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Journal of Industrial and Management Optimization

March 2022 , Volume 18 , Issue 2

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Electricity supply chain coordination with carbon abatement technology investment under the benchmarking mechanism
Wei Chen, Yongkai Ma and Weihao Hu
2022, 18(2): 713-730 doi: 10.3934/jimo.2020175 +[Abstract](1470) +[HTML](567) +[PDF](953.66KB)
Abstract:

The introduction of the benchmarking mechanism into the electricity industry has influenced whether utility firms choose to invest in carbon abatement technology. This study presents an electricity supply chain that includes a utility firm as the leader and a retailer as the follower to decide on the electricity price and carbon abatement technology investment. The study discusses the impact of the benchmarking mechanism on the decision-making of the electricity supply chain enterprises. The main conclusions are as follows: (1) Investing in carbon abatement technology increased electricity demand, customer surplus, and profits of the electricity supply chain enterprises. (2) Carbon abatement technology investment and profits of the supply chain enterprises increased with the unit carbon quota. (3) A revenue-sharing and cost-sharing contract could be used to coordinate the electricity supply chain.

Perturbation of Image and conjugate duality for vector optimization
Manxue You and Shengjie Li
2022, 18(2): 731-745 doi: 10.3934/jimo.2020176 +[Abstract](1203) +[HTML](528) +[PDF](325.31KB)
Abstract:

This paper aims at employing the image space approach to investigate the conjugate duality theory for general constrained vector optimization problems. We introduce the concepts of conjugate map and subdifferential by using two types of maximums. We also construct the conjugate duality problems via a perturbation method. Moreover, the separation condition is proposed by means of vector weak separation functions. Then, it is proved to be a new sufficient condition, which ensures the strong duality theorem. This separation condition is different from the classical regular conditions in the literature. Simultaneously, the application to a nonconvex multi-objective optimization problem is shown to verify our main results.

Planning rolling stock maintenance: Optimization of train arrival dates at a maintenance center
Hanyu Gu, Hue Chi Lam and Yakov Zinder
2022, 18(2): 747-772 doi: 10.3934/jimo.2020177 +[Abstract](1913) +[HTML](539) +[PDF](1733.92KB)
Abstract:

A railway network is an indispensable part of the public transportation system in many major cities around the world. In order to provide a safe and reliable service, a fleet of passenger trains must undergo regular maintenance. These maintenance operations are lengthy procedures, which are planned for one year or a longer period. The planning specifies the dates of trains' arrival at the maintenance center and should take into account the uncertain duration of maintenance operations, the periods of validity of the previous maintenance, the desired number of trains in service, and the capacity of the maintenance center. The paper presents a nonlinear programming formulation of the considered problem and several optimization procedures which were compared by computational experiments using real world data. The results of these experiments indicate that the presented approach is capable to be used in real world planning process.

Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems
Lateef Olakunle Jolaoso and Maggie Aphane
2022, 18(2): 773-794 doi: 10.3934/jimo.2020178 +[Abstract](1274) +[HTML](625) +[PDF](442.64KB)
Abstract:

Using the concept of Bregman divergence, we propose a new subgradient extragradient method for approximating a common solution of pseudo-monotone and Lipschitz continuous variational inequalities and fixed point problem in real Hilbert spaces. The algorithm uses a new self-adjustment rule for selecting the stepsize in each iteration and also, we prove a strong convergence result for the sequence generated by the algorithm without prior knowledge of the Lipschitz constant. Finally, we provide some numerical examples to illustrate the performance and accuracy of our algorithm in finite and infinite dimensional spaces.

General drawdown based dividend control with fixed transaction costs for spectrally negative Lévy risk processes
Wenyuan Wang and Ran Xu
2022, 18(2): 795-823 doi: 10.3934/jimo.2020179 +[Abstract](1268) +[HTML](490) +[PDF](1295.33KB)
Abstract:

For spectrally negative Lévy risk processes we consider a generalized version of the De Finetti's optimal dividend problem with fixed transaction costs, where the ruin time is replaced by a general drawdown time in the framework. We identify a condition under which a band–type impulse dividend strategy is optimal among all admissible impulse strategies. As a consequence, we are able to extend the previous results on ruin time based impulse dividend optimization problem to those on drawdown time based impulse dividend optimization problems. A new type of drawdown function is proposed at end, and various numerical examples are presented to illustrate the existence of those optimal impulse dividend strategies under different assumptions.

Energy management method for an unpowered landing
Xiaoxiao Li, Yingjing Shi, Rui Li and Shida Cao
2022, 18(2): 825-841 doi: 10.3934/jimo.2020180 +[Abstract](1111) +[HTML](485) +[PDF](1124.98KB)
Abstract:

The unpowered landing of unmanned aerial vehicle (UAV) is a critical stage, which affects the safety of flight. To solve the problem of the unpowered landing of UAV, an energy management scheme is proposed. After the cruise is over, the aircraft shuts down the engine and begins to land. When the aircraft is in the high altitude, the dynamic pressure is too large, and it is difficult to open the speed brake. When the aircraft is in the low altitude, it is close to the runway. The method of S-turn may make the aircraft veer off the runway and may be unable to land. So two different schemes of high altitude and low altitude are designed to control energy. In the high altitude, when the energy is too high, it takes the S-turn scheme to consume excess energy. At the same time, the availability and reasonability of the S-turn scheme is demonstrated. In the low altitude, the open angle of speed brake is controlled to adjust the energy consumption. Finally, the simulation results are given to illustrate the availability of energy management.

Coordinating a supply chain with demand information updating
Honglin Yang and Jiawu Peng
2022, 18(2): 843-872 doi: 10.3934/jimo.2020181 +[Abstract](1542) +[HTML](530) +[PDF](795.83KB)
Abstract:

We investigate how to coordinate a two-echelon supply chain in which a supplier builds production capacity in advance and a manufacturer makes the ordering decision based on updated demand information. By combining European call option and buyback mechanisms, we propose a new hybrid option-buyback contract to coordinate such a supply chain with demand information updating. We construct a two-stage optimization model in that the supplier offers option price and the manufacturer decides initial ordering quantity in the first stage, then the supplier offers exercise price and buyback price and the manufacturer decides final ordering quantity in the second stage after demand information is updated. In both the centralized and decentralized settings, we analytically derive the optimal equilibrium solutions of two-stage ordering quantity. Particularly, we obtain closed-form formulae to describe the members' optimal behavior with a bivariate uniformly distribution. We prove that the proposed contracts can realize the perfect coordination of the supply chain and analyze how the proposed contracts affect the members' decisions. The theoretical results show that, by tuning the option price or buyback price, the supply chain profit can be arbitrarily split between the members, which is a desired property for supply chain coordination. Compared with the standard option and buyback contract, the proposed contract results in a greater supply chain profit and achieves Pareto improvement for the supply chain members. Furthermore, extending the baseline model focusing on price-independent demand to the case of price-dependent demand, we show that the proposed contract still can achieve supply chain coordination. Numerical examples are also conducted to complement the theoretical results.

Cost of fairness in agent scheduling for contact centers
Onur Şimşek and O. Erhun Kundakcioglu
2022, 18(2): 873-896 doi: 10.3934/jimo.2021001 +[Abstract](1397) +[HTML](580) +[PDF](843.21KB)
Abstract:

We study a workforce scheduling problem faced in contact centers with considerations on a fair distribution of shifts in compliance with agent preferences. We develop a mathematical model that aims to minimize operating costs associated with labor, transportation of agents, and lost customers. Aside from typical work hour-related constraints, we also try to conform with agents' preferences for shifts, as a measure of fairness. We plot the trade-off between agent satisfaction and total operating costs for Vestel, one of Turkey's largest consumer electronics companies. We present insights on the increased cost to have content and a fair environment on several agent availability scenarios.

A model and two heuristic methods for The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet
Ömer Arslan and Selçuk Kürşat İşleyen
2022, 18(2): 897-932 doi: 10.3934/jimo.2021002 +[Abstract](1649) +[HTML](561) +[PDF](613.65KB)
Abstract:

The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet considers a supply chain, which comprises multiple producers, potential distribution centers (DCs) with opening capacity levels and geographically scattered retailers each of which has deterministic demand over a discrete planning horizon. The goal is determining a set of DCs with their capacity levels to open, assigning retailers to the opened DCs, finding product quantities to be ordered by and distributed from opened DCs and determining the fleet and routes to satisfy the demands of retailers with minimum cost. A mixed-integer linear programming model is proposed to describe the problem, which is strengthened by two valid inequalities. Since the commercial solver can only solve the very small-sized instances within a reasonable time, two heuristic methods are developed. Results show that the proposed valid inequalities are effective and both methods provide important savings in acceptable run times compared to the commercial solver.

Optimal investment and reinsurance to minimize the probability of drawdown with borrowing costs
Yu Yuan, Zhibin Liang and Xia Han
2022, 18(2): 933-967 doi: 10.3934/jimo.2021003 +[Abstract](1456) +[HTML](488) +[PDF](533.3KB)
Abstract:

We study the optimal investment and reinsurance problem in a risk model with two dependent classes of insurance businesses, where the two claim number processes are correlated through a common shock component and the borrowing rate is higher than the lending rate. The objective is to minimize the probability of drawdown, namely, the probability that the value of the wealth process reaches some fixed proportion of its maximum value to date. By the method of stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation, we investigate the optimization problem in two different cases and divide the whole region into four subregions. The explicit expressions for the optimal investment/reinsurance strategies and the minimum probability of drawdown are derived. We find that when wealth is at a relatively low level (below the borrowing level), it is optimal to borrow money to invest in the risky asset; when wealth is at a relatively high level (above the saving level), it is optimal to save more money; while between them, the insurer is willing to invest all the wealth in the risky asset. In the end, some comparisons are presented to show the impact of higher borrowing rate and risky investment on the optimal results.

Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices
Longxiang Fang, Narayanaswamy Balakrishnan and Wenyu Huang
2022, 18(2): 969-984 doi: 10.3934/jimo.2021004 +[Abstract](927) +[HTML](506) +[PDF](397.08KB)
Abstract:

In this paper, we discuss stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. To begin with, we present the hazard rate order of parallel systems with two scale proportional hazards components equipped with starting devices for two different cases: first when the starting devices with different probability have the same scale proportional hazards components, and the second when the different scale proportional hazards components have the same starting devices probability. Next, we present the usual stochastic order of parallel systems with \begin{document}$ n $\end{document} scale proportional hazards components equipped with starting devices. Finally, we provide some numerical examples to illustrate all the results established here.

Two-agent integrated scheduling of production and distribution operations with fixed departure times
Yunqing Zou, Zhengkui Lin, Dongya Han, T. C. Edwin Cheng and Chin-Chia Wu
2022, 18(2): 985-1007 doi: 10.3934/jimo.2021005 +[Abstract](1171) +[HTML](496) +[PDF](408.83KB)
Abstract:

We consider integrated scheduling of production and distribution operations associated with two customers (agents). Each customer has a set of orders to be processed on the single production line at a supplier on a competitive basis. The finished orders of the same customer are then packed and delivered to the customer by a third-party logistics (3PL) provider with a limited number of delivery transporters. The number of orders carried in a delivery transporter cannot exceed its delivery capacity. Each transporter incurs a fixed delivery cost regardless of the number of orders it carries, and departs from the 3PL provider to a customer at fixed times. Each customer desires to minimise a certain optimality criterion involving simultaneously the customer service level and the total delivery cost for its orders only. The customer service level for a customer is related to the times when its orders are delivered to it. The problem is to determine a joint schedule of production and distribution to minimise the objective of one customer, while keeping the objective of the other customer at or below a predefined level. Using several optimality criteria to measure the customer service level, we obtain different scenarios that depend on optimality criterion of each customer. For each scenario, we either devise an efficient solution procedure to solve it or demonstrate that such a solution procedure is impossible to exist.

Stabilization of 2-d Mindlin-Timoshenko plates with localized acoustic boundary feedback
Yubiao Liu, Chunguo Zhang and Tehuan Chen
2022, 18(2): 1009-1034 doi: 10.3934/jimo.2021006 +[Abstract](1009) +[HTML](535) +[PDF](424.4KB)
Abstract:

In this paper, we investigate the well-posedness and the asymptotic stability of a two dimensional Mindlin-Timoshenko plate imposed the so-called acoustic control by a part of the boundary and a Dirichlet boundary condition on the remainder. We first establish the well-posedness results of our model based on the theory of linear operator semigroup and then prove that the system is not exponentially stable by using the frequency domain approach. Finally, we show that the system is polynomially stable with the aid of the exponential or polynomial stability of a system with standard damping acting on a part of the boundary.

Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms
Masoud Rabbani, Nastaran Oladzad-Abbasabady and Niloofar Akbarian-Saravi
2022, 18(2): 1035-1062 doi: 10.3934/jimo.2021007 +[Abstract](1356) +[HTML](1101) +[PDF](1979.23KB)
Abstract:

The shortage of relief vehicles capacity is a common issue throughout disastrous situations due to the abundance of injured people who need urgent medical aid. Hence, ambulances fleet management is highly important to save as many injured individuals as possible. In this regard, the present paper defines different patient groups based on their needs and characteristics. In order to provide the affected people with proper and timely medical aid, changes in their health status are also considered. A Mixed-integer Linear Programming (MILP) model is proposed to find the best sequence of routes for each ambulance and minimize the latest service completion time (SCT) as well as the number of patients whose condition gets worse because of receiving untimely medical services. Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to find high-quality solutions over a short time. In the end, Lorestan province, Iran, is considered as a case study to assess the model's performance and analyze the sensitivity of solutions with respect to the major parameters, which results in insightful managerial suggestions.

A unified analysis for scheduling problems with variable processing times
Ji-Bo Wang, Bo Zhang and Hongyu He
2022, 18(2): 1063-1077 doi: 10.3934/jimo.2021008 +[Abstract](1018) +[HTML](506) +[PDF](400.48KB)
Abstract:

This paper considers single-machine scheduling problems with variable processing times, in which the actual processing time of a job is a function of its additional resources, starting time, and position in a sequence. Four problems arising from two criteria (a scheduling cost and a total resource consumption cost) are investigated. Under the linear and convex resource consumption functions, we provide unified approaches and consequently prove that these four problems are solvable in polynomial time.

A control parametrization based path planning method for the quad-rotor uavs
Jinlong Guo, Bin Li and Yuandong Ji
2022, 18(2): 1079-1100 doi: 10.3934/jimo.2021009 +[Abstract](1276) +[HTML](498) +[PDF](2842.9KB)
Abstract:

A time optimal path planning problem for the Quad-rotor unmanned aerial vehicles (UAVs) is investigated in this paper. A 3D environment with obstacles is considered, which makes the problem more challenging. To tackle this challenge, the problem is formulated as a nonlinear optimal control problem with continuous state inequality constraints and terminal equality constraints. A control parametrization based method is proposed. Particularly, the constraint transcription method together with a local smoothing technique is utilized to handle the continuous inequality constraints. The original problem is then transformed into a nonlinear program. The corresponding gradient formulas for both of the cost function and the constraints are derived, respectively. Simulation results show that the proposed path planning method has less tracking error than that of the rapid-exploring random tree (RRT) algorithm and that of the A star algorithm. In addition, the motor speed has less changes for the proposed algorithm than that of the other two algorithms.

Spectral norm and nuclear norm of a third order tensor
Liqun Qi, Shenglong Hu and Yanwei Xu
2022, 18(2): 1101-1113 doi: 10.3934/jimo.2021010 +[Abstract](1158) +[HTML](492) +[PDF](307.74KB)
Abstract:

The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order tensor is equal to the square root of the spectral norm of three positive semi-definite biquadratic tensors, and the square roots of the nuclear norms of those three positive semi-definite biquadratic tensors are lower bounds of the nuclear norm of that third order tensor. This provides a way to estimate and to evaluate the spectral norm and the nuclear norm of that third order tensor. Some upper and lower bounds for the spectral norm and nuclear norm of a third order tensor, by spectral radii and nuclear norms of some symmetric matrices, are presented.

Robust control in green production management
Jian-Xin Guo and Xing-Long Qu
2022, 18(2): 1115-1132 doi: 10.3934/jimo.2021011 +[Abstract](1212) +[HTML](523) +[PDF](629.67KB)
Abstract:

This study proposes a robust control model for a production management problem related to dynamic pricing and green investment. Contaminants produced during the production process contribute to the accumulation of pollution stochastically. We derive optimal robust controls and identify conditions under which some concerns about model misspecification are discussed. We observe that optimal price and investment control decrease in the degree of robustness. We also examine the cost of robustness and the relevant importance of contributions in the overall value function. The theoretical results are applied to a calibrated model regarding production management. Finally, we compare robust choices with those in the benchmark stochastic model. Numerical simulations show that robust decision-making can indeed adjust investment decisions based on the level of uncertainty.

A new adaptive method to nonlinear semi-infinite programming
Ke Su, Yumeng Lin and Chun Xu
2022, 18(2): 1133-1144 doi: 10.3934/jimo.2021012 +[Abstract](1129) +[HTML](472) +[PDF](307.23KB)
Abstract:

In this paper, we propose a new adaptive method for solving nonlinear semi-infinite programming(SIP). In the presented method, the continuous infinite inequality constraints are transformed into equivalent equality constraints in integral form. Based on penalty method and trust region strategy, we propose a modified quadratic subproblem, in which an adaptive parameter is considered. The acceptable criterion of the trial point is adjustable according to the value of this adaptive parameter and the improvements that made by the current iteration. Compared with the existing methods, our method is more flexible. Under some reasonable conditions, the convergent properties of the proposed algorithm are proved. The numerical results are reported in the end.

Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming
Mahdi Karimi and Seyed Jafar Sadjadi
2022, 18(2): 1145-1160 doi: 10.3934/jimo.2021013 +[Abstract](1690) +[HTML](548) +[PDF](540.15KB)
Abstract:

In recent years, numerous studies have been conducted regarding inventory control of deteriorating items. However, due to the complexity of the solution methods, various real assumptions such as discrete variables and capacity constraints were neglected. In this study, we presented a multi-item inventory model for deteriorating items with limited carrier capacity. The proposed research considered the carrier, which transports the order has limited capacity and the quantity of orders cannot be infinite. Dynamic programming is used for problem optimization. The results show that the proposed solution method can solve the mixed-integer problem, and it can provide the global optimum solution.

Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider
Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker and Guo-Qiang Yang
2022, 18(2): 1161-1183 doi: 10.3934/jimo.2021014 +[Abstract](1424) +[HTML](510) +[PDF](604.6KB)
Abstract:

This paper investigates decisions in a three-echelon closed-loop supply chain composed of one manufacturer, one retailer, and one third-party logistics provider (3PL), with the retailer being dominant. Inspired by game theory, we develop an equilibrium model for a retailer-led, closed-loop supply chain under logistics outsourcing. We derive the optimal forward and reverse logistics decisions of each supply chain member. This article analyzes the effects of market size, consumers' sensitivity to sales prices, the proportion of logistics costs, consumers' environmental awareness, and consumers' sensitivity to recycling prices on decision-making process. Finally, we provide a numerical example to verify the validity of our conclusions. Our results indicate that the higher the manufacturer's share in the forward logistics cost, the higher the sales price, the wholesale price, and the forward logistics service price, and the lower the order quantity. The higher the manufacturer's share in the reverse logistics costs, the lower the recycling price, the transfer price, and the recycling amount, and the higher the reverse logistics service price. Whether it is forward logistics or not, the higher the manufacturer's share in the logistics costs, the lower the profits of each member.

Time-consistent investment-reinsurance strategy with a defaultable security under ambiguous environment
Shan Liu, Hui Zhao and Ximin Rong
2022, 18(2): 1185-1222 doi: 10.3934/jimo.2021015 +[Abstract](1400) +[HTML](549) +[PDF](576.04KB)
Abstract:

This paper considers an investment and reinsurance problem with a defaultable security for an insurer in an environment with parameter uncertainties. Suppose that the insurer is ambiguous about the insurance claims. Specifically, the insurance claim is exponentially distributed and the rate parameter is uncertain. The insurer is allowed to invest in a financial market consisting of a risk-free bond, a stock whose price process satisfies the Heston's SV model and a defaultable bond. Moreover, the insurer is allowed to purchase proportional reinsurance and aims to maximize the smooth ambiguity utility proposed in Klibanoff et al. [15]. By applying stochastic control approach, we establish the extended HJB system and derive the time-consistent investment-reinsurance strategy for the post-default case and the pre-default case, respectively. Finally, a sensitivity analysis is provided to illustrate the effects of model parameters on the equilibrium reinsurance-investment strategy under the smooth ambiguity.

Branching improved Deep Q Networks for solving pursuit-evasion strategy solution of spacecraft
Bingyan Liu, Xiongbing Ye, Xianzhou Dong and Lei Ni
2022, 18(2): 1223-1245 doi: 10.3934/jimo.2021016 +[Abstract](1305) +[HTML](694) +[PDF](1179.42KB)
Abstract:

With the continuous development of space rendezvous technology, more and more attention has been paid to the study of spacecraft orbital pursuit-evasion differential game. Therefore, we propose a pursuit-evasion game algorithm based on branching improved Deep Q Networks to obtain a space rendezvous strategy with non-cooperative target. Firstly, we transform the optimal control of space rendezvous between spacecraft and non-cooperative target into a survivable differential game problem. Next, in order to solve this game problem, we construct Nash equilibrium strategy and test its existence and uniqueness. Then, in order to avoid the dimensional disaster of Deep Q Networks in the continuous behavior space, we construct a TSK fuzzy inference model to represent the continuous space. Finally, in order to solve the complex and timeconsuming self-learning problem of discrete action sets, we improve Deep Q Networks algorithm, and propose a branching architecture with multiple groups of parallel neural Networks and shared decision modules. The simulation results show that the algorithm achieves the combination of optimal control and game theory, and further improves the learning ability of discrete behaviors. The algorithm has the comparative advantage of continuous space behavior decision, can effectively deal with the continuous space chase game problem, and provides a new idea for the solution of spacecraft orbit pursuit-evasion strategy.

Inverse single facility location problem on a tree with balancing on the distance of server to clients
Shahede Omidi and Jafar Fathali
2022, 18(2): 1247-1259 doi: 10.3934/jimo.2021017 +[Abstract](1022) +[HTML](477) +[PDF](625.13KB)
Abstract:

We introduce a case of inverse single facility location problem on a tree where by minimum modifying in the length of edges, the difference of distances between the farthest and nearest clients to a given facility is minimized. Two cases are considered: bounded and unbounded nonnegative edge lengths. In the unbounded case, we show the problem can be reduced to solve the problem on a star graph. Then an \begin{document}$ O(nlogn) $\end{document} algorithm is developed to find the optimal solution. For the bounded edge lengths case an algorithm with time complexity \begin{document}$ O(n^2) $\end{document} is presented.

Solution method for discrete double obstacle problems based on a power penalty approach
Kai Zhang, Xiaoqi Yang and Song Wang
2022, 18(2): 1261-1274 doi: 10.3934/jimo.2021018 +[Abstract](1145) +[HTML](479) +[PDF](741.73KB)
Abstract:

We develop a power penalty approach to a finite-dimensional double obstacle problem. This problem is first approximated by a system of nonlinear equations containing two penalty terms. We show that the solution to this penalized equation converges to that of the original obstacle problem at an exponential rate when the coefficient matrices are \begin{document}$ M $\end{document}-matrices. Numerical examples are presented to confirm the theoretical findings and illustrate the efficiency and effectiveness of the new method.

Optimality conditions of fenchel-lagrange duality and farkas-type results for composite dc infinite programs
Gang Li, Yinghong Xu and Zhenhua Qin
2022, 18(2): 1275-1293 doi: 10.3934/jimo.2021019 +[Abstract](906) +[HTML](539) +[PDF](354.17KB)
Abstract:

This paper is concerned with a DC composite programs with infinite DC inequalities constraints. Without any topological assumptions and generalized increasing property, we first construct some new regularity conditions by virtue of the epigraph technique. Then we give some complete characterizations of the (stable) Fenchel-Lagrange duality and the (stable) Farkas-type assertions. As applications, corresponding assertions for the DC programs with infinite inequality constraints and the conic programs with DC composite function are also given.

A globally convergent BFGS method for symmetric nonlinear equations
Weijun Zhou
2022, 18(2): 1295-1303 doi: 10.3934/jimo.2021020 +[Abstract](982) +[HTML](505) +[PDF](322.79KB)
Abstract:

A BFGS type method is presented to solve symmetric nonlinear equations, which is shown to be globally convergent under suitable conditions. Compared with some existing Gauss-Newton-based BFGS methods whose iterative matrix approximates the Gauss-Newton matrix, an important feature of the proposed method lies in that the iterative matrix is an approximation of the Jacobian, which greatly reduces condition number of the iterative matrix. Numerical results are reported to support the theory.

On the optimal control problems with characteristic time control constraints
Changjun Yu, Shuxuan Su and Yanqin Bai
2022, 18(2): 1305-1320 doi: 10.3934/jimo.2021021 +[Abstract](1062) +[HTML](541) +[PDF](381.75KB)
Abstract:

In this paper, we consider a class of optimal control problems with control constraints on a set of characteristic time instants. By applying the control parameterization technique, these constraints are imposed on the subdomains that contain the characteristic time points. The values of the control functions as well as the lengths for their corresponding subdomains become decision variables. Time-scaling transformation is an effective technique to optimize the length of each subdomain in a new time horizon. However, the characteristic time instants in the original time horizon become variable time instants in the new time horizon, and hence the control constraints imposed on these characteristic time points are difficult to be formulated in the new time horizon. We propose a surrogate condition and show that the characteristic time control constraints will be satisfied once the surrogate condition holds. Moreover, this surrogate condition is easy to formulate in the new time horizon. The resulting approximate problem can be readily solved by many existing computational methods for solving constrained optimal control problems. Finally, we conclude this paper by solving two examples.

Asymptotics for VaR and CTE of total aggregate losses in a bivariate operational risk cell model
Yishan Gong and Yang Yang
2022, 18(2): 1321-1337 doi: 10.3934/jimo.2021022 +[Abstract](1028) +[HTML](482) +[PDF](900.31KB)
Abstract:

This paper considers a bivariate operational risk cell model, in which the loss severities are modelled by some heavy-tailed and weakly (or strongly) dependent nonnegative random variables, and the frequency processes are described by two arbitrarily dependent general counting processes. In such a model, we establish some asymptotic formulas for the Value-at-Risk and Conditional Tail Expectation of the total aggregate loss. Some simulation studies are also conducted to check the accuracy of the obtained theoretical results via the Monte Carlo method.

Integrated dynamic interval data envelopment analysis in the presence of integer and negative data
Pooja Bansal and Aparna Mehra
2022, 18(2): 1339-1363 doi: 10.3934/jimo.2021023 +[Abstract](1084) +[HTML](579) +[PDF](500.51KB)
Abstract:

The conventional data envelopment analysis (DEA) models presume that the values of input-output variables of the decision-making units (DMUs) are precisely known. However, some real-life situations can authoritatively mandate the data to vary in concrete fine-tuned ranges, which can include negative values and measures that are allowed to take integer values only. Our study proposes an integrated dynamic DEA model to accommodate interval-valued and integer-valued features that can take negative values. The proposed one-step model follows the directional distance function approach to determine the efficiency of DMUs over time in the presence of carryovers connecting the consecutive periods. We use the pessimistic and optimistic standpoints to evaluate the respective lower and upper bounds of the interval efficiency scores of the DMUs. We compare our proposed approach with a few relevant studies in the literature. We also validate our model on a synthetically generated dataset. Furthermore, we showcase the proposed procedure's applicability on a real dataset from 2014 to 2018 of airlines operating in India.

Effects of disruption risk on a supply chain with a risk-averse retailer
Min Li, Jiahua Zhang, Yifan Xu and Wei Wang
2022, 18(2): 1365-1391 doi: 10.3934/jimo.2021024 +[Abstract](1143) +[HTML](574) +[PDF](1332.26KB)
Abstract:

This paper studies a supply chain consisting of two unreliable suppliers and a retailer, where the two suppliers' default risks are correlated. We use a mean-variance function to characterize the retailer's risk aversion. In the case of exogenous wholesale prices, we find that the retailer's risk aversion has a non-monotonic effect on its total ordering quantity. We also show that when the suppliers' default correlation increases, the retailer's total ordering quantity is non-increasing. In the case of endogenous wholesale prices, we find that the profits of the suppliers and the retailer are non-monotonic in retailer's risk aversion level or suppliers' default correlation. As risk aversion level increases, the retailer becomes less sensitive to wholesale prices. Finally, the numerical results indicate that when the suppliers' delivery rates are different, the supplier with a low delivery rate can benefit from the retailer's risk aversion under certain conditions.

Robust optimal strategies of DC pension plans with stochastic volatility and stochastic income under mean-variance criteria
Hao Chang, Jiaao Li and Hui Zhao
2022, 18(2): 1393-1423 doi: 10.3934/jimo.2021025 +[Abstract](1329) +[HTML](437) +[PDF](711.81KB)
Abstract:

This paper studies a robust optimal investment problem under the mean-variance criterion for a defined contribution (DC) pension plan with an ambiguity-averse member (AAM), who worries about model misspecification and aims to find robust optimal strategy. The member has access to a risk-free asset (i.e., cash or bank account) and a risky asset (i.e., the stock) in a financial market. In order to get closer to the actual environment, we assume that both the income level and stock price are driven by Heston's stochastic volatility model. A continuous-time mean-variance model with ambiguity aversion for a DC pension plan is established. By using the Lagrangian multiplier method and stochastic optimal control theory, the closed-form expressions for robust efficient strategy and efficient frontier are derived. In addition, some special cases are derived in detail. Finally, a numerical example is presented to illustrate the effects of model parameters on the robust efficient strategy and the efficient frontier, and some economic implications have been revealed.

CCR model-based evaluation on the effectiveness and maturity of technological innovation
Liling Lin and Linfeng Zhao
2022, 18(2): 1425-1437 doi: 10.3934/jimo.2021026 +[Abstract](1058) +[HTML](481) +[PDF](295.53KB)
Abstract:

As there are many indexes for evaluating technological innovation in enterprises, it is hard to quantify all those indexes. Therefore, common evaluation methods cannot be applied to solve the absolute value of the evaluation indexes. Therefore, this study used the nonparametric CCR model based on input-output to estimate the relative value of evaluation index, and took dual programming tool to obtain the judgment basis for the most effective and optimal solution. Based on the software evaluation criteria, this paper proposed the concept of "maturity in technological innovation, " its four levels, and an evaluation standard for maturity. Based on the homogeneity, the paper selected four Beijing enterprises as evaluation samples. After comparing and analyzing the efficiency, scale return, production surface projection and maturity, we found that the evaluation results conform to the reality of sampling enterprises. CCR model was used to evaluate decision-making units with multiple inputs and outputs. The results show that this method can help accurately obtain the relative order and the enterprises' ability to make technological innovation. Thus, CCR model is able to help enterprises formulate policies on technological innovation.

Optimizing micro-algae production in a raceway pond with variable depth
Todd Hurst and Volker Rehbock
2022, 18(2): 1439-1451 doi: 10.3934/jimo.2021027 +[Abstract](972) +[HTML](571) +[PDF](524.87KB)
Abstract:

We present a modified model of algae growth in a raceway pond with the additional feature of variable pond depth. This requires an additional state variable to model depth as well as additional control to allow for variable outflow. We apply numerical optimal control methods to this model and show that the lipid yield of the process can be increased by 67% compared to that obtained with a fixed pond depth.

Can the reform of green credit policy promote enterprise eco-innovation? A theoretical analysis
Sheng Wu, Liangpeng Wu and Xianglian Zhao
2022, 18(2): 1453-1485 doi: 10.3934/jimo.2021028 +[Abstract](1215) +[HTML](556) +[PDF](10055.96KB)
Abstract:

The weakness that China's traditional credit fails to effectively limit enterprise emissions has become increasingly evident. Although the industry-oriented green credit policy has achieved certain effects on environmental performance through the differentiated resource allocation of the industries, banking financial institutions have the ambiguity in the definition of the credit object and the characteristics of profit maximization, which cannot achieve the essential purpose of green credit sustainably. Hence, we propose a new eco-innovation-oriented green credit policy. We prove theoretically that the new green credit is feasible and can be used as an exogenous driver for improving enterprises' eco-innovation. Contrasting with traditional credit, the newly proposed credit policy is an expansionary monetary policy, which has the characteristics of expanding credit lines and differential interest rates. Utilizing evolutionary game theory, we calculate the evolution stability conditions of green credit and eco-innovation. The results show that the key to green credit to maintaining sustainable development is the return on investment due to eco-innovation. Our theoretical analysis also reveals that environmental benefit-cost ratios and adjustment cost parameters of different assets are the important factors for green credit.

Merging short-term and long-term planning problems in home health care under continuity of care and patterns for visits
Semih Yalçındağ and Ettore Lanzarone
2022, 18(2): 1487-1504 doi: 10.3934/jimo.2021029 +[Abstract](1071) +[HTML](632) +[PDF](321.61KB)
Abstract:

Home Health Care (HHC) human resource management is a complex process. Moreover, as patients are assisted for a long time, their demand for care evolves in terms of type and frequency of visits. Under continuity of care, this uncertain evolution must be considered even when scheduling the visits in the short-term, as the corresponding operator-to-patient assignments could generate overtimes and unbalanced workloads in the long-term, which must be fixed by reassigning some patients and deteriorating the continuity of care. On the other hand, the operator-to-patient assignment problem under continuity of care over a long time period could generate solutions that are infeasible when the scheduling constraints are considered. We analyze the trade-offs between the two problems, to analyze the conditions in which they can be sequentially solved or an integration is required. In particular, we take an assignment and scheduling model for short-term planning, an operator-to-patient assignment model over a long time horizon, and we merge them into a new combined model. Results on a set of realistic instances show that the combined model is necessary when the number of patterns is limited and the variability of patients' demands is high, whereas simpler models deserve to be applied in less critical situations.

2020 Impact Factor: 1.801
5 Year Impact Factor: 1.688
2020 CiteScore: 1.8

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