Reinaldo Morabito

An AND/OR-graph approach to the container loading problem

The container loading problem consists of packing boxes of various sizes into available containers in such a way as to optimize an objective function. In this paper we deal with the special case where there is just one available container and the objective is to maximize the total volume (or the total utility value, supposing that each box has a utility value) of the loaded boxes. We firstly present three heuristic solution methods for the unconstrained problem. Two of them solve the original three-dimensional problem by layers and by stacks reducing it into several problems with lower dimensions. The third one consists of representing possible loading patterns as complete paths in an AND/OR-graph. Bounds and heuristics are proposed in order to reduce the solution space. A proper heuristic is also given to treat the constrained problem by using the AND/OR-graph approach. Moreover, computational results are presented by solving a number of examples.

Staged and constrained two-dimensional guillotine cutting problems: An AND/OR-graph approach

Abstract An AND/OR-graph approach has been proposed by Morabito et al. to solve non-staged and unconstrained two-dimensional guillotine cutting problems. Basically, this approach consists of representing cutting patterns as complete paths in an AND/OR graph (where nodes and arcs correspond to rectangles and cuts, respectively) and choosing a search strategy to traverse or enumerate the nodes of the graph. In this present paper, the AND/OR-graph approach is extended to solve staged and constrained problems. Computational experiments with examples from the literature are performed and indicate that this approach generates good and fast solutions using a microcomputer. In addition to the fact that the AND/OR-graph approach can handle important constraints, it can be easily extended to solve cutting and packing problems with multiple dimensions.

Three-dimensional container loading models with cargo stability and load bearing constraints

Mathematical models for the problem of loading rectangular boxes into containers, trucks or railway cars have been proposed in the literature, however, there is a lack of studies which consider realistic constraints that often arise in practice. In this paper, we present mixed integer linear programming models for the container loading problem that consider the vertical and horizontal stability of the cargo and the load bearing strength of the cargo (including fragility). The models can also be used for loading rectangular boxes on pallets where the boxes do not need to be arranged in horizontal layers on the pallet. A comprehensive performance analysis using optimization software with 100s of randomly generated instances is presented. The computational results validate the models and show that they are able to handle only problems of a moderate size. However, these models might be useful to motivate future research exploring other solution approaches to solve this problem, such as decomposition methods, relaxation methods, heuristics, among others.

Production planning in furniture settings via robust optimization

Production planning procedures in small-size furniture companies commonly consists of decisions with respect to production level and inventory policy, while attempting to minimize trim-loss, backlogging and overtime usage throughout the planning horizon. Managing these decisions in a tractable way is often a challenge, especially considering the uncertainty of data. In this study, we employ robust optimization tools to derive robust combined lot-sizing and cutting-stock models when production costs and product demands are uncertainty parameters. Our motivation over the traditional two-stage stochastic programming approach is the absence of an explicit probabilistic description of the input data, as well as avoiding to deal with a large number of scenarios. The results concerning uncertainty in the cost coefficients were illustrative and confirmed previous studies. Regarding uncertainty in product demands, we provide some insights into the relationship between the budgets of uncertainty, fill rates and optimal values. Moreover, when uncertainty affects both costs and demands simultaneously, optimal values are worse for large variability levels. Numerical evidence indicated that less conservative budgets of uncertainty result in reasonable service levels with cheaper global costs, while worst-case deterministic approaches generate relatively good fill rates, but with prohibitive global costs.

Towards unified formulations and extensions of two classical probabilistic location models

We give a unified view of Daskins Maximum Expected Covering Location Problem (MEXCLP) and ReVelle and Hogans Maximum Availability Location Problem (MALP), identifying similarities and dissimilarities between these models and showing how they relate to each other. These models arise in the location of servers in congested emergency systems. An existing extension of MEXCLP is reviewed; we then develop an extension of MALP and give the corresponding mathematical formulation. These two extensions are obtained when the simplifying assumptions of the original models are dropped and Larsons hypercube model is embedded into local search methods. In this paper these methods are further enhanced by the use of simulated annealing. Computational results are given for problems available in the literature.

An optimization approach for ambulance location and the districting of the response segments on highways

In this paper we present a method to optimize the configuration and operation of emergency medical systems on highways. Different from the approaches studied in the previous papers, the present method can support two combined configuration decisions: the location of ambulance bases along the highway and the districting of the response segments. For example, this method can be used to make decisions regarding the optimal location and coverage areas of ambulances in order to minimize mean user response time or remedy an imbalance in ambulance workloads within the system. The approach is based on embedding a well-known spatially distributed queueing model (hypercube model) into a hybrid genetic algorithm to optimize the decisions involved. To illustrate the application of the proposed method, we utilize two case studies on Brazilian highways and validate the findings via a discrete event simulation model.

Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queueing model

This paper studies the application of the hypercube queueing model to SAMU-192, the urban Emergency Medical Service of Campinas in Brazil. The hypercube is a powerful descriptive model to represent server-to-customer systems, allowing the evaluation of a wide variety of performance measures for different configurations of the system. In its original configuration, SAMU-192 had all ambulances centralized in its central base. This study analyzes the effects of decentralizing ambulances and adding new ambulances to the system, comparing the results to the ones of the original situation. It is shown that, as a larger number of ambulances are decentralized, mean response times, fractions of calls served by backups and other performance measures of the system are improved, while the ambulance workloads remain approximately constant. However, total decentralization as suggested by the system operators of SAMU-192 may not produce satisfactory results.

Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model

In this study we analyse the ambulance deployment of an emergency medical system on a Brazilian highway connecting the cities of São Paulo and Rio de Janeiro. Our focus is on the mean response time of the system to an emergency call, viewed as an important component of the user service. To evaluate the system performance we applied the hypercube model, a well-known tool for planning server-to-customer systems, which is based on spatially distributed queuing theory. The results showed that the model can be effective in supporting design and operational decisions, in particular to reduce the workload unbalancing among the ambulances.

Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem

This paper introduces an evolutionary algorithm as a procedure to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot-sizing and scheduling of raw materials in tanks and soft drinks in bottling lines, where setup costs and times depend on the previous items stored and bottled. A multi-population genetic algorithm approach with a novel representation of solutions for individuals and a hierarchical ternary tree structure for populations is proposed. Computational tests include comparisons with an exact approach for small-to-moderate-sized instances and with real-world production plans provided by a manufacturer.

An AND/OR-graph approach to the solution of two-dimensional non-guillotine cutting problems

This work is concerned with unconstrained two-dimensional non-guillotine cutting problems, where a rectangular plate is cut into a number of rectangular pieces in such a way as to optimize an objective function. We reduce the state-space of the problem by considering non-guillotine cutting patterns which are combinations of guillotine and simple non-guillotine cuts. These cutting patterns are represented as complete paths in an AND/OR-graph and a branch and bound method is described. We provide rules and heuristics that reduce the graph search and present computational results from randomly generated examples as well as from the literature.