Bi-objective Linear Programming Model Research Articles

Assembly line balancing and worker assignment considering workers’ expertise and perceived physical effort

In manual assembly systems, workers’ differences in terms of skills, level of expertise and perceived physical effort largely affect the assembly line balancing and system performance. Traditional long-term strategic decisions may not respond to workforce changes and needs, resulting in frequent requests for line rebalancing. In this study, we propose a methodological framework and an easy-to-use Assembly Line Worker Assignment and Rebalancing Problem with different options: workers’ assignment considering their performance variability, integration of worker dependent physical exertion constraints and possibility to use trainers to assist inexperienced workers. A bi-objective linear programming model is proposed aiming to minimise the cycle time and the number of reassigned tasks to respect the initial design while integrating new workers with different characteristics. The -constraint approach is used to build Pareto frontiers for this bi-objective problem. This approach is applied to three real cases. The obtained results show that the developed model can be successfully used in manufacturing companies to help the production managers to deal with workforce turnover and skills heterogeneity.

Life cycle evaluation of microalgae based biorefinery supply network: A sustainable multi-criteria approach

Due to enjoying such features as ability to produce high volumes of oil and reducing and eliminating environment carbon dioxide, microalgae is a promising solution for producing biofuels. In order to help the commercialization of this emerging industry, the present study offers a sustainable mixed integer linear programming model (MILP) for designing and planning microalgae biofuel production and distribution network. As objective functions, this model considers minimizing the total cost of the network and maximizing greenhouse gas emission saving simultaneously. In order to design microalgae biofuel sustainable production and distribution network, a two-stage approach is developed. In order to reduce computational complexity, at first place, data envelopment analysis approach (DEA) and Combinative Distance-Based Assessment (CODAS) approach as well as best worst method (BWM) are developed respectively for determining the location of suitable candidates for establishing microalgae production facilities and constructing biorefinery based on economic, social and environmental criteria. In the second stage, the environmental effects of microalgae biofuel supply chain network are measured using one of the newest and most effective methods that is based upon environmental life cycle assessment as well as OpenLCA software and then followed by formulizing a bi-objective linear programming model. For solving the offered model, augmented epsilon constraint method is used. Finally, a realistic case study conducted at national level concerning microalgae biofuel supply chain. The results indicate that based on the offered model by replacing fossil fuels with biofuel we can achieve greenhouse gases emission saving by 99 %.

Consideration of workforce differences in assembly line balancing and worker assignment problem

Abstract Workforce differences in terms of skill, age, gender and physical measures have a large impact on production systems performance. Moreover, the role of differences between workers can be particularly seen in assembly lines, where a vast range of tasks are performed manually, and workers are involved widely. In this work, we introduce a new assembly line balancing and worker assignment model with consideration of workers’ diversity in terms of both workers’ expertise and perceived physical effort to implement an age-inclusive workforce. Here, a new Worker Task Categorization Matrix is introduced to assure the complete involvement of the individual during the balancing process. Following, a bi-objective linear programming model is proposed and solved by using the ϵ -constraint approach. Finally, we test and validate the model through a real-case application.

Collaborative two-echelon multicenter vehicle routing optimization based on state–space–time network representation

Collaboration among service providers in a logistics network can greatly increase their operation efficiencies and reduce transportation emissions. This study proposes, formulates and solves a collaborative two-echelon multicenter vehicle routing problem based on a state–space–time (CTMCVRP-SST) network to facilitate collaboration and resource sharing in a multiperiod state–space–time (SST) logistics network. The CTMCVRP-SST aims to facilitate collaboration in logistics networks by leveraging the spatial-temporal properties of logistics demands and resources to optimize the distribution of logistics resources in space and time to meet logistics demands. A three-component solution framework is proposed to solve CTMCVRP-SST. First, a bi-objective linear programming model based on resource sharing in a multiperiod SST network is formulated to minimize the number of vehicles and the total cost of the collaborative operation. Second, an integrated algorithm consisting of SST-based dynamic programming (DP), improved K-means clustering and improved non-dominated sorting genetic algorithm-II (Im-NSGAII) is developed to obtain optimal routes. Third, a cost gap allocation model is employed to design a collaborative mechanism that encourages cooperation among logistics service providers. Using this solution framework, the coalition sequences (i.e., the order of each logistics provider joining a collaborative coalition) are designed and the stability of the coalitions based on profit allocations is studied. Results show that the proposed algorithm outperforms existing algorithms in minimizing the total cost with all other constraints being the same. An empirical case study of a logistics network in Chongqing suggests that the proposed collaboration mechanism with SST network representation can reduce costs, improve transportation efficiency, and contribute to efficient and sustainable logistics network operations.

Hybrid discrete differential evolution algorithm for biobjective cyclic hoist scheduling with reentrance

Cyclic hoist scheduling problems in automated electroplating lines and surface processing shops attract many attentions and interests both from practitioners and researchers. In such systems, parts are transported from a workstation to another by a material handling hoist. The existing literature mainly addressed how to find an optimal cyclic schedule to minimize the cycle time that measures the productivity of the lines. The material handling cost is an important factor that needs to be considered in practice but seldom addressed in the literature. This study focuses on a biobjective cyclic hoist scheduling problem to minimize the cycle time and the material handling cost simultaneously. We consider the reentrant workstations that are usually encountered in real-life lines but inevitably make the part-flow more complicated. The problem is formulated as a biobjective linear programming model with a given hoist move sequence and transformed into finding a set of Pareto optimal hoist move sequences with respect to the bicriteria. To obtain the Pareto optimal or near-optimal front, a hybrid discrete differential evolution (DDE) algorithm is proposed. In this hybrid evolutional algorithm, the population is divided into several subpopulations according to the maximal work-in-process (WIP) level of the system and the sizes of subpopulations are dynamically adjusted to balance the exploration and exploitation of the search. We propose a constructive heuristic to generate initial subpopulations with different WIP levels, hybrid mutation and crossover operators, an evaluation method that can tackle infeasible individuals and a one-to-one greedy tabu selection method. Computational results on both benchmark instances and randomly generated instances show that our proposed hybrid DDE algorithm outperforms the basic DDE algorithm and can solve larger-size instances than the existing ε-constraint method.

A bi-objective model for analysing the potential impacts of water pricing and regulation strategies on the performance of irrigated agriculture

Regulations are the most common public policy instrument for governments to support sustainable agriculture, including rules governing land and water use, chemical inputs and food quality. Irrigated agriculture in Europe has been directly influenced by changes in the regulatory context by various EU policies based upon the price of water. This study aims to assess the multiple impacts of the Common Agricultural Policies (CAP) on social sustainability in rural areas. The consequences of policy change were evaluated, using a bi-objective linear programming model that simulates farmers' preferred behaviour. The output of the model consists of economic, social and environmental indicators aimed at quantifying the impact of the scenarios on different aspects of sustainability relevant for irrigated farming systems. The results show a clear trade-off between socio-economic and environmental sustainability. This emphasises the need to balance water conservation with agricultural policy and rural development objectives. The approach is illustrated using a case study on fruit production in East Anglia, UK.

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.

A Portfolio Selection Model Based on Possibility Theory Using Fuzzy Two-stage Algorithm

The uncertainty of a financial market is traditionally dealt with probabilistic approaches. However, there are many non-probabilistic factors that affect the financial markets such that the return rate of risky assets may be regarded as fuzzy number, which is a powerful tool used to describe an uncertain environment with vagueness and ambiguity and some type of fuzziness. In this paper, the conventional probabilistic mean-variance model can be simplified as a bi-objective linear programming model based on possibility theory. Furthermore, the fuzzy two-stage algorithm is applied to solve our proposed bi-objective model. Finally, a numerical example of the portfolio selection problem is given to illustrate our proposed effective means and variances. The results of the example also show that the fuzzy two-stage algorithm solving the model is effective and feasible.

A stochastic possibilistic programming model for bank hedging decision problems

Abstract For a practical bank hedging decision optimization problem, interest rates and price of futures contract may involve both fuzziness and randomness. For subjective nature of satisfaction, maximum desired values of loan demand, deposit supply and ratio of desired loan to deposit are often fuzzy. In this study, we consider and solve a stochastic possibilistic programming model of bank hedging decision problems with the above characters. We first use the expected value to obtain an auxiliary possibilistic linear programming problem which is further resolved by use of β-level cut. An (crisp) auxiliary bi-objective linear programming model is then proposed and solved by our augmented maximum approach. For illustration purpose, a numerical bank hedging decision problem is solved.

Possibilistic linear programming for managing interest rate risk

Abstract In this study, we consider the linear programming problem with the objective of the investment discounted value, where the interest rate is imprecise and has a triangular possibilistic distribution. An (crisp) auxiliary bi-objective linear programming model is proposed to resolve this possibilistic nature. Furthermore, we develop an extended Zimmermann approach, called augmented max-min approach, for solving this auxiliary bi-objective linear programming problem and other multiple objective linear programming problems. Finally, a numerical bank balance sheet problem, where interest rates, price of futures contract, loan demand, deposit supply and ratio of desired loan to deposit are assumed to be fuzzy, is solved for illustrating the new approach.