The Bin Packing Problem with Precedence Constraints

Abstract

Given a set of identical capacitated bins, a set of weighted items and a set of precedences among such items, we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satised. The problem, denoted as the Bin Packing Problem with Precedence Constraints (BPP-P), has a very intriguing combinatorial structure and models many assembly and scheduling issues.According to our knowledge the BPP-P has received little attention in the literature, and in this paper we address it for the first time with exact solution methods. In particular, we develop reduction criteria, a large set of lower bounds, a Variable Neighborhood Search upper bounding technique and a branch-and-bound algorithm. We show the eectiveness of the proposed algorithms by means of extensive computational tests on benchmark instances and comparison with standard integer linear programming techniques

A branch-and-price algorithm for the temporal bin packing problem

“…It would be interesting to study if these formulations, especially the ones based on the arc flow mechanism (see, e.g., Valério de Carvalho [39] and [20]), could be effectively used to tackle the TBPP as well. Finally, it would be interesting to introduce additional real-world features to the TBPP; for instance, precedence constraints between the items (see, e.g., Dell'Amico et al [18]) or item class set-up costs (see, e.g., Furini et al [25]).…”

Improved integer programming models for simple assembly line balancing and related problems

“…In this latter case, we also compare the results of the new model with the results obtained with the tailored branch‐and‐bound algorithm of Dell'Amico et al. (). The detailed results reported in the tables below are available online at http://www.inf.ufrgs.br/algopt/albp.…”

“…It has been studied recently by Dell'Amico et al. (), who propose a mathematical model, lower bounds, as well as heuristic and exact algorithms.…”

“…We show how the model for the U‐shaped assembly line balancing problem (UALBP‐1) proposed by Urban () and the model for the bin packing problem with precedence constraints (BPP‐P), which has been recently introduced by Dell'Amico et al. () can be improved by the formulations proposed in this paper. Urban's model is widely used in the literature as originally proposed (Aase et al., ; Gökçen and Aǧpak, ; Chiang et al., ; Erin, ; Kara and Tekin, ; Aǧpak et al., ), and a better model may improve the results in these applications.…”

Aplicación del método de composición musical al problema de asignación de unidades de enseñanza y aprendizaje

“…En particular es común en instituciones educativas de nivel superior, y normalmente implican la asignación de profesores, aulas, laboratorios, cursos, exámenes, entre otros, a horarios establecidos [13][14]. Un caso especial de este tipo de problemas es conocido como currículo académico, en el que se busca determinar el periodo escolar en el que un estudiante deberá cursar cada una de las materias requeridas para poder completar su licenciatura, de tal forma que se cumplan con restricciones, como seriaciones, y se optimice una función objetivo, como cargas académicas balanceadas durante toda la carrera [7]. Con frecuencia, para resolver el problema resultante se recurre a procesos manuales que requieren gran cantidad de tiempo y que en muchas ocasiones deben repetirse al modificar algún curso.…”