annealing (CSA) meta-heuristics. The paper reports results of SA and CSA algorithms using data sets available in literature for facility size N = 12, period T = 5 and Gaussian distribution product demand. In addition, to show the applicability of MO-SDFLP for bigger demand based disaster, SA and CSA is also tested on bigger problem i.e. N = 30 for T = 5. It is observed that CSA performs better than SA.

Cross-efficiency evaluation is a useful approach to ranking decision making units (DMUs) in data envelopment analysis (DEA). The possible existence of multiple optimal weights for the DEA may reduce the usefulness of the cross-efficiency evaluation since the ranking is according to the choice of weights that different DMUs make. Most of existing approaches for cross-efficiency evaluation employ the average cross-efficiency to further discriminate among the DEA efficient units or focus on how to determine input and output weights uniquely, but lay little emphasis on the consideration of the ranges and variances of cross-efficiencies as alternative ranking factors. In this paper we consider cross-efficiency intervals and their variances for ranking DMUs. The aggressive and benevolent formulations are taken into account at the same time. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The signal-to-noise (SN) ratio, originally designed for optimizing the robustness of a process, is constructed as a numerical index for ranking DMUs. A nonlinear fractional program with bound constraints is formulated to find the optimal value of the SN ratio. By model reduction and variable substitution, this nonlinear fractional program is transformed into a quadratic one for deriving the global optimum solution. With the derived SN ratios, we are able to fully rank all DMUs accordingly. Two examples are given to illustrate the effectiveness of the methodology proposed in this paper.

This paper describes the structure of optimal policies for discounted periodic-review single-commodity total-cost inventory control problems with fixed ordering costs for finite and infinite horizons. There are known conditions in the literature for optimality of $$(s_t,S_t)$$ policies for finite-horizon problems and the optimality of (s, S) policies for infinite-horizon problems. The results of this paper cover the situation, when such assumption may not hold. This paper describes a parameter, which, together with the value of the discount factor and the horizon length, defines the structure of an optimal policy. For the infinite horizon, depending on the values of this parameter and the discount factor, an optimal policy either is an (s, S) policy or never orders inventory. For a finite horizon, depending on the values of this parameter, the discount factor, and the horizon length, there are three possible structures of an optimal policy: (1) it is an $$(s_t,S_t)$$ policy, (2) it is an $$(s_t,S_t)$$ policy at earlier stages and then does not order inventory, or (3) it never orders inventory. The paper also establishes continuity of optimal value functions and describes alternative optimal actions at states $$s_t$$ and s.

In this paper, we define the standard LRP as a deterministic, static, discrete, single-echelon, single-objective location-routing problem in which each customer (vertex) must be visited exactly once for the delivery of a good from a facility, and in which no inventory decisions are relevant. We review the literature on the standard LRP published since the survey by Nagy and Salhi appeared in 2006. We provide concise paper excerpts that convey the central ideas of each work, discuss recent developments in the field, provide a numerical comparison of the most successful heuristic algorithms, and list promising topics for further research.

In order to break the tie of efficient decision-making units, super-efficiency data envelopment analysis is proposed to fully discriminate them. Recently, a slacks-based version of the super slacks-based measure (S-SBM) is developed and a novel two-stage approach is proposed to calculate both super-efficiency score by the S-SBM model and efficiency score by the slacks-based measure model. In this paper, we extend the approach to consider continuity of efficiency scores. We illustrate the discontinuity of efficiency measure, and define a continuous slacks-based measure which is proved continuous and directly calculated. An interesting efficiency zone category is also provided. In addition, this paper investigates the relationship among the super-efficiency measures of the proposed approach and some existing approaches under variable returns to scale.

In this paper, a deterministic inventory control model with deterioration is developed. Here, the deterioration rate follows stochastic deterioration, especially Weibull distribution deterioration. A time-dependent demand approach is introduced to show the applicability of our proposed model and to be up-to-date with respect to time. The main purpose of the paper is to investigate the optimal retailer's replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks. Keeping in mind the criterion of modern era, we consider that the holding cost is totally dependent on time, and shortages are allowed for this model. Subject to the formulated model, we minimize the total inventory cost. The mathematical model is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution with regard to important parameters is also carried out to elaborate the quality, e.g., stability, of our result and to possibly modify our model. The paper ends with a conclusion and an outlook to future studies.

For solving a sequential decision-making problem in a non-Markovian domain, standard dynamic programming (DP) requires a complete mathematical model; hence, a totally model-based approach. By contrast, this paper describes a totally model-free approach by actor-critic reinforcement learning with recurrent neural networks. The recurrent connections (or context units) in neural networks act as an implicit form of internal state (i.e., history memory) for developing sensitivity to hidden non-Markovian dependencies, rendering the process Markovian implicitly and automatically in a totally model-free fashion. That is, the model-free recurrent-network agent neither learns transitional probabilities and associated rewards, nor by how much the state space should be enlarged so that the Markov property holds. For concreteness, we illustrate time-lagged path problems, in which our learning agent is expected to learn a best (history-dependent) policy that maximizes the total return, the sum of one-step transitional rewards plus special “bonus” values dependent on prior transitions or decisions. Since we can obtain an optimal solution by model-based DP, this is an excellent test on the learning agent for understanding its model-free learning behavior. Such actor-critic recurrent-network learning might constitute a mechanism which animal brains use when experientially acquiring skilled action. Given a concrete non-Markovian problem example, the goal of this paper is to show the conceptual merit of totally model-free learning with actor-critic recurrent networks, compared with classical DP (and other model-building procedures), rather than pursue a best recurrent-network learning strategy.

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.

The discrete time “bomber problem” has been one of the longest standing open problems in operations research. In particular, the validity of one of the natural monotonicity conjectures—known as property (B)—has been an unresolved issue since 1968. In this paper we report 41 counterexamples to property (B) of this problem. We have found them by computing the exact solutions for nearly one million pairs of parameter values utilizing the GNU multiple precision arithmetic library. All our counterexamples can readily be verified using a simple Mathematica program included in this paper.

This paper proposes a multi-start randomized heuristic for solving real-life crew rostering problems in airlines. The paper describes realistic constrains, regulations, and rules that have not been considered in the literature so far. Our algorithm is designed to provide quality solutions satisfying these real-life specifications while, at the same time, it aims at balancing the workload distribution among the different crewmembers. Thus, our approach promotes corporate social responsibility by distributing the workload in a fair way and avoiding that some crewmembers get unnecessarily overstressed. Despite its importance in real-life applications, these aspects have seldom been considered in the crew scheduling literature, where most solving approaches refer to simplified models and are tested on non-realistic benchmarks. The experimental tests show that our algorithm is capable of generating feasible quality solutions to real-life crew rostering problems in just a few seconds. These times are orders of magnitude lower than the times currently employed by some airlines to obtain a single feasible solution, since the ‘optimal’ solutions provided by most commercial software usually require additional adjustments in order to meet all the real-life specifications.

The quay crane scheduling problem is one of the major problems of quayside operational planning in container terminals. The operational efficiency of quay cranes is a large determinant of the overall container terminal efficiency; thus, in an effort to maximize throughput, more and more emphasis is placed on systematically addressing and improving quay crane operations. However, the resulting formulations are highly complex and thus not solvable using commercial software. In the first part of the present paper, we develop a formulation that overcomes this challenge. This allows for solving the model using CPLEX, even for large size instances, which other notable work from the literature fails to solve. The second part of this paper addresses a crucial point which has rarely been accounted for, which is ship stability. A heuristic is developed to solve the extended problem, as it is no longer solvable in CPLEX. The remaining objective of this work is to extend this problem to the multi-ship case. However, once again the problem is insolvable for large instances using CPLEX, even without accounting for stability constraints. We develop a Lagrangian relaxation based algorithm that decomposes the problem by ship, which is solved efficiently as a single ship case. The Lagrangian multipliers are updated using the cutting plane method and the solution of the Lagrangian master problem provides an upper bound on the optimal value of the Lagrangian lower bound. Upper bounds on the optimal value of the original problem are obtained using a constructive heuristic, and through computational experiments we demonstrate the performance of the Lagrangian relaxation-based procedures.

This paper addresses an assembly line balancing problem in which each station is allowed to have more than one worker, with minimization of two objectives: (i) the number of workers used in the line and (ii) the number of stations opened in the line. Each station has an own workpiece, and workers at the same station simultaneously perform different assembly tasks on its workpiece. For solving the balancing problem of these lines, a new mixed integer programming formulation is presented, and then a simulated annealing based heuristic method is proposed. The new formulation requires less number of variables and constraints. The basic property of the proposed heuristic is that it is directly applied to Gantt representations of problem's solutions. Moreover, the paper includes some important neighborhood generation properties for Gantt representations of solutions. Both methods are compared with existing methods available in the literature. Experimental study indicates that the proposed methods can yield promising results.

One of the primary objectives of this paper is to generalize Hunter’s bound to m-regular hypergraphs. In particular, new upper and lower bounds for the probability of the union of events is provided in this paper. The lower bounds generalize Hunter’s bound as well. All new bounds are derived from the dual feasible solutions of Boole’s linear programming problem.

This paper provides a simple framework for the valuation of exotic derivatives within shadow costs of incomplete information and short sales. The specific features of the OTC markets with comparison to the organized markets require an additional investment to obtain information about the financial products, to process data, to elaborate models, etc. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton’s (J Fianance 42:483–510, 1987) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (Rev Quant Finance Account 7:119–136, 1996) who propose incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales. Our methodology incorporates shadow costs of incomplete information and short sales in the options and their underlying securities. We provide formulas using the standard Black and Scholes method or the martingale method. Since shadow costs are important in the presence of illiquidity, the formulas are useful for the valuation of OTC derivatives.

Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper studies SVM when the data points are uncertain. With some properties known for the distributions, chance-constrained SVM is used to ensure the small probability of misclassification for the uncertain data. As infinite number of distributions could have the known properties, the robust chance-constrained SVM requires efficient transformations of the chance constraints to make the problem solvable. In this paper, robust chance-constrained SVM with second-order moment information is studied and we obtain equivalent semidefinite programming and second order cone programming reformulations. The geometric interpretation is presented and numerical experiments are conducted. Three types of estimation errors for mean and covariance information are studied in this paper and the corresponding formulations and techniques to handle these types of errors are presented.

A sustainability program is about implementing essential sustainability practices at various intensities that will not harm people because of firm actions. This paper formulates an optimization model to identify an optimal intensity of implementation of selected sustainability practices referred as sustainability program for maximising manufacturing industry sustainability performance for a known set of budgetary and minimum thresholds constraints with respect to economic, social and socio-economic criteria. Besides modelling the paper proposes a random search procedure embedding the NN to determine the optimal sustainability program and explains the usefulness with a sample problem. Sensitivity analysis is carried out to understand the behaviour of the model. It is observed that the sustainability performances depend on the constraints such as budget limitation and threshold values of performance criterion.

Conventional data envelopment analysis (DEA) models make the assumption of non-negativity and real values in the input and output of the systems that are under study. This paper combines these two interrelated ideas. One is the non-radial measurement of efficiency by establishing an aggregate directional distance formulation of the DEA model (ADDM). Another is the introduction of an integer directional distance function. Usually, directional distance formulations of DEA and ADDM projections of efficient targets for inefficient decision making units (DMUs) have non-integer values. In this paper directional distance function is modified and a mixed integer directional distance formulation of DEA is proposed. This model guarantees integer targets for inefficient DMUs and is applicable to measure efficiency even when input and output variables are negative integer values.

This paper deals with the stochastic portfolio selection problem when the loss in the portfolio return is considered as a recourse cost. We suppose that the investor would penalize infeasible solutions for uncertain constraints with the most probable highest recourse cost rather than with the expected recourse cost as in the traditional recourse approach. This novel approach which is mixed with a goal programming approach is used to solve a multi-objective stochastic portfolio selection model. We illustrate the paper results by an empirical example using the weekly returns of the Standard & Poor’s 100 securities between January 2001 and November 2011.

Optimization models have a wide range of applications in economics and game theory. This special issue of the Annals of Operations Research contains selected and refereed papers on the topic optimization models with economic and game theoretic applications. Most of the papers in this special issue were presented at the International Symposium on Applied Optimization and Game Theoretic Models (ISAOGTM13) held during January 9–11, 2013, at the Indian Statistical Institute, Delhi Centre. This International Symposiumwas designed to promote research and applications in applied optimization and game theory by bringing together leading experts and other specialists in the field around the world with young scholars. This symposium mainly focused on classical and modern optimization theory, algorithms (local and global aspects), stochastic optimization, structured optimization, as well as related topics in applied mathematics that contain applications of optimization models in economics and game theory. Around 120 participants including speakers participated in this symposium. This symposium was an event under the project optimization and reliability modeling funded by the Indian Statistical Institute. Having broad international appeal it provided an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives, dealingwith topics of fundamental importance in applied optimization and other related sciences (economics, physics, engineering). A special session titled Professor Santosh N. Kabadi Memorial Session was organized on combinatorial optimization to recall the memory of our dear friend Professor Santosh N. Kabadi, University of New