Rebalancing Problem Research Articles

An efficient algorithm for U-type assembly line re-balancing problem with stochastic task times

PurposeChanging the product characteristics and demand quantity resulting from the variability of the modern market leads to re-assigned tasks and changing the cycle time on the production line. Therefore, companies need re-balancing of their assembly line instead of balancing. The purpose of this paper is to propose an efficient algorithm approach for U-type assembly line re-balancing problem using stochastic task times.Design/methodology/approachIn this paper, a genetic algorithm is proposed to solve approach for U-type assembly line re-balancing problem using stochastic task times.FindingsThe performance of the genetic algorithm is tested on a wide variety of data sets from literature. The task times are assumed normal distribution. The objective is to minimize total re-balancing cost, which consists of workstation cost, operating cost and task transposition cost. The test results show that proposed genetic algorithm approach for U-type assembly line re-balancing problem performs well in terms of minimizing total re-balancing cost.Practical implicationsDemand variation is considered for stochastic U-type re balancing problem. Demand change also affects cycle time of the line. Hence, the stochastic U-type re-balancing problem under four different cycle times are analyzed to present practical case.Originality/valueAs per the authors’ knowledge, it is the first time that genetic algorithm is applied to stochastic U-type re balancing problem. The large size data set is generated to analyze performance of genetic algorithm. The results of proposed algorithm are compared with ant colony optimization algorithm.

Customer Incentive Rebalancing Plan in Free-Float Bike-Sharing System with Limited Information

Free-float bike-sharing (FFBS) systems have increased in popularity as a sustainable travel mode in recent years, especially in the urban areas of China. Despite the convenience such systems offer to customers, it is not easy to maintain an effective balance in the distribution of bikes. This study considers the dynamic rebalancing problem for FFBS systems, whereby user-based tactics are employed by incentivizing users to perform repositioning activities. Motivated by the fact that the problem is frequently faced by FFBS system operators entering a new market with limited information on travel demand, we adopt the ranking and selection approach to select the optimal incentive plan. We describe the system dynamics in detail, and formulate a profit maximization problem with a constraint on customer service level. Through numerical studies, we first establish that our procedure can select the optimal incentive plan in a wide range of scenarios. Second, under our incentive plan, the profit and service level can be improved significantly compared with the scenario without incentive provision. Third, in most cases, our procedure can achieve the optimal solution with a reasonable sample size.

The Static Bike Sharing Rebalancing Problem with Forbidden Temporary Operations

This paper introduces and solves the static bike rebalancing problem with forbidden temporary operations. In this problem, one aims at finding a minimum cost route in which a vehicle performs a series of pickup and delivery operations while satisfying demand and capacity constraints. In addition, a vehicle can visit stations multiple times but cannot use them to temporarily store or provide bikes. Apart from bike rebalancing, the problem also models courier service transportation and repositioning of inventory between retail stores, where temporary operations are frequently disliked because they require additional manual work and service time. We present some theoretical results concerning problem complexity and worst-case analysis, and then propose three exact algorithms based on different mathematical formulations. Extensive computational results on instances involving up to 80 stations show that an exact algorithm based on a minimal extended network produces the best average results. The online appendix is available at https://doi.org/10.1287/trsc.2018.0859 .

Portfolio rebalancing under uncertainty using meta-heuristic algorithm

In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain parameters and different belief degrees will produce different efficient frontiers, and affect the performance of the proposed model. Moreover, CPPI strategy performs as an insurance mechanism and limits downside risk in bear markets while it allows potential benefit in bull markets. Finally, using a globally optimisation solver and genetic algorithm (GA) for solving the model, we concluded that the problem size is an important factor in solving portfolio rebalancing problem with uncertain parameters and to gain better results, it is recommended to use a meta-heuristic algorithm rather than a global solver.

Portfolio rebalancing under uncertainty using meta-heuristic algorithm

In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain parameters and different belief degrees will produce different efficient frontiers, and affect the performance of the proposed model. Moreover, CPPI strategy performs as an insurance mechanism and limits downside risk in bear markets while it allows potential benefit in bull markets. Finally, using a globally optimization solver and genetic algorithm (GA) for solving the model, we concluded that the problem size is an important factor in solving portfolio rebalancing problem with uncertain parameters and to gain better results, it is recommended to use a meta-heuristic algorithm rather than a global solver.

The Bike sharing Rebalancing Problem with Stochastic Demands

In this paper we deal with the stochastic version of a problem arising in the context of self-service bike sharing systems, which aims at determining minimum cost routes for a fleet of homogeneous vehicles in order to redistribute bikes among stations. The Bike sharing Rebalancing Problem with Stochastic Demands is a variant of the one-commodity many-to-many pickup and delivery vehicle routing problem where demands at each station are represented by random variables, with associated probability distributions, that depend on stochastic scenarios. We develop stochastic programming models that are solved using different approaches, in particular, the L-Shaped and branch-and-cut. Moreover, we also propose heuristic algorithms based on an innovative use of positive and negative correlations among stations’ stochastic demands, as well as an efficient strategy for checking feasibility. The proposed solution approaches are evaluated and compared by means of extensive computational experiments on newly realistic benchmark instances.

The QLBS Q-Learner Goes NuQLear: Fitted Q Iteration, Inverse RL, and Option Portfolios

The QLBS model is a discrete-time option hedging and pricing model that is based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines the famous Q-Learning method for RL with the Black-Scholes (-Merton) model's idea of reducing the problem of option pricing and hedging to the problem of optimal rebalancing of a dynamic replicating portfolio for the option, which is made of a stock and cash. Here we expand on several NuQLear (Numerical Q-Learning) topics with the QLBS model. First, we investigate the performance of Fitted Q Iteration for a RL (data-driven) solution to the model, and benchmark it versus a DP (model-based) solution, as well as versus the BSM model. Second, we develop an Inverse Reinforcement Learning (IRL) setting for the model, where we only observe prices and actions (re-hedges) taken by a trader, but not rewards. Third, we outline how the QLBS model can be used for pricing portfolios of options, rather than a single option in isolation, thus providing its own, data-driven and model independent solution to the (in)famous volatility smile problem of the Black-Scholes model.

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

Developing a multi-commodity multi-period mathematical model based on the travelling salesman problem for solving bike sharing rebalancing problem

The rebalance problem in the bike sharing system includes operational decisions to respond to demand fluctuations in the kidneys Bicycle stations, so that by redistributing bikes among the stations...

Free-floating bike sharing: Solving real-life large-scale static rebalancing problems

Free-floating bike sharing (FFBS) is an innovative bike sharing model. FFBS saves on start-up cost, in comparison to station-based bike sharing (SBBS), by avoiding construction of expensive docking stations and kiosk machines. FFBS prevents bike theft and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. However, like SBBS, the success of FFBS depends on the efficiency of its rebalancing operations to serve the maximal demand as possible.Bicycle rebalancing refers to the reestablishment of the number of bikes at sites to desired quantities by using a fleet of vehicles transporting the bicycles. Static rebalancing for SBBS is a challenging combinatorial optimization problem. FFBS takes it a step further, with an increase in the scale of the problem. This article is the first effort in a series of studies of FFBS planning and management, tackling static rebalancing with single and multiple vehicles. We present a Novel Mixed Integer Linear Program for solving the Static Complete Rebalancing Problem. The proposed formulation, can not only handle single as well as multiple vehicles, but also allows for multiple visits to a node by the same vehicle. We present a hybrid nested large neighborhood search with variable neighborhood descent algorithm, which is both effective and efficient in solving static complete rebalancing problems for large-scale bike sharing programs.Computational experiments were carried out on the 1 Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP) instances used previously in the literature and on three new sets of instances, two (one real-life and one general) based on Share-A-Bull Bikes (SABB) FFBS program recently launched at the Tampa campus of University of South Florida and the other based on Divvy SBBS in Chicago. Computational experiments on the 1-PDTSP instances demonstrate that the proposed algorithm outperforms a tabu search algorithm and is highly competitive with exact algorithms previously reported in the literature for solving static rebalancing problems in SBSS. Computational experiments on the SABB and Divvy instances, demonstrate that the proposed algorithm is able to deal with the increase in scale of the static rebalancing problem pertaining to both FFBS and SBBS, while deriving high-quality solutions in a reasonable amount of CPU time.

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem

The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station must be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.

A generalized pivotal quantity approach to portfolio selection

ABSTRACTThe major problem of mean–variance portfolio optimization is parameter uncertainty. Many methods have been proposed to tackle this problem, including shrinkage methods, resampling techniques, and imposing constraints on the portfolio weights, etc. This paper suggests a new estimation method for mean–variance portfolio weights based on the concept of generalized pivotal quantity (GPQ) in the case when asset returns are multivariate normally distributed and serially independent. Both point and interval estimations of the portfolio weights are considered. Comparing with Markowitz's mean–variance model, resampling and shrinkage methods, we find that the proposed GPQ method typically yields the smallest mean-squared error for the point estimate of the portfolio weights and obtains a satisfactory coverage rate for their simultaneous confidence intervals. Finally, we apply the proposed methodology to address a portfolio rebalancing problem.

Models and algorithms for the optimization of real-world routing and logistics problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.

A destroy and repair algorithm for the Bike sharing Rebalancing Problem

In this paper, we deal with the Bike sharing Rebalancing Problem (BRP), which is the problem of driving a fleet of capacitated vehicles to redistribute bicycles among the stations of a bike sharing system. We tackle the BRP with a destroy and repair metaheuristic algorithm, which makes use of a new effective constructive heuristic and of several local search procedures. The computational effort required for the neighborhood explorations is reduced by means of a set of techniques based on the properties of feasible BRP solutions. In addition, the algorithm is adapted to solve the one-commodity Pickup and Delivery Vehicle Routing Problem with maximum Duration (1-PDVRPD), which is the variant of the BRP in which a maximum duration is imposed on each route.Extensive computational results on instances from the literature and on newly-collected large-size real-world instances are provided. Our destroy and repair algorithm compares very well with respect to an exact branch-and-cut algorithm and a previous metaheuristic algorithm in the literature. It improves several best-known solutions, providing high quality results on both problem variants.

A Bi-Objective Approach to an Assembly Line Re-Balancing Problem: Model and Differential Evolution Algorithms

A Bi-Objective Approach to an Assembly Line Re-Balancing Problem: Model and Differential Evolution Algorithms

Re-balancing problem for assembly lines: new mathematical model and exact solution method

Purpose – The purpose of this study is to develop a new mathematical model and an exact solution method for an assembly line rebalancing problem. When an existing assembly line has to be adapted to a new production context, the line balancing, resources allocation and component management solutions have to be revised. The objective is to minimize the number of modifications to be done in the initial line in order to reduce the time and investment needed to meet new production requirements. The proposed model is evaluated via a computational experiment. The obtained results the efficacy of the proposed method. Design/methodology/approach – This paper develops a new mathematical model and an exact solution method for an assembly line rebalancing problem with the objective to minimize the number of modifications to be done in the initial line to reduce the time and investments needed to meet new production requirements. Findings – The computational experiments show the efficacy of the proposed method. Originality/value – These reconfiguration costs were analysed for different part-feeding policies that can be adopted in an assembly line.

A multiobjective portfolio rebalancing model incorporating transaction costs based on incremental discounts

In this paper, we propose a multiobjective model of portfolio rebalancing problem considering return, risk and liquidity as key financial criteria. Further, a more realistic situation of financial market is considered where the portfolio, at the end of a typical time period, will be modified by buying and/or selling asset(s) in response to changing conditions. We assume that the transaction costs are paid on the basis of incremental discounts and are adjusted in the net return of the portfolio. A real-coded genetic algorithm (RGGA) is developed to solve the portfolio rebalancing problem and build an optimal portfolio. An empirical study is included to illustrate the behaviour of the proposed model using data of some randomly selected assets listed on the National Stock Exchange (NSE), Mumbai, India.

The bike sharing rebalancing problem: Mathematical formulations and benchmark instances

Bike sharing systems offer a mobility service whereby public bicycles, located at different stations across an urban area, are available for shared use. These systems contribute towards obtaining a more sustainable mobility and decreasing traffic and pollution caused by car transportation. Since the first bike sharing system was installed in Amsterdam in 1965, the number of such applications has increased remarkably so that hundreds of systems are now operating all over the world.In a bike sharing system, users can take a bicycle from a station, use it to perform a journey and then leave it at a station, not necessarily the same one of departure. This behavior typically leads to a situation in which some stations become full and others are empty. Hence, a balanced system requires the redistribution of bicycles among stations.In this paper, we address the Bike sharing Rebalancing Problem (BRP), in which a fleet of capacitated vehicles is employed in order to re-distribute the bikes with the objective of minimizing total cost. This can be viewed as a special one-commodity pickup-and-delivery capacitated vehicle routing problem. We present four mixed integer linear programming formulations of this problem. It is worth noting that the proposed formulations include an exponential number of constraints, hence, tailor-made branch-and-cut algorithms are developed in order to solve them.The mathematical formulations of the BRP were first computationally tested using data obtained for the city of Reggio Emilia, Italy. Our computational study was then extended to include bike sharing systems from other parts of the world. The information derived from the study was used to build a set of benchmark instances for the BRP which we made publicly available on the web. Extensive experimentation of the branch-and-cut algorithms presented in this paper was carried out and an interesting computational comparison of the proposed mathematical formulations is reported. Finally, several insights on the computational difficulty of the problem are highlighted.

Expected value multiobjective portfolio rebalancing model with fuzzy parameters

In this paper we develop a multicriteria credibilistic framework for portfolio rebalancing. We use an expected value model with fuzzy parameters considering return, risk and liquidity as key financial criteria. The transaction costs are assumed to be paid on the basis of incremental discounts and are adjusted in the net return of the portfolio. A solution procedure based on fuzzy goal programming and a hybrid intelligent algorithm that combines fuzzy simulation with a real-coded genetic algorithm is presented to solve the portfolio rebalancing problem. The approach adopted here has the advantage of handling the multicriteria portfolio rebalancing problem where the fuzzy parameters are characterized by general functional forms. An empirical study is included to demonstrate the effectiveness of the solution approach and efficiency of the model in practical applications of rebalancing an existing portfolio.

A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment

In this paper we propose multicriteria credibilistic framework for portfolio rebalancing (adjusting) problem with fuzzy parameters considering return, risk and liquidity as key financial criteria. The portfolio risk is characterized by a risk curve that represents each likely loss of the portfolio return and the corresponding chance of its occurrence rather than a single pre-set level of the loss. Furthermore, we consider an investment market scenario where, at the end of a typical time period, the investor would like to modify his existing portfolio by buying and/or selling assets in response to changing market conditions. We assume that the investor pays transaction costs based on incremental discount schemes associated with the buying and/or selling of assets, which are adjusted in the net return of the portfolio. A hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm is developed to solve the portfolio rebalancing (adjusting) problem. The proposed solution approach is useful particularly for the cases where fuzzy parameters of the problem are characterized by general functional forms.