On Rearrangement of Items Stored in Stacks

There are $n \ge 2$ stacks, each filled with $d$ items, and one empty stack. Every stack has capacity $d > 0$. A robot arm, in one stack operation (step), may pop one item from the top of a non-empty stack and subsequently push it onto a stack not at capacity. In a {\em labeled} problem, all $nd$ items are distinguishable and are initially randomly scattered in the $n$ stacks. The items must be rearranged using pop-and-pushs so that in the end, the $k^{\rm th}$ stack holds items $(k-1)d +1, \ldots, kd$, in that order, from the top to the bottom for all $1 \le k \le n$. In an {\em unlabeled} problem, the $nd$ items are of $n$ types of $d$ each. The goal is to rearrange items so that items of type $k$ are located in the $k^{\rm th}$ stack for all $1 \le k \le n$. In carrying out the rearrangement, a natural question is to find the least number of required pop-and-pushes. Our main contributions are: (1) an algorithm for restoring the order of $n^2$ items stored in an $n \times n$ table using only $2n$ column and row permutations, and its generalization, and (2) an algorithm with a guaranteed upper bound of $O(nd)$ steps for solving both versions of the stack rearrangement problem when $d \le \lceil cn \rceil$ for arbitrary fixed positive number $c$. In terms of the required number of steps, the labeled and unlabeled version have lower bounds $\Omega(nd + nd{\frac{\log d}{\log n}})$ and $\Omega(nd)$, respectively

Optimizing the Rearrangement Process in a Dedicated Warehouse

Determining the optimal storage assignment for products in a dedicated warehouse has been addressed extensively in the Facility Logistics literature. However, the process of implementing a particular storage assignment given the current location of products has not received much attention in the existing literature. Typically, warehouses use downtime or overtime to remove products from their current location and move them to the suggested location. This work presents the Rearrange-While-Working (RWW) policy to optimize the process of rearranging a dedicated warehouse. The RWW policy seeks to relocate products in a warehouse from the initial arrangement to the optimal arrangement while serving a list of storages and retrievals. This study considers three scenarios: (1) when there is only one empty location in the warehouse and the material handling equipment (MHE) is idle (i.e. reshuffling policy); (2) when there is only one empty location in the warehouse under the RWW policy; (3) when there are multiple empty locations in the warehouse under the RWW policy. In the first case, the MHE can make any movement desired as it is idle. In the other cases, the movements correspond to a list of storages and retrievals that need to be served. In these cases it is assumed that products can only be moved when they are requested. After being used, they are returned to the warehouse. Several heuristics are presented for each scenario. The proposed heuristics are shown to perform satisfactorily in terms of solution quality and computational time

Tabu Search Heuristics for the Crane Sequencing Problem

Determining the sequence of relocating items (or resources) moved by a crane from existing positions to newly assigned locations during a multiperiod planning horizon is a complex combinatorial optimisation problem, which exists in power plants, shipyards, and warehouses. Therefore, it is essential to develop a good crane route technique to ensure efficient utilisation of the crane as well as to minimize the cost of operating the crane. This problem was defined as the Crane Sequencing Problem (CSP). In this paper, three construction and three improvement algorithms are presented for the CSP. The first improvement heuristic is a simple Tabu Search (TS) heuristic. The second is a probabilistic TS heuristic, and the third adds diversification and intensification strategies to the first. The computational experiments show that the proposed TS heuristics produce high-quality solutions in reasonable computation time

Mathematical models for the warehouse reassignment problem

For several decades, researchers have developed optimization techniques forwarehouse operations. These techniques are related in particular to the materialhandling, the order picking and storage assignment strategies for a myriad of warehouse configurations. It is often neglected that these strategies need to be regularlyadjusted in order to adapt to changes in technology, in the demand and/or product offers. Most research on storage assignment provide excellent methods to determine where products should be located. However, the handling part of the problem is often set aside. Moving from one setup to another requires a large amount of work and disturbs regular order-picking operations. This chapter presents the warehouse reassignment problem in order to minimize the total workload to reassign the products to their new locations. We demonstrate how one can move from an out-of-date storage assignment to a better one, in a minimum of working time. We introduce three different mathematical formulations and compare them through extensive computational experiments in order to identify the best one.<br/

Mathematical models for the warehouse reassignment problem

For several decades, researchers have developed optimization techniques forwarehouse operations. These techniques are related in particular to the materialhandling, the order picking and storage assignment strategies for a myriad of warehouse configurations. It is often neglected that these strategies need to be regularlyadjusted in order to adapt to changes in technology, in the demand and/or product offers. Most research on storage assignment provide excellent methods to determine where products should be located. However, the handling part of the problem is often set aside. Moving from one setup to another requires a large amount of work and disturbs regular order-picking operations. This chapter presents the warehouse reassignment problem in order to minimize the total workload to reassign the products to their new locations. We demonstrate how one can move from an out-of-date storage assignment to a better one, in a minimum of working time. We introduce three different mathematical formulations and compare them through extensive computational experiments in order to identify the best one.<br/

Solution Techniques for a Crane Sequencing Problem

In the areas of power plant maintenance, shipyard and warehouse management, resources (items) assigned to locations need to be relocated. It is essential to develop efficient techniques for relocating items to new locations using a crane such that the sum of the cost of moving the items and the cost of loading/unloading the items is minimised. This problem is defined as the crane sequencing problem (CSP). Since the CSP determines the routes for a crane to relocate items, it is closely related to some variants of the travelling salesman problem. However, the CSP considers the capacities of locations and intermediate drops (i.e. preemptions) during a multiple period planning horizon. In this article, a mathematical model and hybrid ant systems are developed for the CSP. Computational experiments were conducted to evaluate the performances of the proposed techniques, and results show that the proposed heuristics are effective

Solution techniques for a crane sequencing problem

In shipyards and power plants, relocating resources (items) from existing positions to newly assigned locations are costly and may represent a significant portion of the overall project budget. Since the crane is the most popular material handling equipment for relocating bulky items, it is essential to develop a good crane route to ensure efficient utilization and lower cost. In this research, minimizing the total travel and loading/unloading costs for the crane to relocate resources in multiple time periods is defined as the crane sequencing problem (CSP). In other words, the objective of the CSP is to find routes such that the cost of crane travel and resource loading/unloading is minimized. However, the CSP considers the capacities of locations and intermediate drops (i.e., preemptions) during a multiple period planning horizon. Therefore, the CSP is a unique problem with many applications and is computationally intractable. A mathematical model is developed to obtain optimal solutions for small size problems. Since large size CSPs are computationally intractable, construction algorithms as well as improvement heuristics (e.g., simulated annealing, hybrid ant systems and tabu search heuristics) are proposed to solve the CSPs. Two sets of test problems with different problem sizes are generated to test the proposed heuristics. In other words, extensive computational experiments are conducted to evaluate the performances of the proposed heuristics