The Single-Row Facility Layout Problem (SRFLP) is one of the most studied facility layout problems in the literature. It asks for an optimal arrangement of departments with given lengths on a row such that the weighted sum of all centre-to-centre distances between department pairs is minimised. Real-world facility layouts may require taking different restrictions on the placement of departments into account, such as arrangement on a fixed position, pairwise placement, or precedence considerations. Therefore, we consider the constrained Single-Row Facility Layout Problem (cSRFLP) that additionally considers positioning, ordering, and relation constraints on single-row facility layouts. In this work, we suggest a new Integer Linear Programming (ILP) formulation for the cSRFLP, which outperforms the best available exact approach in literature. In an extensive computational study, we apply our ILP approach as well as an LP-based cutting plane algorithm on SRFLP and cSRFLP instances from the literature. We provide optimal cSRFLP layouts as well as strong lower bounds for instances with up to 42 departments. Further, we present new results for SRFLP instances from the literature. Additionally, we demonstrate the individual impact of the constraint sets on the run times of cSRFLP instances to emphasise further research on this rarely studied practice-oriented Facility Layout Problem.

The steadily growing popularity of grocery home-delivery services is most likely based on the convenience experienced by its customers. However, the perishable nature of the products imposes certain requirements during the delivery process. The customer must be present when the delivery arrives so that the delivery process can be completed without interrupting the cold chain. Therefore, the grocery retailer and the customer must mutually agree on a time window during which the delivery can be guaranteed. This concept is referred to as the attended home delivery (AHD) problem in the scientific literature. The phase during which customers place orders, usually through a web service, constitutes the computationally most challenging part of the logistical processes behind such services. The system must determine potential delivery time windows that can be offered to incoming customers and incrementally build the delivery schedule as new orders are placed. Typically, the underlying optimization problem is a vehicle routing problem with a time windows. This work is concerned with a case given by an international grocery retailer’s online shopping service. We present an analysis of several efficient solution methods that can be employed to AHD services. A framework for the operational planning tools required to tackle the order placement process is provided. However, the basic framework can easily be adapted to be used for many similar vehicle routing applications. We provide a comprehensive computational study comparing several algorithmic strategies, combining heuristics utilizing local search operations and mixed-integer linear programs, tackling the booking process. Finally, we analyze the scalability and suitability of the approaches.

We discuss a new facility layout problem, the so-called Directed Circular Facility Layout Problem . The aims to find an optimal arrangement of machines on a circular material handling system such that the total weighted sum of the center-to-center distances between all pairs of machines measured in clockwise direction is minimized. Several real-world applications, like for example the optimal arrangement of a set of cutting tools on a tool turret, can be modeled as a . Further, the generalizes a couple of layout problems that are well-discussed in literature. We show that the can be modeled as a Linear Ordering Problem . Hence, it can be solved efficiently by using exact and heuristic approaches for the . First, we apply a Semidefinite Programming as well as an Integer Linear Programming approach. Moreover, we use a Tabu Search and a Variable Neighborhood Search heuristic, for solving the . Finally, we compare the practical performance of our approaches in a computational study.