Use of linear physical programming and Bayesian updating for design issues in reverse logistics

Reverse logistics aims at capturing the remaining value in end-of-use products. This also means saving natural resources, energy, clean air and water, landfill space, and money. Strategic planning (also called designing) of a reverse supply chain is a challenging problem due to various crucial issues, such as what end-of-use products to collect, where to collect them, how to reprocess them, where to reprocess them, etc. To this end, this paper addresses the following two crucial issues, and proposes a quantitative decision-making model for each of them: (i) how to select efficient collection centres? and (ii) how to evaluate whether repairing an end-of-use product is more sensible than remanufacturing/recycling the same? For the first problem, we propose a Linear Physical Programming model, and for the second problem, we employ Fuzzy Logic and Bayesian Updating. The models are demonstrated via numerical examples.     

Homogeneous magnet design using linear programming

We introduce a technique for designing homogeneous magnets using linear programming, We first show that minimum-power homogeneous magnet design can be cast as a linear programming problem. We also show that the method is applicable to minimum conductor mass superconducting magnet design. The method has several advantages over existing techniques including: it allows complete flexibility in arbitrary geometric constraints on both the coil locations and the shape of the homogeneous volume; it guarantees a globally optimal solution; and it offers rapid computation speed (about 30 s). Three resistive magnet design examples and one shielded superconducting magnet design are presented to illustrate the flexibility of the method     

The use of linear programming for the design of SAW filters andfilterbanks

A linear programming algorithm is proposed for designing surface acoustic wave (SAW) filters or filterbanks with arbitrary amplitude and phase responses. A modified sampling theorem representation is employed for the transducer frequency responses which allows the number of independent variables to be minimized without degrading the filter characteristics. The method can also be used as part of an iterative procedure to generate optimal corrections for second order effects such as diffraction and circuit loading. A simplified algorithm for this procedure is given, and the method is illustrated with theoretical and experimental data from a three channel contiguous SAW filterbank design. Although the method given in this paper is formulated primarily for SAW filters, it is equally applicable to FIR digital filter design     

A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers’ performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.     

Theoretical estimation of dwell and consolidation times in rotary tablet machines

Abstract

Knowledge of the time-dependent mechanical properties of pharmaceutical materials is critical to understanding of the compaction of tablets. In effort to determine the time-scale involved during compaction, equations for the dwell time and the consolidation time are proposed in this paper. Expressions for the consolidation time are obtained from generally accepted equations for punch displacement and separation between punch tips. These equations are deduced for rotary tablet machines with pressure rollers of the same and of different sizes. Specifically, the equations are applied to calculate the dwell and consolidation times for Manesty Betapress and Korsch Pharmapress Rotary tablet machines. The results are graphically presented.     

Multi-objective design optimization of reconfigurable machine tools: a modified fuzzy-Chebyshev programming approach

A reconfigurable manufacturing system (RMS) is designed for rapid adjustment of functionalities in response to market changes. A RMS consists of a number of reconfigurable machine tools (RMTs) for processing different jobs using different processing modules. The potential benefits of a RMS may not be materialized if not properly designed. This paper focuses on RMT design optimization considering three important yet conflicting factors: configurability, cost and process accuracy. The problem is formulated as a multi-objective model. A mechanism is developed to generate and evaluate alternative designs. A modified fuzzy-Chebyshev programming (MFCP) method is proposed to achieve a preferred compromise of the design objectives. Unlike the original fuzzy-Chebyshev programming (FCP) method which imposes an identical satisfaction level for all objectives regardless of their relative importance, the MFCP respects their priority order. This method also features an adaptive satisfaction-level-dependent process to dynamically adjust objective weights in the search process. A particle swarm optimization algorithm (PSOA) is developed to provide quick solutions. The application of the proposed approach is demonstrated using a reconfigurable boring machine. Our computational results have shown that the combined MFCP and PSOA algorithm is efficient and robust. The advantages of the MFCP over the original FCP are also illustrated based on the results.     

Extension of the hybrid linear programming method to optimize simultaneously the design and operation of groundwater utilization systems

This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for solving practical groundwater management problems.     

Experimental results and wear predictions of petal tools that freely rotate

It is difficult to calculate the wear produced by free-pinned tools because their angular movement is not entirely predictable. We analyze the wear produced with free-pinned ring tools, using both simulations and experiments. We conclude that the wear of an incomplete ring is directly proportional to the ring's angular size, independently of the mean radius of the ring. We present an algorithm for calculation of the wear produced by free-pinned petal tools, as they can be considered a linear combination of incomplete free-pinned ring tools. Finally, we apply this result to the enhancement of a defective flat surface and to making a concave spheric surface.     

Theoretical estimation of dwell and consolidation times in rotary tablet machines

Knowledge of the time-dependent mechanical properties of pharmaceutical materials is critical to understanding of the compaction of tablets. In effort to determine the time-scale involved during compaction, equations for the dwell time and the consolidation time are proposed in this paper. Expressions for the consolidation time are obtained from generally accepted equations for punch displacement and separation between punch tips. These equations are deduced for rotary tablet machines with pressure rollers of the same and of different sizes. Specifically, the equations are applied to calculate the dwell and consolidation times for Manesty Betapress and Korsch Pharmapress Rotary tablet machines. The results are graphically presented.     

Solid-phase dwell times in the central and peripheral parts of a gas-solid jet

Dwell-time measurements are reported for the core and periphery of a fluidized bed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 4, pp. 642–647, April, 1979.     

Optimal structural design under stochastic uncertainty by stochastic linear programming methods

In the optimal plastic design of mechanical structures one has to minimize a certain cost function under the equilibrium equation, the yield condition and some additional simple constraints, like box constraints. A basic problem is that the model parameters and the external loads are random variables with a certain probability distribution. In order to get reliable/robust optimal designs with respect to random parameter variations, by using stochastic optimization methods, the original random structural optimization problem must be replaced by an appropriate deterministic substitute problem. Starting from the equilibrium equation and the yield condition, the problem can be described in the framework of stochastic (linear) programming problems with ‘complete fixed recourse’. The main properties of this class of substitute problems are discussed, especially the ‘dual decomposition’ data structure which enables the use of very efficient special purpose LP-solvers.     

Use of molecular characteristics to calculate viscosity of mineral solutions

The possibility of using molecular characteristics in the determination of the thermophysical parameters of fluids is shown. Approximate equations for the calculation of the dynamic viscosity of aqueous solutions of mineral salts are obtained through the use of similarity theory and molecular data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 1, pp. 85–89, January, 1974.     

Application of geometric programming to transformer design

This paper considers the transformer design optimization problem. In its most general form, the design problem requires minimizing the total mass (or cost) of the core and wire material while ensuring the satisfaction of the transformer ratings and a number of design constraints. The constraints include appropriate limits on efficiency, voltage regulation, temperature rise, no-load current, and winding fill factor. The design optimization seeks a constrained minimum mass (or cost) solution by optimally setting the transformer geometry parameters and the relevant electrical and magnetic quantities. In cases where the core dimensions are fixed, the optimization problem calls for a constrained maximum volt-ampere or minimum loss solution. This paper shows that the above design problems can be formulated in geometric programming (GP) format. The importance of the GP format stems from two main features. First, GP provides an efficient and reliable solution for the design optimization problem with several variables. Second, it guarantees that the obtained solution is the global optimum. The paper includes a demonstration of the application of the GP technique to transformer design. It also includes a comparative study to emphasize the advantage of including the transformer core dimensions as variables in the design problem.     

Influence of dwell times on the thermomechanical fatigue behavior of a directionally solidified Ni-base superalloy

In-phase (IP) and out-of-phase (OP) thermomechanical fatigue tests with T = 100–750 °C and optional dwells of 20 min at 750 °C were carried out on directionally solidified Ni-base Alloy 247 LC DS. Introducing dwells reduced the lifetime for both phase angles to about one sixth. Specific damage mechanisms were internal carbide and carbide–matrix interface cracks in IP tests and crack propagation along {1 1 1}-microtwin planes in OP tests. Introducing dwells intensified both effects, thus contributing to the lifetime reduction. During dwells, the gauge length may exhibit transversal creep because of extensometer forces distorting the strain measurement.     

Use of the method of local weight functions to calculate stress intensity factors

The method of local weight functions is used to determine stress-intensity factors (SIF) in the case of circular and elliptical cracks. The SIFs K₂ and K₃ are also calculated for the circular crack. The results illustrate the satisfactory accuracy of the given method and its efficiency compared to the methods used previously.Translated from Problemy Prochnosti, No. 10, pp. 59–67, October, 1994.     

Calculation of the move limits for the sequential linear programming method

The sequential linear programming (SLP) method is one of the easiest optimization techniques used to treat non-linear optimization problems. The successful application of the method is based on the proper choice of the move limits, which are unfortunately uncertain in the SLP algorithm. To enhance the efficiency and reliability of the SLP algorithm, six methods are proposed to calculate the move limits. The first three methods use the constraint equations to compute the minimum variations needed from the current design point to reach the constraint boundaries. The fourth method incorporates the cost function information as well as the constraints to figure out the move limits. The last two methods form a quadratic programming (QP) subproblem and solve for the change of the quadratic cost function. The move limits used in SLP are then computed from the estimated change of the linear cost function from the QP solution. Four numerical examples are employed to demonstrate the solution process by the methods proposed. The advantages and disadvantages of these methods are discussed.     

A linear programming model to optimize the decision-making to managing cogeneration system

A mathematical linear programming (LP) model was developed to optimize the decision-making for managing a cogeneration facility as a potential clean-development mechanism project in a hospital in Palestine. The model was developed to optimize the cost of energy and the cost of installation of a small cogeneration plant under constraints on electricity-and-heat supply and demand balances. In the model, the sources of electricity are either from cogeneration or public utilities and it was calculated the least cost to supply electricity and heat to the hospital. The hospital is using heat for their operation and that made the application for the cogeneration to be attractive and feasible. In this study, we will develop the LP model and will show the results and the time schedule for the cogeneration. This developed LP model can be used and run to any cogeneration application with little modification.     

Computer tools for integrated conceptual design

This paper outlines the conceptual design process with reference to the integrated computer-aided design tool known as Schemebuilder, and the related work of the Lancaster University Engineering Design Centre. The aim of the Lancaster EDC is to provide highly integrated support for the rapid creation and evaluation of a wide range of outline design schemes. Particular attention is paid to the design of mechatronic systems and devices.     

Application of semi-definite programming to the design of multi-response experiments

The need to be able to design experiments with multiple responses is becoming apparent in many real-world applications. The generation of an optimal design to estimate the parameters of a multi-response model is a challenging problem. Currently available algorithms require the solution of many optimization problems in order to generate an optimal design. In this paper, the problem of multi-response D-optimal design is formulated as a semi-definite programming model and a relaxed form of it is solved using interior-point solvers. The main advantage of the proposed method lies in the amount of computation time taken to generate a D-optimal design for multi-response models. The proposed method is tested on several test problems and is shown to be very efficient with optimal designs being found very quickly in all cases. The robustness of the generated designs with respect to the variance-covariance matrix is also assessed for the test problems in order to show how a sensitivity analysis can be performed. The characteristics of the proposed method are also compared with those of other existing methods.