The automotive industry’s operations face a critical dilemma: achieving high productivity while maintaining adequate ergonomic standards. High-volume production amplifies this condition, because the frequency of task execution keeps ergonomic risk ever-present. This work presents a real case from an automotive body parts assembly line. The objectives are to minimize the maximum individual ergonomic risk throughout job-rotation periods along a daily journey, and to optimize productivity by determining the optimal worker-to-workstation assignments. The Occupational Repetitive Action (OCRA) index is used to assess the risk of upper extremity musculoskeletal disorders. To solve this bi-objective problem, two algorithms are proposed: an ε -constraint approach and a Tchebychev method. Both are grounded in a novel Integer Linear Programming (ILP) model tailored to integrate ergonomic and productivity considerations. The algorithms generated a complete Pareto front of 16 efficient solutions within a reasonable computational time. Managerial insights are derived, highlighting the inherent trade-off between the makespan and ergonomic risk, providing valuable guidelines for balancing worker well-being and productivity in assembly-line operations.
Many mathematical models are based on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle problems, standard and generalized semi-infinite problems, robust optimization, Lagrange duality, bicriteria optimization problems, minimax problems, decomposition, and two-stage stochastic optimization. Some connections to vector optimization and variational inequalities are discussed as well.
Compromise programming is based on the concept of the ideal point and relies on distance functions for evaluation purposes. Analysts usually rely on graphical methods to construct the non-dominated frontier to select the best alternatives when dealing with two criteria. However, this graphical analysis becomes more complex when dealing with three or more criteria. To solve this limitation, this work proposes a graphical extension of compromise programming in which the ideal point is replaced with an ideal polygon, and the distance functions to the ideal point are replaced with area functions within multiaxis graphs. We evaluate alternatives by relying on two novel area functions of the polygons formed by the degree of achievement of each criterion on a graph. In addition to reporting novel theoretical results, we illustrate our method with graphical and quantitative analyses of the degree of development of cooperative banking in Europe using five indicators.
It is well-known that duality theory is a fundamental tool in various areas of mathematics. There are great advantages to including or using the dual problem and duality statements. Especially, solving the dual problem can be done using other methods of analysis or numerical mathematics. We consider a primal vector optimization problem with an objective function acting between a linear topological space X and a linear topological space Y equipped with a pointed closed convex cone D⊂ Y with nonempty interior. The feasible set is supposed to be a closed convex cone. The aim of this paper is to construct a simple and easy-to-handle dual problem by exploiting the special structure of the primal problem and using a suitable nonlinear scalarization. The computation of the dual image set involves the minimization of a nonlinear scalarization of the primal vector-valued objective function subject to only one linear inequality constraint. We introduce a new concept of upper semicontinuity for a vector-valued function and prove (weak and strong) duality statements under the assumption that the vector-valued objective function is D-quasiconvex and D-upper semicontinuous. Furthermore, we study special cases.
This article investigates the steady-state behavior of a single-server retrial queue in which arriving units select one of two heterogeneous service types, each followed by an optional immediate re-service of the same type. Units encountering a busy server join a retrial orbit and attempt to access the server after a random delay governed by classical retrial policy. Using the supplementary variable technique, we have derived the Laplace–Stieltjes transforms of the probability generating functions for the number of units in the orbit and in the system. The stochastic decomposition property is established, and pivotal system characteristics, such as the mean and variance of the orbit size, system size, and waiting times both in orbit and in the system are obtained. To validate the analytical results and study the effect of key system parameters, numerical experiments are conducted across three service time distributions namely, exponential, 2-stage Erlang and Hyper-exponential distribution. A cost optimization is carried out employing the parabolic method to identify the optimal arrival rate that minimizes the total expected operating cost per unit time.
