Maximum Number Of Bins Research Articles

Simulation-based time-efficient and energy-efficient performance analysis of an overhead robotic compact storage and retrieval system

This paper evaluates an overhead robotic compact storage and retrieval system (ORCSRS), which is a novel automated compact system where basic storage and handling containers are stacked on top of one another to form bin stacks on each plane. Bin-picking robots and track-changing robots are assigned to carry bins with the target stock keeping units (SKUs) to the picker to fulfill orders. We develop a discrete event simulation model to analyze the performance of an ORCSRS in terms of efficiency and energy consumption. Performance indicators such as throughput, robot utilization, and system energy consumption are obtained for both single-SKU and multi-SKUs cases and both dedicated and shared storage policies coupled with random and zoned stacks. Our results provide valuable suggestions for the optimal design of an ORCSRS, such as the best layout for optimizing throughput, number of robots required to achieve a given throughput in a limited warehouse area, and the maximum number of bins that should be stored in one stack.

Sequencing assembly lines to facilitate synchronized just-in-time part supply

The problem of sequencing assembly lines consists of determining the order in which a given set of products is launched down the line. Since individual products may require different parts in different quantities, the production sequence has a big influence on line-side inventory. Classically, sequences are often optimized with the goal of attaining level schedules, i.e., the part demand should be smooth during the planning horizon. However, this approach does not necessarily work well if parts are delivered at discrete points in time in bulk quantities. In this paper, we consider a production system where bins of parts are delivered periodically by a tow train from a central depot at fixed times. Due to the limited space at the assembly line, the maximum number of bins in stock at any time at any station should be minimal. We propose an exact solution method based on combinatorial Benders decomposition as well as bounding procedures and heuristics for this problem. The algorithms are shown to perform well both on instances from the literature and on new data sets. We also investigate whether classic level scheduling methods are effective at reducing line-side stock in an assembly system supplied by tow train, and to what degree line-side stock can be traded off for more frequent deliveries.

Selfish bin packing with cardinality constraints

Bin packing with cardinality constraints is a variant of bin packing. In this problem, items with sizes of at most 1 are to be partitioned (or packed) into subsets called bins, such that the total size of items packed into a bin would not exceed 1, and each bin would contain at most k items, for a given integer parameter k>1.We consider a class of games resulting from this problem by seeing the items as selfish players, trying to be packed into a (valid) bin where the total size of items is maximized. Such games always admit pure Nash equilibria. We analyze the Price of Anarchy (PoA) of such games, defined as the asymptotic worst case ratio between the maximum number of bins in a pure Nash equilibrium (NE), and the minimum number of bins in any valid solution, that is, the number of bins in a socially optimal solution. We provide a complete analysis of the PoA as a function of k; we prove that for k=2, any NE is an optimal solution, for k⩾4, the PoA is exactly 2−1k, and for k=3, the PoA is exactly 117.

Dynamic bin packing of unit fractions items

This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary times. We want to pack a sequence of unit fractions items (i.e., items with sizes 1 / w for some integer w ≥ 1 ) into unit-size bins, such that the maximum number of bins ever used over all time is minimized. Tight and almost-tight performance bounds are found for the family of any-fit algorithms, including first-fit, best-fit, and worst-fit. In particular, we show that the competitive ratio of best-fit and worst-fit is 3, which is tight, and the competitive ratio of first-fit lies between 2.45 and 2.4942. We also show that no on-line algorithm is better than 2.428-competitive.

Guest Editors’ Forward

The 12th Annual International Computing and Combinatorics Conference (COCOON’2006) was held at the Institute of Information Science, Academia Sinica, in Taipei, Taiwan on August 15–18, 2006. 137 extended abstracts were submitted from 27 countries and regions in the world, of which 52 were accepted (including a merged paper from two extended abstracts). Among those accepted extended abstracts, five very nice papers in the area of algorithm design and analysis were selected and invited to this special issue of Algorithmica for COCOON’2006. These five papers all went through the normal review process of Algorithmica and were accepted for publication. The papers in this special issue represent various exciting aspects of the current algorithmic research. Bereg et al.’s paper develops a simple polynomial time approximation scheme (PTAS) for the geometric problem of finding a sequence of lines to cut a convex n-gon out of a convex m-gon such that the cost of the cutting sequence is minimized. Chan et al.’s paper considers a general dynamic bin packing problem in which the items may arrive to and depart from the packing at arbitrary time and whose objective is to minimize the maximum number of bins used over all time; they obtain an interesting improved lower bound of the competitive ratio for the online version and new results for the resource augmentation version of the problem.