Optimal Solutions For Small Size Instances Research Articles

Model and metaheuristics for robotic two-sided assembly line balancing problems with setup times

Two-sided robotic assembly lines are employed to assemble large-sized high-volume products, where robots are allocated to the workstations to perform the tasks and human workers are replaced for achieving lower cost and greater flexibility in production. In the two-sided robotic assembly lines, setup times are unavoidable and it has been ignored in most of the reported works. There has been limited attention on this till date. This paper focusses on the robotic two-sided assembly line with consideration of sequence-dependent setup times and robot setup times. A new mixed integer linear programming model is developed with the objective of optimizing the cycle time. Due to the NP-hard nature of the considered problem, this paper proposes a set of metaheuristics to solve this considered problem, where two main scenarios with low and high setup time’s variability are considered. Computational results verify that this new model is capable to achieve the optimal solutions for small-size instances whereas the simple adoption of the published mathematical model might produce wrong solutions for the considered problem. A comprehensive study with 13 algorithms demonstrates that the two variants of artificial bee colony algorithm and migrating bird optimization algorithm are capable to achieve the optimality for small-size instances and to obtain promising results for large-size instances.

Single Machine Scheduling Considering Time Value of Money

Abstract Under the background of Industry 4.0, this paper studies the single machine scheduling problem by taking into account the time value of money and tardiness penalty. We establish a mixed integer nonlinear programming model for the considered problem, and then convert the above model into a novel integer linear programming model. Regarding the factor of time value of money, we mainly aim to find an optimal or near optimal processing sequence of the jobs such that the total future value of profits is maximized. We employ CPLEX to output optimal solutions for small-size instances. For large-size instances, we propose the genetic algorithm to produce near optimal solutions.

Robust vehicle routing problem with hard time windows under demand and travel time uncertainty

Due to an increase in customer-oriented service strategies designed to meet more complex and exacting customer requirements, meeting a scheduled time window has become an important part of designing vehicle routes for logistics activities. However, practically, the uncertainty in travel times and customer demand often means vehicles miss these time windows, increasing service costs and decreasing customer satisfaction. In an effort to find a solution that meets the needs of real-world logistics, we examine the vehicle routing problem with hard time windows under demand and travel time uncertainty. To address the problem, we build a robust optimization model based on novel route-dependent uncertainty sets. However, due to the complex nature of the problem, the robust model is only able to tackle small-sized instances using standard solvers. Therefore, to tackle large instances, we design a two-stage algorithm based on a modified adaptive variable neighborhood search heuristic. The first stage of the algorithm minimizes the total number of vehicle routes, while the second stage minimizes the total travel distance. Extensive computational experiments are conducted with modified versions of Solomon’s benchmark instances. The numerical results show that the proposed two-stage algorithm is able to find optimal solutions for small-sized instances and good-quality robust solutions for large-sized instances with little increase to the total travel distance and/or the number of vehicles used. A detailed analysis of the results also reveals several managerial insights for decision-makers in the logistics industry.

Two heuristics for coordinating production planning and transportation planning

In this study, a coordinated production and transportation planning problem is addressed. A fleet of heterogeneous vehicles is considered. The transportation costs consist of two terms: a term represents the fixed cost for each vehicle used and another term for the variable cost which is the marginal transportation cost times the transportation quantity. The problem is formulated as a mixed-integer linear programming model (MILP) and a Non-Linear Programming model (NLP). The problem is unsolvable when the size increases beyond a certain magnitude. Therefore, two heuristics are developed. One of them is a decomposition-based heuristic (termed DBH). It combines solutions by decomposing the original problem into production and transportation subproblems and iteratively improves the combined solutions. The other heuristic is based on Lagrangian relaxation (called LRBH). The performance of these heuristics is evaluated by comparing their results with optimal solutions for small-sized instances and with Lagrangian-relaxation-based lower bounds for medium- or large-sized instances. The results indicate that although these heuristics use distinct mechanisms, they are both efficient and have comparable performances. The average cost gap for DBH as well as LRBH is around compared with optimal solutions. They are 4.43 and , respectively, when compared with Lagrangian-relaxation-based lower bounds.

Algorithms solving the Internet shopping optimization problem with price discounts

AbstractThe Internet shopping optimization problem arises when a customer aims to purchase a list of goods from a set of web-stores with a minimum total cost. This problem is NP-hard in the strong sense. We are interested in solving the Internet shopping optimization problem with additional delivery costs associated to the web-stores where the goods are bought. It is of interest to extend the model including price discounts of goods.The aim of this paper is to present a set of optimization algorithms to solve the problem. Our purpose is to find a compromise solution between computational time and results close to the optimum value. The performance of the set of algorithms is evaluated through simulations using real world data collected from 32 web-stores. The quality of the results provided by the set of algorithms is compared to the optimal solutions for small-size instances of the problem. The optimization algorithms are also evaluated regarding scalability when the size of the instances increases. The set of results revealed that the algorithms are able to compute good quality solutions close to the optimum in a reasonable time with very good scalability demonstrating their practicability.

Algorithms for common due-date assignment and sequencing on a single machine with sequence-dependent setup times

This paper focuses on the single machine sequencing and common due-date assignment problem for the objective of minimizing the sum of the penalties associated with earliness, tardiness and due-date assignment. Unlike the previous research articles on this class of scheduling problem, we consider sequence-dependent setup times that make the problem much more difficult. To solve the problem, a branch and bound algorithm, which incorporates the method to obtain lower and upper bounds as well as a dominance property to reduce the search space, is suggested that gives the optimal solutions for small-sized instances. Heuristic algorithms are suggested to obtain solutions for large-sized problems within a reasonable computation time. The performances of both the optimal and heuristic algorithms, in computational experiments on randomly generated test instances, are reported.