Balancing assembly lines with variable parallel workplaces: Problem definition and effective solution procedure

Assembly line balancing problems (ALBP) arise whenever an assembly line is configured, redesigned or adjusted. An ALBP consists of distributing the total workload for manufacturing any unit of the products to be assembled among the work stations along the line subject to a strict or average cycle time. Traditionally, stations are considered to be manned by one operator, respectively, or duplicated in form of identical parallel stations, each also manned by a single operator. In practice, this assumption is usually too restrictive. This is particularly true for large products like cars, trucks, busses and machines, which can be handled by several operators performing different tasks at the same time. Only restricted research has been done on such parallel workplaces within the same station though they have significant relevance in real-world assembly line settings.     

Balancing and scheduling tasks in assembly lines with sequence-dependent setup times

The classical Simple Assembly Line Balancing Problem (SALBP) has been widely enriched over the past few years with many realistic approaches and much effort has been made to reduce the distance between the academic theory and the industrial reality. Despite this effort, the scheduling of the execution of tasks assigned to every workstation following the balancing of the assembly line has been scarcely reported in the scientific literature. This is supposed to be an operational concern that the worker should solve himself, but in several real environments, setups between tasks exist and optimal or near-optimal tasks schedules should be provided inside each workstation. The problem presented in this paper adds sequence-dependent setup time considerations to the classical SALBP in the following way: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time. After formulating a mathematical model for this innovative problem and showing the high combinatorial nature of the problem, eight different heuristic rules and a GRASP algorithm are designed and tested for solving the problem in reasonable computational time.     

An application of the branch,bound, and remember algorithm to a new simple assembly line balancing dataset

The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database.     

A branch-and-bound algorithm to minimize the line length of a two-sided assembly line

A new branch-and-bound algorithm is presented to solve the two-sided assembly line balancing problem of type 1 (TALB-1). First, a pair of two directly facing station is defined as a position, and then the two-sided assembly line (TAL) is relaxed to a one-sided assembly line (OAL). Some new lower bound on positions are computed, and dominance rules and reduction rules for the one-sided assembly line balancing problem of type 1 (OALB-1) are extended and incorporated into a station-oriented assignment procedure for the TALB-1 problem. Finally, the tests are carried out on a well-known benchmark set of problem instances, and experimental results demonstrate that the proposed procedure is efficient.     

Incorporating ergonomic risks into assembly line balancing

In manufacturing, control of ergonomic risks at manual workplaces is a necessity commanded by legislation, care for health of workers and economic considerations. Methods for estimating ergonomic risks of workplaces are integrated into production routines at most firms that use the assembly-type of production. Assembly line re-balancing, i.e., re-assignment of tasks to workers, is an effective and, in case that no additional workstations are required, inexpensive method to reduce ergonomic risks. In our article, we show that even though most ergonomic risk estimation methods involve nonlinear functions, they can be integrated into assembly line balancing techniques at low additional computational cost. Our computational experiments indicate that re-balancing often leads to a substantial mitigation of ergonomic risks.     

Enhanced multi-Hoffmann heuristic for efficiently solving real-world assembly line balancing problems in automotive industry

In production systems of automobile manufacturers, multi-variant products are assembled on paced final assembly lines. The assignment of operations to workplaces and workers deter mines the productivity of the manufacturing process. In research, various exact and heuristic solution procedures have been developed for different versions of the so-called assembly line balancing problem.     

Performance guarantee for edf under overload

Earliest deadline first (edf) is a widely used algorithm for online deadline scheduling. It has been known for long that edf is optimal for scheduling an underloaded, single-processor system; recent results on the extra-resource analysis of edf further revealed that edf when using moderately faster processors can achieve optimal performance in the underloaded, multi-processor setting. This paper initiates the extra-resource analysis of edf for overloaded systems, showing that edf supplemented with a simple form of admission control can provide a similar performance guarantee in both the single and multi-processor settings.     

On the integrality ratio for tree augmentation

We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches . This refutes a conjecture of Cheriyan, Jordán, and Ravi [J. Cheriyan, T. Jordán, R. Ravi, On 2-coverings and 2-packings of laminar families, in: Proceedings, European Symposium on Algorithms, 1999, pp. 510–520. A longer version is on the web: http://www.math.uwaterloo.ca/jcheriyan/publications.html] that the integrality ratio is .     

Differential approximation of min sat, max sat and related problems

We present differential approximation results (both positive and negative) for optimal satisfiability, optimal constraint satisfaction, and some of the most popular restrictive versions of them. As an important corollary, we exhibit an interesting structural difference between the landscapes of approximability classes in standard and differential paradigms.     

Pointlike sets with respect to R and J

We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety of all finite R-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute -pointlike sets, where denotes the pseudovariety of all finite J-trivial semigroups. We finally show that, in contrast with the situation for , the natural adaptation of Henckell’s algorithm to computes pointlike sets, but not all of them.     

clever or smart: Strategies for the online target date assignment problem

In this paper, we consider the Online Target Date Assignment Problem (OnlineTDAP) for general downstream problems, where the downstream cost are nonnegative, additive and satisfy the triangle inequality.We analyze algorithm smart, which was introduced by Angelelli et al. [3] and give its exact competitive ratio depending on the number of requests. Since the obtained competitive ratio is at most we answer the question posed in Angelelli et al. [4] if smart has a competitive ratio strictly less than 2.Moreover, we introduce a new algorithm called clever and show that this strategy has a competitive ratio of 3/2. We show that this is asymptotically optimal by proving that no online algorithm can perform better than 3/2−ε.     

On Lie p-algebras of cohomological dimension one

We prove that a Lie $p$-algebra of cohomological dimension one is one-dimensional, and discuss related questions.     

Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3

The best approximation algorithm for Max Cut in graphs of maximum degree 3 uses semidefinite programming, has approximation ratio 0.9326, and its running time is Θ(n^3.5logn); but the best combinatorial algorithms have approximation ratio 4/5 only, achieved in O(n²) time [J.A. Bondy, S.C. Locke, J. Graph Theory 10 (1986) 477–504; E. Halperin, et al., J. Algorithms 53 (2004) 169–185]. Here we present an improved combinatorial approximation, which is a 5/6-approximation algorithm that runs in O(n²) time, perhaps improvable even to O(n). Our main tool is a new type of vertex decomposition for graphs of maximum degree 3.     

Realizations and LP

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 (4) (2008) 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. (The second of these is actually weaker than just stated, but this is not the place for a detailed formulation.) The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode (Eds.), Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223].     

ALPS: Matrices with nonpositive off-diagonal entries

The purpose of this paper is to characterize and interrelate various degrees of stability and semipositivity for real square matrices having nonpositive off-diagonal entries. The major classes considered are the sets of diagonally stable, stable, and semipositive matrices, denoted respectively by $\text{A}$, $\text{L}$, and $\text{S}$. The conditions defining these classes are weakened, and the resulting classes are examined. Their relationship to the classes of real matrices $\text{P}$ and $\text{P}$₀, whose off-diagonal entries are nonpositive and whose principal minors are respectively all positive and all nonnegative, is also included.     

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.