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Automated storage and retrieval system design with variant lane depths

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期314卷 630-646页

作者： Dong, Wenquan Jin, Mingzhou Univ Tennessee Knoxville Dept Ind & Syst Engn Knoxville TN 37996 USA Texas State Univ Ingram Sch Engn San Marcos TX USA

This paper models a warehouse design problem with 2D automated storage and retrieval system (AS/RS) and 3D AS/RS as options, where 3D racks may have different depths. The design problem is first modeled as a mixedinteger nonlinear program to minimize investment and maximize throughput under various business needs, such as cost structure, responsiveness requirement, demand rates, and inventory levels. The model is then converted to a mixed-integer program based on optimality conditions. A basic branch-and-bound algorithm and a modified one are developed to overcome computational challenges. A high throughput expectation leads to a design with shallow storage racks, while high land/equipment costs have opposite impacts. When demand rates are similar across SKUs, heterogeneously distributed inventory levels lead to racks with different depths and assigning SKUs with higher inventory levels to deeper racks. More heterogeneous demand rates also make rack depths more variant and have SKUs with higher demand rates assigned to shallower racks. In other words, the heterogeneities of inventory levels and demand rates have a contradictory effect on the SKU-to-rack assignment and result in racks with more uniform depths when SKUs with high demand also have high inventory levels, which is often the case in practice.

关键词： Warehouses AS/RS Multi -deep systems Analytical and numerical modelling branch and bound algorithm Performance analysis

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Order acceptance and scheduling in a parallel machine environment with weighted completion time

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EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2018年第4期12卷 535-557页

作者： Palakiti, Venkata Prasad Mohan, Usha Ganesan, Viswanath Kumar Indian Inst Technol Madras Dept Management Studies Madras Tamil Nadu India Tata Consultancy Syst Ltd Decis Sci & Algorithm Lab Madras 600036 Tamil Nadu India

This paper studies the order acceptance and scheduling (OAS) problem in an identical parallel machine environment where orders are characterised by their revenues, processing times and weights. A mixed integer linear programming (MILP) model is presented for the problem with the objective of maximising the revenue minus the scheduling cost. The problem is NP-hard and a branch and bound (B&B) algorithm is developed to solve the problem. An extension of the B&B algorithm is proposed to solve very large problem instances to obtain 6-optimal solutions. The B&B algorithm and the extended B&B are evaluated for their performances against the solutions obtained by solving the MILP problem formulation using CPLEX solver through computational experiments.

关键词： order acceptance scheduling parallel machines branch and bound algorithm B&B

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MULTIOBJECTIVE OPTIMUM DESIGN IN MIXED INTEGER AND DISCRETE DESIGN VARIABLE PROBLEMS

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AIAA JOURNAL 1990年第4期28卷 670-675页

作者： HAJELA, P SHIH, CJ University of Florida Gainesville Florida

A min-max variant of the global criterion approach is proposed to obtain solutions to multiobjective optimum design problems involving a mix of continuous, discrete, and integer design variables. This modified global criterion approach is used in conjunction with a branch-and-bound algorithm, where the latter was configured especially to accommodate a mix of integer and discrete design variables. The use of a weighting strategy with the proposed method allows the generation of a set of Pareto optimal (noninferior) solutions for both convex and nonconvex problems. The solution strategy is applied to structural design problems involving vector design functions. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Structural Design branch and bound algorithm Nonlinear Programming Fiber Volume Fraction Simply Supported Beams Composite Structures Material Properties Structural Weight Tensile Strength Aeroplane

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STACKING-SEQUENCE OPTIMIZATION OF SIMPLY SUPPORTED LAMINATES WITH STABILITY AND STRAIN CONSTRAINTS

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AIAA JOURNAL 1992年第8期30卷 2132-2137页

作者： NAGENDRA, S HAFTKA, RT GURDAL, Z VIRGINIA POLYTECH INST & STATE UNIV AEROSP & OCEAN ENGNBLACKSBURGVA 24061

An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.

关键词： Laminated Composites branch and bound algorithm Genetic algorithm Taylor Series Aspect Ratio

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A symmetrical linear maxmin approach to disjoint bilinear programming

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MATHEMATICAL PROGRAMMING 1999年第3期85卷 573-592页

作者： Audet, C Hansen, P Jaumard, B Savard, G Rice Univ Houston TX 77005 USA Ecole Hautes Etud Commerciales GERAD Montreal PQ H3T 2A7 Canada Ecole Polytech Montreal PQ H3C 3A7 Canada GERAD Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada

The disjoint bilinear programming problem can be reformulated using two distinct linear maxmin programming problems. There is a simple bijection between the optimal solutions of the reformulations and the bilinear problem. Moreover, the number of local optima of the reformulations is less or equal to that of the bilinear problem. In that sense, the reformulations do not introduce additional complexity. Necessary optimality conditions (complementarity and monotonicity) of both reformulations are used to obtain a finitely convergent and exact branch and bound algorithm for the bilinear problem. Determining if the optimal value of a bilinear programming problem is bounded is shown to be strongly NP-complete. The proposed algorithm may be used to answer this question.

关键词： disjoint bilinear problem linear maxmin problem branch and bound algorithm global optimization

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Trains scheduling problem with multiple lines

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SCIENTIFIC REPORTS 2024年第1期14卷 1-20页

作者： Danavulapadu, Venkata Prathap Singamsetty, Purusotham Vellore Inst Technol Sch Adv Sci Dept Math Vellore 632014 Tamil Nadu India

This study explores the problem of train scheduling (or) train timetabling and its impact on the administration of railway management. This is a highly dependable and effective public transportation system. The problem considers both single and multiple tracks along with multiple platforms with varying train capacities (like speed, passengers, and so on). Let the tracks link two major stations source and destination with intermediate stations. A subset of intermediate stations will function as junctions. A finite number of trains be available at the source for the passengers/cargo transit movements. The profit which is generated from the shipment of passengers between a pair of stations is known in advance. The train's travel time between the stations and halting time at the stations are predefined. The arrival and departure times at the stations are calculated through the travel time and halting time. All the trains should starts from the source station and continue the journey through the intermediate stations to reach the destination station. Overtaking of the trains is permitted only at the intermediate stations. The trains must make a halt at one or more intermediate stations before reaching the destination. Now the objective is to find the best train operating schedule that maximizes the profit within the admissible travel time threshold. A zero-one integer linear programming is used to model this problem mathematically. For a better understanding of this problem, a case study is considered from the Indian railway network with two major stations Chennai and Hyderabad. A branch and bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(B\&B)$$\end{document} algorithm is proposed to determine an optimal operating schedule. In addition, the experiments are carried out on a wide range

关键词： Train scheduling Routing branch and bound algorithm Zero-one integer programming

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Concavity cuts for disjoint bilinear programming

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MATHEMATICAL PROGRAMMING 2001年第2期90卷 373-398页

作者： Alarie, S Audet, C Jaurnard, B Savard, G Ecole Polytech GRPR Montreal PQ H3C 3A7 Canada Ecole Polytech GERAD Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Genie Elect & Genie Informat Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linens maxmin reformulations, leading to two sets of concavity cuts. We first examine the depth of these cuts by considering the assumptions on the boundedness of the feasible regions of both maxmin and bilinear formulations. We next propose a branch and bound algorithm which make use of concavity cuts. We also present a procedure that eliminates degenerate solutions. Extensive computational experiences are reported. Sparse problems with up to 500 variables in each disjoint sets and 100 constraints, and dense problems with up to 60 variables again in each sets and 60 constraints are solved in reasonable computing times.

关键词： concavity cuts disjoint bilinear programming linear maxmin programming branch and bound algorithm global optimization

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Global optimization algorithm for a generalized linear multiplicative programming

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2012年第1-2期40卷 551-568页

作者： Jiao, Hongwei Liu, Sanyang Chen, Yongqiang Xidian Univ Dept Math Sci Xian 710071 Peoples R China Henan Inst Sci & Technol Dept Math Xinxiang 453003 Peoples R China Henan Normal Univ Coll Math & Informat Xinxiang 453007 Peoples R China

This article present a branch and bound algorithm for globally solving generalized linear multiplicative programming problems with coefficients. The main computation involve solving a sequence of linear relaxation programming problems, and the algorithm economizes the required computations by conducting the branch and bound search in R-p, rather than in R-n, where p is the number of rank and n is the dimension of decision variables. The proposed algorithm will be convergent to the global optimal solution by means of the subsequent solutions of the series of linear relaxation programming problems. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.

关键词： Multiplicative programming Global optimization branch and bound algorithm Deterministic algorithm

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Formulating and solving a multi-mode resource-collaboration and constrained scheduling problem (MRCCSP)

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ANNALS OF OPERATIONS RESEARCH 2013年第1期206卷 311-339页

作者： Pinto, Gaby Ben-Dov, Yariv T. Rabinowitz, Gad Jerusalem Coll Engn JCE Dept Ind Engn & Management IL-91035 Jerusalem Israel Ben Gurion Univ BGU Negev Dept Ind Engn & Management IL-84105 Beer Sheva Israel

The main motivation of this study is to provide, for the first time, a formulation and solution for a class of production scheduling problems (as in cluster tools) characterized mainly by resource collaboration to perform an operation and while allowing batches and considering alternative production methods. We develop a formulation for the new problem and term it a multiple mode per operation, resource collaboration, and constrained scheduling problem (MRCCSP). Some of the important new characteristics we consider are: multiple products (families);multiple orders (jobs) per family;precedence restrictions among the operations that constitute a job;alternative modes for the performance of an operation (each of which needs a set of collaborating resources) may be defined;complementary and exclusive restrictions between operation-modes;batch production is allowed;and setup times may depend on sequence and batch-size. The objective of the MRCCSP is to minimize makespan. We formulate the MRCCSP as a mixed integer linear programming model, and acknowledging the considerable size of the monolithic formulation required, we prescribe a specific method to achieve size reduction. Finally, a customized branch and bound algorithm for optimally solving this problem is proposed and examined experimentally.

关键词： Resource-sharing and scheduling problem Resource constrained scheduling problem Mixed integer linear programming branch and bound algorithm

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Minimizing maximum tardiness and delivery costs with batch delivery and job release times

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APPLIED MATHEMATICAL MODELLING 2015年第16期39卷 4909-4927页

作者： Rostami, Mohammad Kheirandish, Omid Ansari, Nima Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Dept Ind Engn Tehran 14174 Iran

Due to high delivery costs, manufacturers are usually required to dispatch their jobs as batches. However, this approach causes several crucial problems in scheduling-related objective functions such as minimizing the maximum tardiness. In this study, we address the scheduling of a set of jobs with specific release times, which need to be processed by a single machine and dispatched to a customer or another machine in a batch delivery condition. Each batch has a particular delivery cost. The aim is to minimize the costs of maximum tardiness plus delivery. First, a mixed integer programming (MIP) model is developed and solved by the CPLEX solver within the GAMS modeling environment. Next, a branch and bound algorithm is developed based on the LP relaxation of the MIP model. Using heuristics, appropriate values for the upper and lower bounds are predicted. The heuristics and pruning rules can obtain the solutions of large problems in logical run times. The problem can be deduced as being NP-hard, so the MIP model is not expected to be solved for extremely large sizes within a reasonable (i.e., polynomially-bounded) CPU time. Hence, by exploiting the features of the problem, two metaheuristic algorithms are developed, i.e., a fast discrete particle swarm optimization and a genetic algorithm. Finally, we present computational results to analyze and verify the solutions obtained. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Batch delivery branch and bound algorithm Discrete particle swarm optimization algorithm Genetic algorithm Maximum tardiness Release time

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