# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

May 2021 , Volume 17 , Issue 3

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2021, 17(3): 1025-1055 doi: 10.3934/jimo.2020010 +[Abstract](1440) +[HTML](582) +[PDF](663.81KB)
Abstract:

In order to reduce environment impacts of manufacturing processes and fill in research gaps that most previous separated optimization of process planning and scheduling ignored influences of process planning on scheduling, a multi-objective integrated optimization model of process planning and scheduling for reducing carbon emissions in manufacturing processes is proposed. The model aims at minimizing makespan and carbon emissions in manufacturing processes by integrated optimizing machining methods for all machining features of workpieces, machine allocations of processes, process routes and machining sequence of workpieces. Because there are many parameters in the proposed model needed to be optimized and they are interactional, a four segment encoding method is designed and a Non-dominated Sorting Genetic Algorithm II is adopted to solve the proposed model. A case study including three workpieces with twenty-three machining features to be processed by turning, milling, drilling, boring and grinding is used to verify the proposed integrated model and algorithm. Results show that the proposed integrated optimization method can further reduce carbon emissions and makespan in manufacturing processes compared with conventional separated optimization of process planning and scheduling. The proposed integrated optimization method is validated.

2021, 17(3): 1057-1068 doi: 10.3934/jimo.2020011 +[Abstract](1248) +[HTML](552) +[PDF](479.44KB)
Abstract:

In this paper, we display a method for the computation of convergence bounds for a non-stationary two-processor heterogeneous system with catastrophes, server failures and repairs when all parameters varying with time. Based on the logarithmic norm of linear operators, the bounds on the rate of convergence and the main limiting characteristics of the queue-length process are obtained. Finally a numerical example is presented to show the effect of parameters.

2021, 17(3): 1069-1100 doi: 10.3934/jimo.2020012 +[Abstract](1574) +[HTML](620) +[PDF](1766.53KB)
Abstract:

This study considers a variant of the vehicle routing problem (VRP) called the heterogeneous VRP with simultaneous pickup and delivery (HVRPSPD). The HVRPSPD may broadly be defined as identifying the minimum cost routes and vehicle types. To solve the HVRPSPD, first, we propose a polynomial-size mixed integer programming formulation. Because the HVRPSPD is an NP-hard problem, it is difficult to determine the optimal solution in a reasonable time for moderate and large-size problem instances. Hence, we develop a hybrid metaheuristic approach based on the simulated annealing and local search algorithms called SA-LS. We conduct a computational study in three stages. First, the performance of the mathematical model and SA-LS are investigated on small and medium-size HVRPSPD instances. Second, we compare SA-LS with the constructive heuristics, nearest neighborhood and Clarke-Wright savings algorithms, adapted for the HVRPSPD. Finally, the performance of SA-LS is evaluated on the instances of the heterogeneous VRP (HVRP), which is a special case of the HVRPSPD. Computational results demonstrate that the mathematical model can solve small-size instances optimally up to 35 nodes; SA-LS provides good quality solutions for medium and large-size problems. Moreover, SA-LS is superior to simple constructive heuristics and can be a preferable solution method to solve HVRP and VRPSPD instances successfully.

2021, 17(3): 1101-1118 doi: 10.3934/jimo.2020013 +[Abstract](954) +[HTML](510) +[PDF](612.13KB)
Abstract:

This paper explores the retailer's optimal lot sizing and quantity backordering for a deteriorating production system with a two-state Markov production process in which quantity discounts are provided by the supplier. The products are sold with the policy of free reasonable repair warranty employing the fraction of nonconforming items in a lot size. Unlike the traditional economic production quantity (EPQ) model with warranty policy based on the elapsed time of the system in the control state follows an exponential distribution, this paper not only constructs an alternative mathematical model for EPQ model based on the fraction of nonconforming items in a lot size for an imperfect production system but also extends the topics of optimal quantity and shortage to a wider scope of academic research and further finds that some results are different from the traditional EPQ models. We seek to minimize the expected total relevant cost through optimal lot sizing and quantity backordering. We also demonstrate that the optimal lot size is bounded in a finite interval. An efficient algorithm is developed to determine the optimal solution. Moreover, a numerical example is given and sensitivity analysis is conducted to highlight management insights.

2021, 17(3): 1119-1145 doi: 10.3934/jimo.2020014 +[Abstract](1086) +[HTML](573) +[PDF](706.24KB)
Abstract:

This paper considers the designs of the periodic window functions in the filter window banks. First, the filter window bank with the constant synthesis periodic window functions is considered. The total number of the nonzero coefficients in the impulse responses of the analysis periodic window functions is minimized subject to the near perfect reconstruction condition. This is an \begin{document}$L_0$\end{document} norm optimization problem. To find its solution, the \begin{document}$L_0$\end{document} norm optimization problem is approximated by the \begin{document}$L_1$\end{document} norm optimization problem. Then, the column of the constraint matrix corresponding to the element in the solution with the smallest magnitude is removed. Next, it is tested whether the feasible set corresponding to the new \begin{document}$L_0$\end{document} norm optimization problem is empty or not. By repeating the above procedures, a solution of the \begin{document}$L_0$\end{document} norm optimization problem is obtained. Second, the filter window bank with the time varying synthesis periodic window functions is considered. Likewise, the design of the periodic window functions in both the analysis periodic window functions and the synthesis periodic window functions is formulated as an \begin{document}$L_0$\end{document} optimization problem. However, this \begin{document}$L_0$\end{document} norm optimization problem is subject to a quadratic matrix inequality constraint. To find its solution, the set of the synthesis periodic window functions is initialized. Then, the set of the analysis periodic window functions is optimized based on the initialized set of the synthesis periodic window functions. Next, the set of the synthesis periodic window functions is optimized based on the found set of the analysis periodic window functions. Finally, these two procedures are iterated. It is shown that the iterative algorithm converges. A design example of a filter window bank with the constant synthesis periodic window functions and a design example of a filter window bank with the time varying synthesis periodic window functions are illustrated. It is shown that the near perfect reconstruction condition is satisfied, whereas this is not the cases for the nonuniform filter banks with the conventional samplers and the conventional block samplers.

2021, 17(3): 1147-1171 doi: 10.3934/jimo.2020015 +[Abstract](1228) +[HTML](587) +[PDF](608.88KB)
Abstract:

In this paper we investigate the management of a defined benefit pension plan under a model with random coefficients. The objective of the pension sponsor is to minimize the solvency risk, contribution risk and the expected terminal value of the unfunded actuarial liability. By measuring the solvency risk in terms of the variance of the terminal unfunded actuarial liability, we formulate the problem as a mean-variance problem with an additional running cost. With the help of a system of backward stochastic differential equations, we derive a time-consistent equilibrium strategy towards investment and contribution rate. The obtained equilibrium strategy turns out to be a good candidate for a stable contribution plan. When the interest rate is given by the Vasicek model and all other coefficients are deterministic, we obtain closed-form solutions of the equilibrium strategy and efficient frontier.

2021, 17(3): 1173-1185 doi: 10.3934/jimo.2020016 +[Abstract](955) +[HTML](481) +[PDF](366.41KB)
Abstract:

The alternating direction method of multipliers (ADMM) is one of the most well-known optimization scheme for solving linearly constrained separable convex problem. In the literature, Fortin and Glowinski proved that the step size for updating the Lagrange multiplier of the ADMM can be chosen in the open interval of zero to the golden ratio. But, it is still unknown whether the dual step size can be larger than the golden ratio. In this paper, for the case where one function term is strongly convex and the associate coefficient matrix is full column rank, we present an affirmative answer to the above question. We then derive an exact relationship between the modulus and the dual step size. Our analysis deepens the understanding of the convergence properties of the ADMM.

2021, 17(3): 1187-1202 doi: 10.3934/jimo.2020017 +[Abstract](848) +[HTML](508) +[PDF](2791.21KB)
Abstract:

This paper develops a game theoretical model for a supply chain consisting of one manufacturer and one retailer who chooses one of two strategies: implementing fit revelation or not implementing fit revelation. Firstly, the fit revelation strategy of the retailer in the decentralized supply chain is analyzed. When the market scale is medium, the fit revelation strategy is implementing fit revelation and only good-fit consumer will buy the product; otherwise, it is not implementing fit revelation. The results are counterintuitive because people may believe that it would be better to let consumers know more information about the product when the market scale is low. Implementing fit revelation is not always beneficial for consumers. When the market scale is sufficiently low, good-fit and bad-fit consumers both prefer not implementing fit revelation. Secondly, the paper also considers the case in which the manufacturer decides whether to implement fit revelation. Sometimes, the retailer and the manufacturer prefer themselves to facilitate fit revelation. Thirdly, the effect of decentralization is investigated. Numerical examples show that the interval in which implementing fit revelation is optimal is larger under the centralized setting than that under the decentralized setting. The decentralization decreases the probability to implement fit revelation.

2021, 17(3): 1203-1233 doi: 10.3934/jimo.2020018 +[Abstract](1077) +[HTML](755) +[PDF](730.8KB)
Abstract:

In reality, when facing a defined contribution (DC) pension fund investment problem, the fund manager may not have sufficient confidence in the reference model and rather considers some similar alternative models. In this paper, we investigate the robust equilibrium control-measure policy for an ambiguity-averse and risk-averse fund manger under the mean-variance (MV) criterion. The ambiguity aversion is introduced by adopting the model uncertainty robustness framework developed by Anderson. The risk aversion model is state-dependent, and takes a linear form of the current wealth level after contribution. Moreover, the fund manager faces stochastic labor income risk and allocates his wealth among a risk-free asset and a risky asset. We also propose two complicated ambiguity preference functions which are economically meaningful and facilitate analytical tractability. Due to the time-inconsistency of the resulting stochastic control problem, we attack it by using the game theoretical framework and the concept of subgame perfect Nash equilibrium. The extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations and the verification theorem for our problem are established. The explicit expressions for the robust equilibrium policy and the corresponding robust equilibrium value function are derived by stochastic control technique. In addition, we discuss two special cases of our model, which shows that our results extend some existing works in the literature. Finally, some numerical experiments are conducted to demonstrate the effects of model parameters on our robust equilibrium policy.

2021, 17(3): 1235-1252 doi: 10.3934/jimo.2020019 +[Abstract](900) +[HTML](496) +[PDF](6275.91KB)
Abstract:

Subspace clustering segments a collection of data from a union of several subspaces into clusters with each cluster corresponding to one subspace. The geometric information of the dataset reflects its intrinsic structure and can be utilized to assist the segmentation. In this paper, we propose side-information-induced reweighted sparse subspace clustering (SRSSC) for high-dimensional data clustering. In our method, the geometric information of the high-dimensional data points in a target space is utilized to induce subspace clustering as side-information. We solve the method by iterating the reweighted \begin{document}$l_1$\end{document}-norm minimization to obtain the self-representation coefficients of the data and segment the data using the spectral clustering framework. We compare the performance of our proposed algorithm with some state-of-the-art algorithms using synthetic data and three famous real datasets. Our proposed SRSSC algorithm is the simplest but the most effective. In the experiments, the results of these clustering algorithms verify the effectiveness of our proposed algorithm.

2021, 17(3): 1253-1267 doi: 10.3934/jimo.2020020 +[Abstract](963) +[HTML](469) +[PDF](644.9KB)
Abstract:

Many real-world networks such as freight, power and long distance transportation networks are represented as multi-source multi-sink stochastic flow network. The objective is to transmit flow successfully between the source and the sink nodes. The reliability of the capacity vector of the assigned components is used an indicator to find the best flow strategy on the network. The Components Assignment Problem (CAP) deals with searching the optimal components to a given network subject to one or more constraints. The CAP in multi-source multi-sink stochastic flow networks with multiple commodities has not yet been discussed, so our paper investigates this scenario to maximize the reliability of the capacity vector subject to an assignment budget. The mathematical formulation of the problem is defined, and a proposed solution based on genetic algorithms is developed consisting of two steps. The first searches the set of components with the minimum cost and the second searches the flow vector of this set of components with maximum reliability. We apply the solution approach to three commonly used examples from the literature with two sets of available components to demonstrate its strong performance.

2021, 17(3): 1269-1287 doi: 10.3934/jimo.2020021 +[Abstract](949) +[HTML](500) +[PDF](477.36KB)
Abstract:

In order to solve the problem that the mechanism model of nonlinear system with uncertainty is difficult to establish, a modeling method of nonlinear system based on Asynchronous Fuzzy Cognitive Network (AFCN) is proposed. This method combines fuzzy cognitive network with time-lag system, and extends the node state values and weights of fuzzy cognitive network to the time interval, which enhances the adaptability of the model. At the same time an improved constrained chicken swarm optimization algorithm(ICCSOA) is proposed to identify model parameters of AFCN. A lag matrix corresponding to the actual measured values of the system lag of the nodes in the AFCN model is introduced, and a correction term including the difference between the measured values and the predicted values of the system is added to the model parameter updating mechanism. The simulation experiment results of goethite process system shows this modeling method can be used to model complex systems with uncertainties or partial missing data. The control model based on the established system model can make correct control decisions. ICCSOA has the advantages of fast convergence speed and accurate learning results, whose global search ability and convergence accuracy are higher than those of CSO algorithm, which can be widely used to the modeling of uncertain systems.

2021, 17(3): 1289-1314 doi: 10.3934/jimo.2020022 +[Abstract](1349) +[HTML](570) +[PDF](501.31KB)
Abstract:

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.

2021, 17(3): 1315-1341 doi: 10.3934/jimo.2020023 +[Abstract](1065) +[HTML](558) +[PDF](1953.36KB)
Abstract:

The emergence of electric vehicle wireless charging technology, where a whole lane can be turned into a charging infrastructure, leads to new challenges in the design and analysis of road networks. From a network perspective, a major challenge is determining the most important nodes with respect to the placement of the wireless charging lanes. In other words, given a limited budget, cities could face the decision problem of where to place these wireless charging lanes. With a heavy price tag, a placement without a careful study can lead to inefficient use of limited resources. In this work, the placement of wireless charging lanes is modeled as an integer programming problem. The basic formulation is used as a building block for different realistic scenarios. We carry out experiments using real geospatial data and compare our results to different network-based heuristics.

Reproducibility: all datasets, algorithm implementations and mathematical programming formulation presented in this work are available at https://github.com/hmwesigwa/smartcities.git

2021, 17(3): 1343-1355 doi: 10.3934/jimo.2020024 +[Abstract](924) +[HTML](474) +[PDF](352.45KB)
Abstract:

In this brief, the problem of event-triggered mixed \begin{document}${H_\infty }$\end{document} and passive control for a class of discrete-time stochastic Markov jump systems with bounded inputs is addressed. In order to reduce the frequency of the variation of the controller, an effective triggered scheme, called event-triggered scheme, is proposed, where unlike the traditional triggered scheme, not all sampling states are required to be transmitted to the controller. The event-triggered controller, which is designed using Lyapunov functional analysis approach and slack matrices, can ensure that the resulting system is stochastically stable with a prescribed mixed \begin{document}${H_\infty }$\end{document} and passive performance index. Sufficient conditions in terms of linear matrix inequalities (LMIs) are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

2021, 17(3): 1357-1382 doi: 10.3934/jimo.2020025 +[Abstract](1912) +[HTML](501) +[PDF](915.03KB)
Abstract:

Data envelopment analysis (DEA) is one of the vastly available literature on efficiency analysis. In general, the efficiency of decision making units (DMUs) can be measured from two perspectives, optimistic and pessimistic. Two different perspectives lead to two different conflicting and biased scale efficiency measurements. To deal with the problem, in this paper, we introduce a double frontier approach to integrate both optimistic and pessimistic scale efficiencies' viewpoints in one single scale efficiency term, which will be more realistic and has benchmarking preferences. We first investigate the scale efficiency concept from double frontier perspective in black-box DEA and then extend it to the two-stage DEA framework. Mathematical analysis proved that the double frontier scale efficiency of a two-stage system could be decomposed into the internal stages' double frontier scale efficiencies. Finally, we elaborate applicability and merits of the proposed approach using a case of China's regional R & D value chain in terms of its profitability and marketability.

2021, 17(3): 1383-1410 doi: 10.3934/jimo.2020026 +[Abstract](1039) +[HTML](546) +[PDF](538.85KB)
Abstract:

In this paper, we investigate a multi-period mean-variance asset-liability management problem with stochastic interest rate and seek its time-consistent strategy. The financial market is assumed to be composed of one risk-free asset and multiple risky assets, and the stochastic interest rate is characterized by the discrete-time Vasicek model proposed by Yao et al. (2016a)[38]. We regard this problem as a non-cooperative game whose equilibrium strategy is the desired time-consistent strategy. We derive the analytical expressions of the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by the extended Bellman equation. Some special cases of our model are discussed, and some properties of our equilibrium strategy, including a two-fund separation theorem, are proposed. Finally, a numerical example with real data is given to illustrate our theoretical results.

2021, 17(3): 1411-1422 doi: 10.3934/jimo.2020027 +[Abstract](847) +[HTML](511) +[PDF](398.84KB)
Abstract:

The purpose of this paper is to explore the multiple-server machine interference problem with standby unsuccessful switchover and Bernoulli vacation schedule. Failure times of operating and standby machines are assumed to have exponential distributions and repair times of the failed machines and vacation times of servers are also assumed to have exponential distributions. After the completion of service, the server either goes for a vacation or may continue serving for the next machine. The vacation policy we considered is a single vacation policy. In practice, the switchover may experience a significant failure. The matrix analytical method and recursive method are employed to obtain the steady-state probability vectors, and closed-form expressions of some important system characteristics are obtained. The problem of cost optimization dealt with a number of numerical examples is provided by the Quasi-Newton method, the pattern search method, and the Nelder-Mead simplex direct search method. Expressions of various system characteristics are derived. Sensitivity analysis is performed numerically for system parameters. This paper presents the first time that machine interference problem with unsuccessful switchover for a group of repairable servers with vacations has been obtained, which is quite useful for the decision makers.

2021, 17(3): 1423-1450 doi: 10.3934/jimo.2020028 +[Abstract](1117) +[HTML](490) +[PDF](1311.4KB)
Abstract:

This paper addresses the coordination of pricing, advertising, and production-inventory decisions in a multi-product three-echelon supply chain composed of multiple suppliers, single manufacturer, and multiple retailers. The demand of each product is considered to be non-linearly influenced by the retail price and advertising expenditure. Taking into account the dominant power of the manufacturer and the suppliers' oligopoly competition, this paper aims at obtaining the equilibrium prices at each level of the supply chain and comparing two different scenarios of competitions and cooperation: The former focuses on the situation where the single manufacturer has the dominant power in the supply chain and acts as the leader followed by the retailers and the suppliers simultaneously. The latter implies the situation in which the dominant manufacturer enters cooperation with each independent retailer to boost sales while the suppliers play the role of the followers simultaneously. We develop the Stackelberg-Nash game (SNG), and the Stackelberg-Nash game with cooperation (SNGC) formulations to model the two market structures. The equilibrium decisions are achieved through the optimization methods and the existence and uniqueness properties are explored. Finally, analytical and computational analyses are carried out through a numerical example, and a comprehensive sensitivity analysis is conducted to discuss some managerial insights such as increasing competition among suppliers leads to reducing retail prices.

2021, 17(3): 1451-1469 doi: 10.3934/jimo.2020029 +[Abstract](944) +[HTML](474) +[PDF](532.14KB)
Abstract:

In this paper, we analytically solve the utility maximization problem for a consumption set with multiple habit formation of interaction. Consumption is here composed of habitual and nonhabitual components, where habitual consumption represents the effect of past consumption. We further assume that the individual seeks to maximize his/her expected utility from nonhabitual consumption. Although there is usually no explicit solution of linear dynamic systems in the habit formation model, we study the functional minimum of habitual consumption. To solve the optimization problem with a general utility function, we adopt the convex dual martingale approach to construct the optimal consumption strategy and provide an economic interpretation for nearly every object throughout the solution process.

2021, 17(3): 1471-1483 doi: 10.3934/jimo.2020030 +[Abstract](1441) +[HTML](489) +[PDF](587.97KB)
Abstract:

This paper investigates finite-horizon optimal control problem of completely unknown discrete-time linear systems. The completely unknown here refers to that the system dynamics are unknown. Compared with infinite-horizon optimal control, the Riccati equation (RE) of finite-horizon optimal control is time-dependent and must meet certain terminal boundary constraints, which brings the greater challenges. Meanwhile, the completely unknown system dynamics have also caused additional challenges. The main innovation of this paper is the developed cyclic fixed-finite-horizon-based Q-learning algorithm to approximate the optimal control input without requiring the system dynamics. The developed algorithm main consists of two phases: the data collection phase over a fixed-finite-horizon and the parameters update phase. A least-squares method is used to correlate the two phases to obtain the optimal parameters by cyclic. Finally, simulation results are given to verify the effectiveness of the proposed cyclic fixed-finite-horizon-based Q-learning algorithm.

2021, 17(3): 1485-1504 doi: 10.3934/jimo.2020031 +[Abstract](1085) +[HTML](574) +[PDF](636.69KB)
Abstract:

Manufacturers often face capital constraints when opening up online channel, at this time external financing and internal financing are usually considered. Previous literature has shown that internal financing, turns out to be a better option. To figure out how trade credit financing discount contract affects operations and performances of supply chain, this paper studies the pricing decision of a retailer-dominant dual-channel supply chain with manufacturer's capital constraints. The Stackelberg game models under centralized decision and decentralized decision are constructed. Moreover, this paper conducts research about the effects of revenue-sharing (RS) contract, direct channel price discount (DP) contract and retail channel price discount (RP) contract on the performance of supply chain. Numerical examples are provided to explore the comparison of the optimal pricing strategies and total profits under different contracts. The results show that the retailer prefers RS and DP contracts to RP contract. Among them, RS contract has a broader scope of coordination, while DP contract can achieve a higher profit. The results can serve as insights for decision-makers to choose the most appropriate financial discount contract.

2021, 17(3): 1505-1529 doi: 10.3934/jimo.2020032 +[Abstract](941) +[HTML](602) +[PDF](494.04KB)
Abstract:

Process uncertainty makes remanufacturing operations management sophisticated. To reduce the uncertainty of the timing, quality and quantity of product returns in remanufacturing, motivated by the selling and leasing of electric vehicle batteries, we consider a monopolist vendor who markets her products by adopting two models: (1) a single leasing model, and (2) a single selling model. We first investigate the firm's marketing model with remanufacturing and analyze the impact of the quality level of the returned products on the firm's marketing and remarketing models. Then we compare selling and leasing models. We first find that only when the quality level of returned sold products is relatively high will the vendor choose to remanufacture under the single selling model. Conversely, only when the quality level of returned leased products is relatively low will the vendor decide to remanufacture under the single leasing model. Secondly, we show that the space of remanufacturable quality level under the single selling model is bigger than the space under the single leasing model. Thirdly, selling is more profitable than leasing when the quality level of returned sold products is sufficiently high. These results are further demonstrated by a numerical study. Our study provides firms with guidance on how to optimally adopt remanufacturing and marketing strategies that take into account the quality level of the returned products.

2019  Impact Factor: 1.366