Jochen Rethmann

Storage controlled pile-up systems, theoretical foundations

A pile-up system consists of one or more stacker cranes picking up bins from a conveyor and placing them onto pallets with respect to costumer orders. We give a mathematical definition of the pile-up problem, define a data structure for control algorithms, introduce polynomial time algorithms for deciding whether a system can be blocked by making bad decisions, and show that controlling pile-up systems is in general NP-complete. For pile-up systems with a restricted storage capacity or with a fixed number of pile-up places the pile-up problem is proved to be solvable very efficiently.

Stack-up algorithms for palletizing at delivery industry

Abstract We study the following multi-objective combinatorial stack-up problem from delivery industry. Given a sequence q of labeled bins and two positive integers s and p . The aim is to stack-up the bins by iteratively removing one of the first s bins of the sequence and put it to one of p stack-up places. Each of these places has to contain bins of only one label, bins of different labels have to be placed on different places. If all bins of a label are removed from q , the corresponding place becomes available for bins of another label. We analyze the worst-case performance of simple algorithms for the stack-up problem that are very interesting from a practical point of view. In particular, we show that the so-called Most-Frequently on-line algorithm is (2,2)-competitive and has optimal worst-case on-line performance.

Moving Bins from Conveyor Belts onto Pallets Using FIFO Queues

We study the combinatorial FIFO stack-up problem. In delivery industry, bins have to be stacked-up from conveyor belts onto pallets. Given (k) sequences (q_1, ldots , q_k) of labeled bins and a positive integer (p), the goal is to stack-up the bins by iteratively removing the first bin of one of the (k) sequences and put it onto a pallet located at one of (p) stack-up places. Each of these pallets has to contain bins of only one label, bins of different labels have to be placed on different pallets. After all bins of one label have been removed from the given sequences, the corresponding place becomes available for a pallet of bins of another label. The FIFO stack-up problem is NP-complete in general. In this paper we show that the problem can be solved in polynomial time, if the number (k) of given sequences is fixed.

Algorithms for Controlling Palletizers

Palletizers are widely used in delivery industry. We consider a large palletizer where each stacker crane grabs a bin from one of k conveyors and position it onto a pallet located at one of p stack-up places. All bins have the same size. Each pallet is destined for one customer. A completely stacked pallet will be removed automatically and a new empty pallet is placed at the palletizer. The FIFO Stack-Up problem is to decide whether the bins can be palletized by using at most p stack-up places. We introduce a digraph and a linear programming model for the problem. Since the FIFO Stack-Up problem is computational intractable and is defined on inputs of various informations, we study the parameterized complexity. Based on our models we give xp-algorithms and fpt-algorithms for various parameters, and approximation results for the problem.

A Practical Approach for the FIFO Stack-Up Problem

We consider the FIFO Stack-Up problem which arises in delivery industry, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences q 1, …, q k of labeled bins and a positive integer p. The goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. Each of these pallets has to contain bins of only one label, bins of different labels have to be placed on different pallets. After all bins of one label have been removed from the given sequences, the corresponding stack-up place becomes available for a pallet of bins of another label. The FIFO Stack-Up problem is computational intractable [3]. In this paper we introduce a graph model for this problem, which allows us to show a breadth first search solution. Our experimental study of running times shows that our approach can be used to solve a lot of practical instances very efficiently.

Competivive Analysis of on-line Stack-Up Algorithms

Let q = (b1,...,bn) be a sequence of bins. Each bin is destined for some pallet t. For two given integers s and p, the stack-up problem is to move step by step all bins from q onto their pallets such that the position of the bin moved from q is always not greater than s and after each step there are at most p pallets for which the first bin is already stacked up but the last bin is still missing. If a bin b is moved from q then all bins to the right of b are shifted one position to the left. We determine the performance of four simple on-line algorithms called First-In, First-Done, Most-Frequently, and Greedy with respect to an optimal off-line solution for the stack-up problem.

An approximation algorithm for the stack-up problem

Abstract. We consider the combinatorial stack-up problem motivated by stacking up bins from a conveyor onto pallets. The stack-up problem is to decide whether a given list q of labeled objects can be processed by removing step by step one of the first s objects of q so that the following holds. After each removal there are at most p labels for which the first object is already removed from q and the last object is still contained in q. We give some NP-completeness results and we introduce and analyze a polynomial time approximation algorithm for the stack-up problem.

An Experimental Study of Algorithms for Controlling Palletizers

We consider the FIFO Stack-Up problem which arises in delivery industry, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences (q_1, ldots , q_k) of labeled bins and a positive integer p. The goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. Each of these pallets has to contain bins of only one label, bins of different labels have to be placed on different pallets. After all bins of one label have been removed from the given sequences, the corresponding stack-up place becomes available for a pallet of bins of another label. The FIFO Stack-Up problem is computational intractable (Gurski et al., Math. Methods Oper. Res., [3], ACM Comput. Res. Repos. (CoRR), 2013, [4]). In this paper we consider two linear programming models for the problem and compare the running times of our models for randomly generated sequences using GLPK and CPLEX solvers. We also draw comparisons with a breadth first search solution for the problem (Gurski et al.,Modelling, Computation and Optimization in Information Systems and Management Sciences, 2015, [7]).

On the complexity of the FIFO stack-up problem

We study the combinatorial FIFO stack-up problem. In delivery industry, bins have to be stacked-up from conveyor belts onto pallets with respect to customer orders. Given k sequences