A linear physical programming model for assembly line balancing problem

This paper deals with the mixed-model assembly line balancing problem. This type of line is applied to more than one similar model of a product in an intermixed order. Despite their widespread use, these lines have received little attention in the literature. Metaheuristics, heuristics and mathematical programming techniques are developed to solve these types of assembly line balancing problems. However, linear physical programming method has never used. In this paper, a linear physical programming model is proposed for balancing a mixed-model assembly line. The performance of the proposed model is applied to a numerical example to analyze the usage of the methodology. Five objectives are considered in the model and the outperformance of the methodology is demonstrated by comparing it to a different approach. According to the results, it has been seen that the proposed linear physical programming model is practical and useful approach for mixed-model assembly line balancing problems.

UTILIZING A REDUCED-ORDER MODEL AND PHYSICAL PROGRAMMING FOR PRELIMINARY REACTOR DESIGN OPTIMIZATION

Reactor core design is inherently a multi-objective problem which spans a large design space, and potentially larger objective space. This process relies on high-fidelity models to probe the design space, and sophisticated computer codes to calculate the important physics occurring in the reactor. In the past, the design space has been reduced by individuals with extensive knowledge of reactor core design; however, this approach is not always available. In this paper, we utilize a set of high-fidelity models to generate a reduced-order model, and couple this with a genetic algorithm to quickly and effectively optimize a preliminary design for a prototypical sodium fast reactor. We also examine augmenting the genetic algorithm with physical programming to generate the fitness function(s) that evaluates the degree to which a core has been optimized. Physical programming is used in two variations of multi-objective optimization and is compared with a traditional weighting scheme to examine the solutions present on the Pareto front. Optimization on the reduced-order model produces a set of solutions on the Pareto front for a designer to examine. The uncertainty for the objective functions examined in the reduced-order model is less than 7% for the given designs, and improves as additional data points are employed. Utilizing a reduced-order model can significantly reduce the computation time and storage to perform preliminary optimization. Physical programming was shown to reduce the objective space when compared with a traditional weighting scheme. It also provides an intuitive and computationally efficient way to produce a Pareto front that meets the designer’s objectives.

Collaboration Strategy for a Decentralized Supply Chain Using Linear Physical Programming

In recent years, the environment surrounding companies has become more challenging. It has become more difficult for many companies in the manufacturing industry to possess all the skills they need, such as production, warehousing, and retailing, so they need to outsource certain skills. In supply chains with several companies, each has an optimal strategy. Specifically, supply chains where the solution is decided through negotiations with their partners are defined as “decentralized supply chains.” In such situations, collaborative relationships are important. One possible approach is replenishment contracts between vendors and buyers under the condition that demand for each buyer is constant. In a buyer-dominated supply chain, because the vendor cannot choose solutions that lower the satisfaction of buyers, it is difficult to change the replenishment intervals. The common replenishment epochs (CRE) strategy is one of the methods used to address this issue. The vendor integrates the buyers’ replenishment timings using CRE and provides a price discount on the products to compensate for the increase in the cost to the buyers. The price discount rate is calculated based on the worst reduction rate in the costs incurred by the buyers based on the economic order quantity (EOQ) model. The optimal CRE and discount rate are decided such that the cost incurred by vendor is minimized. The increased emphasis on the worst reduction rates can potentially lead to biases in buyer satisfaction, and the price discount rate is overestimated. Then, the cost of the vendor increases. Hence, through the negotiations with less satisfied buyers, the vendor changes the CRE so that their satisfaction is improved and the price discount is lower. As a result, the vendor can reduce its cost. This study develops a model to find an improved solution after the negotiations. If satisfaction of multiple players is regarded as multi-objective, a solution of multi-player decision-making is obtained using multi-objective optimization. Linear physical programming (LPP) has been applied as a form of multi-objective optimization, and it is possible to determine the weight coefficients using the preference ranges of the objective functions. In addition, by considering the buyers’ preference levels, the constraints of the discount rates are relaxed and the vendor’s cost can be reduced. Therefore, this study develops a model based on the CRE strategy using LPP.

Reconfigurable Satellite Constellation Design for Disaster Monitoring Using Physical Programming

Data collection by satellites during and after a natural disaster is of great significance. In this work, a reconfigurable satellite constellation is designed for disaster monitoring, and satellites in the constellation are made to fly directly overhead of the disaster site through orbital transfer. By analyzing the space geometry relations between satellite orbit and an arbitrary disaster site, a mathematical model for orbital transfer and overhead monitoring is established. Due to the unpredictability of disasters, target sites evenly spaced on the Earth are considered as all possible disaster scenarios, and the optimal reconfigurable constellation is designed with the intention to minimize total velocity increment, maximum and mean reconfiguration time, and standard deviation of reconfiguration times for all target sites. To deal with this multiobjective optimization, a physical programming method together with a genetic algorithm is employed. Numerical results are obtained through the optimization, and different observation modes of the reconfigurable constellation are analyzed by a specific case. Superiority of our design is demonstrated by comparing with the existing literature, and excellent observation performance of the reconfigurable constellation is demonstrated.