Optimizing large-scale inventory networks: An iterative decomposition approach

We present two significant enhancements to the guaranteed-service (GS) model for multiechelon safety stock placement. First, we let each stage's expected inventory cost be a generalized nonconcave non-closed-form function of its incoming and outgoing service time. This allows the GS model to incorporate important phenomena such as variable stage times and nonnested review periods, which previous GS literature has not allowed. Second, we optimize the generalized cost GS model for directed acyclic networks, rather than assembly/distribution networks or trees. For the resulting NP-hard optimization problem, we present a provably optimal algorithm that runs within minutes for 29 chains from a data set of 38 real-world supply chains ranging from 8 to 2,025 stages. We also present two significantly faster yet near-optimal heuristics. One heuristic is motivated by the structure of the formulation's dual space, whereas the other heuristic simply terminates the optimization algorithm after a fixed number of iterations. As a performance benchmark, on the 38 chains, the first heuristic has an average optimality gap of approximately 1.1% and average run time of 88 seconds, whereas the second heuristic has an average optimality gap of 2.8% and an average run time of 5.9 seconds.

The aim of this paper is to compare the performance of a local solution technique—namely Sequential Linear Programming (SLP) employing random starting points—with state-of-the-art global solvers such as Baron and more sophisticated local solvers such as Sequential Quadratic Programming and Interior Point for the pooling problem. These problems can have many local optima, and we present a small example that illustrates how this can occur.We demonstrate that SLP—usually deemed obsolete since the arrival of fast reliable SQP solvers, Interior Point Methods and sophisticated global solvers—is still the method of choice for an important class of pooling problems when the criterion is the quality of the solution found within a given acceptable time budget. On this measure SLP significantly ourperforms all other tested algorithms.In addition we introduce a new formulation, the qq-formulation, for the case of fixed demands, that exclusively uses proportional variables. We compare the performance of SLP and the global solver Baron on the qq-formulation and other common formulations. While Baron with the qq-formulation generates weaker bounds than with the other formulations tested, for both SLP and Baron the qq-formulation finds the best solutions within a given time budget. The qq-formulation can be strengthened by pq-like cuts in which case the same bounds as for the pq-formulation are obtained. However the associated time penalty due to the additional constraints results in poorer solution quality within the time budget.

Numerical implementations of optimization algorithms often use parameters whose values are not strictly determined by the derivation of the algorithm, but must fall in some appropriate range of values. This work describes how fuzzy logic can be used to “control” such parameters to improve algorithm performance. This concept is shown with the use of sequential linear programming (SLP) due to its simplicity in implementation. The algorithm presented in this paper implements heuristics to improve the behavior of SLP based on current iterate values of design constraints and changes in search direction. Fuzzy logic is used to implement the heuristics in a form similar to what a human observer would do. An efficient algorithm, known as the infeasible primal-dual path-following interior-point method, is used for solving the sequence of LP problems. Four numerical examples are presented to show that the proposed SLP algorithm consistently performs better than the standard SLP algorithm.

Move limits definition in structural optimization with sequential linear programming. Part II: Numerical examples

Joint optimization of safety stock placement and supplier selection in a multi-layered distribution network

This paper presents a sequential linear programming approach for the determination of time-optimal controller for nonlinear systems. The sequential linear programming solution is used to update the control profile so as to satisfy the terminal conditions for an assumed maneuver time. A univariant minimization approach which brackets the optimal value of the maneuver time, such as the bisection algorithm is used in an outer loop to converge to the minimum time. The proposed technique is illustrated on two benchmark problems: the attitude control of a spacecraft and the minimum time control of a robot.

The use of optimization in a simulation-based design of automotive, aerospace and consumer products has become a common trend today. Designers are faced with the continuous challenge of reducing manufacturing costs and design cycle times while improving the systems performance and reliability. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and easy availability. However, the inherent conceptual simplicity makes the SLP techniques not globally convergent. This research presents a new algorithm that uses a linearization error and an interior point trust-region method in SLP to truss structures that is both considered sizing and configuration problems. The algorithm may be suitable for large optimization problems where time is a constraint and the optimization may be stopped before convergence is achieved. Results of application studies are presented, illustrating the applicability of the proposed algorithm.

Zebrafish serves as a model organism in morphogenesis studies in cell biology. One of the main difficulties of modeling a specific morphogenetic process come from the proper identification of its key features. To study the influence of geometric constraint in morphogenesis, here this article models the notochord as hard spheres assemble in an elliptical cylinder and optimize the packing density. This article implements linear approximation on the hard sphere constraints and find the optimal packing configuration by the sequential linear programming (SLP) method. During the process, this article modifies the SLP scheme into expanding the spheres in a fixed cylindrical confinement. This article finds the staircase and similar structures becomes predominant as increasing the ellipticity of the confinement. Our study deepens the understanding of the notochord morphogenesis, and also provides methodological guidance on related modeling studies involving geometric constraints.

We investigate the problem of clock network sizing subject to general skew constraints. A novel approach based on sequential linear programming is presented. The original nonlinear programming problem is transformed into a sequence of linear programs by taking the first-order Taylor's expansion of clock path delay with respect to buffer and/or wire widths. For each linear program, the sensitivities of clock path delay, with respect to buffer and/or wire widths, are efficiently updated by applying time-domain analysis to the clock network in a divide-and-conquer fashion. Our technique can take into account power supply and process variations. We demonstrate experimentally that the proposed technique is not only capable of optimizing effectively the skew and area of clock network, but also of providing more accurate delay and skew results compared to the traditional approaches.

A diaphragm spring is an important component of a clutch assembly, characteristics of which depends largely on that of a diaphragm spring. A diaphragm spring is subject to high stress concentration in driving condition, which frequently causes cracks and fracture around finger area. In this paper, behavior of a diaphragm spring is analysed by finite element method to calculate sensitivity of design parameters, which is used to perform optimal design of diaphragm spring shape. As an object function, hoop stresses are taken and minimized to improve durability. Characteristics of the diaphragm is used as equality constraint to maintain the original design purpose and sequential linear programming(SLP) is utilized as an optimization tool. With optimized design, it is verified that concentrated stress is decreased maintaining release load characteristic.

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.

Swarm algorithms have been successfully applied to obtain global optimal solutions for complex problems such as multi-peak problems. However these algorithms have not been applied to complicated structural and mechanical optimization problems since local optimization c apability is still inferior to general numerical optimization methods. This paper discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optim ization problems. Single - and multiobjective optimization techniques using swarm algorithms are combined with a sequential linear programming (SLP) method. In the proposed techniques, swarm optimization algorithms and SLP are conducted simultaneously. Fina lly, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.

Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes L∞ norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when L∞ norms are used. Examples are also provided to illustrate the effectiveness of using L∞ norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.

Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

A discontinuous quasi-upper bound limit analysis approach with sequential linear programming mesh adaptation