Lagrangian Formulation for Energy-efficient Warehouse Design

Energy consumption in modern warehouses is today an important issue which has not received much attention in the scientific community. In this paper it is addressed the problem of warehouse design considering the energy costs incurred by vehicles and equipment in a fully or partially automated facility. Closed-form solutions are obtained by a formulating the Lagrangian of an operational cost function with equality constraints. The contribution of the paper is to develop formulas for reduced energy consumption and pollution, both relevant aspects in sustainable engineering systems. An example applied to a distributor of MRO items is presented. In this version the energy cost is integrated into the formula, modifying the method presented in [1]

Accelerating the B&B algorithm for integer programming based on flatness information: an approach applied to the multidimensional knapsack problem

This paper presents a new branching rule based on the flatness of a polyhedron associated to the set of constraints in an integer linear programming problem. The rule called Flatness II is a heuristic technique used with the branch-and-bound method. The rule is concerned with the minimum integer width vector. Empirical evidence supports the conjecture that the direction with the highest value of the vector’s components indicates a suitable branching direction. The paper provides theoretical results demonstrating that the columns of the matrix A corresponding to a set of constraints Ax≤b may be used to estimate the minimum integer width vector; this fact is used for constructing a new version of the branching rule as was reported in a previous paper by the authors. In addition, the new rule uses a branching direction that chooses the child node closest to the integer value (either up or down). Thus, it uses a variable rule for descending the tree. Every time a new sub-problem is solved, the list of remaining unsolved sub-problems is analyzed, with priority given to those problems with a minimum objective function value estimate. The conclusions of the work are based on knapsack problems from the knapsack OR-Library. From the results, it is concluded that the new rule Flatness II presents low execution times and minimal number of nodes generated

Multicriteria Supplier Classification for DSS: Comparative Analysis of Two Methods

In this paper the analysis of two multicriteria decision making (MCDM) methods for sorting suppliers in industrial environments is presented. The MCDM methods correspond to Electre and FlowSort and both are applied to the classification of providers in an actual case of the local softdrink bottling industry in Chile. The results show that Electre as an outranking method it may well classify suppliers in a similar manner as FlowSort does. Nevertheless, due to the intrinsic underlying fuzzy multicriteria nature of the problem, FlowSort is found to be more suitable method for building a rule-based system based on preference functions for automating the process of suppliers clustering when developing strategies of relationship management in the sense of the Kraljic categories in supply chain management

Improving the productivity of the copper mining process in the Chilean copper industry

This paper presents a linear programming model used for decision making in the mining process of copper concentration from sulphide minerals. The developed model enables the decision maker to select the types of ore to be used in the mix to maximize the metallurgical recovery and the copper grade at the end of the process. The model is of the mixture model of minerals with added economic variables such as processing costs, electric power and others. The process has four sub-processes that are crushing the ore, crushing the crushed ore, flotation of the ground ore to obtain copper concentrate and drying, in which the water is extracted. The model uses a set of variables whose size varies according to the number of lots of minerals and the number of planning days considered. The model may be considered a considerable problem when a long period of time is planned, but has only been implemented with 3.000 variables and 2.000 constraints. The developed model is being implemented in the National mining company, which buys ore from small producers to produce copper concentrate and then melt and refine it to obtain high grade copper. The generated model produces savings of the order of thousand dollars per day, when compared to the current methods of allocating minerals, which represents millions of dollars per year. It also produces a benefit due to the fact that lower operating costs are obtained, with estimate savings of the order of 5% of the current cost.</p

Assessment of steady and unsteady friction models in the draining processes of hydraulic installations

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models

Assessment of Steady and Unsteady Friction Models in the Draining Processes of Hydraulic Installations

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models

Drone Optimization in Factory: Exploring the Minimal Level Vehicle Routing Problem for Efficient Material Distribution

The efficient movement of raw materials within organizations is fundamental to maintaining the seamless progression of production processes. However, these logistical operations can inadvertently compromise overall company efficiency, primarily due to the substantial time invested in transporting materials. This paper introduces an innovative mathematical model specifically designed to optimize the transport of raw materials via drones across multiple workstations. This model employs a novel modification of the traditional multi-level Vehicle Routing Problem by incorporating an additional index and accounting for the drone&rsquo;s energy consumption. We employ a widely-recognized solver for practical resolution and compare it with a heuristic algorithm. The resultant strategies offer promising prospects for the organization studied, introducing robust solutions for elevating the efficiency of raw material transportation

Improving the efficiency of the Branch and Bound algorithm for integer programming based on "flatness" information

This paper describes a strategy for defining priorities for the branching variables in a Branch and Bound algorithm. The strategy is based on shape information about the polyhedron over which we are optimizing. This information is related to measures of the integer width, as provided by the so called "Flatness Theorem". Our selection rule uses that knowledge to define branching priorities on the variables. Computational results with simulated small to medium size integer problems are presented, as well with multi-knapsack problems. These show savings of about 40% in CPU time, as well as in nodes generated in the search tree, and compare favorably with respect to other standard branching rules. (c) 2005 Elsevier B.V. All rights reserved

Optimization of Port Layout to Determine Greenhouse Gas Emission Gaps

Ports are of great strategic importance for a country. Nowadays, compliance with environmental requirements is required, forcing the migration towards clean energies. Therefore, it is necessary for emerging ports, as those in developed countries, to incorporate in their policies the use of electric power in the machinery that moves containers in the terminals. To learn how the problem is addressed in other countries, an extensive bibliographic review is presented. Then, the energy policies and criteria of a group of ports in an emerging country and a European port are studied. Subsequently, in order to determine the gaps between the ports investigated, the layout of the cargo yard of each of the terminals is optimized; the emissions of Carbon Dioxide (CO2) and other Greenhouse Gases (GHG) gases are calculated; and finally, the decrease in emissions when switching from diesel to electricity is estimated. The strategic and operational gaps related to energy management between the emerging and developed countries are discussed. It is concluded that research is needed to investigate how these initiatives impact the city and improve other sustainable aspects