Cyclic scheduling in synchronous production lines

In this paper we address the scheduling problem in unpaced synchronous mixed-model production lines operated under a cyclic scheduling policy. We first discuss operations of a production line with the synchronous transfer of parts. We then present an integer programming formulation of the problem. The problem, however, is W-hard, and for its exact solution we propose an implicit enumeration scheme. We discuss a property of the scheduling problem which allows us to effectively solve large size instances of the problem. We also present an approximate solution procedure with very good avenge performance. Useful managerial insights are obtained as we search for ways to improve the performance of synchronous lines. The relaxation of one of our original assumptions in the scheduling problem formulation results in an easy problem whose solution generates the absolute best in throughput performance configuration of the production line. Implementation of this solution, however, requires increasing the number of buffers in the line. We suggest other performance improvement ways to better balance the tradeoff between throughput and average Work-In-Progress (WIP) inventory in the line.     

Rudolf Schwarz and the concept of Stadtlandschaft

In 1949, an important albeit neglected book on the planning of cities was published in Germany, under the title Von der Bebauung der Erde (Of the Construction/Cultivation of the Earth). Its author, Rudolf Schwarz, was highly appreciated but equally has been marginalized by the architectural historiography of the twentieth century. His book contains a very elaborate theory on planning and the cities, based on the author's Catholic culture, his philosophical attachments to phenomenology, as well as his intellectual affinities with Hans Poelzig, Martin Wagner and Mies van der Rohe. A church-builder himself, Rudolf Schwarz was a prolific writer and a shrewd and inventive designer, but above all a harsh critic of modernity. He thus borrowed the idea of fusion between the city and the landscape, popular among his contemporaries and invested it with symbolic, transcendental meaning, focusing on the idea of the 'high city'. His 'city-landscape' appears to be polarized, but at the same time 'elastic', with 'changeable centres' and a rhizomatic structure, prefiguring later developments in urban theory. This article presents the origins of the concept of Stadtlandschaft , as they appeared in the German cultural and economic geography in the early twentieth century, its adaptation to the city-planning questions of the early 1930s, its later use by the National Socialist planning services and, particularly, its elaboration by Rudolf Schwarz during and after the Second World War.     

QUALITATIVE MONOTONICITY ANALYSIS OF A PROBLEM INVOLVING DIFFERENTIAL EQUATIONS

Monotonicity analysis is applied to an optimum design problem where the constraints are expressed by differential equations and their associated boundary conditions. The qualitative analysis does not utilize explicit or numerical solutions. Instead, the behavior of the equations is determined qualitatively with the aid of maximum principles. Equivalent functional constraints are derived containing information about the monotonic behavior of the design variables. This information is used to determine constraint activity. The results have generality and physical interpretation and may be used subsequently for efficient numerical implementation. The application problem examines the design of a small reflected-core nuclear reactor studied originally as a nonlinear programming problem.     

OPTIMAL STRUCTURAL TOPOLOGY DESIGN USING THE HOMOGENIZATION METHOD WITH MULTIPLE CONSTRAINTS

In applications of the homogenization method for optimal structural topology design the solution is obtained by solving the optimahty conditions directly. This reduces the computational burden by taking advantage of closed-form solutions but it restricts the optimization model to having only one constraint. The article develops a generalized class of convex approximation methods for mathematical programming that can be used for the optimal topology homogenization problem with multiple constraints in-eluded in the model, without substantial reduction in computational efficiency. A richer class of design models can be then addressed using the hotnogenization method. Design examples illustrate the performance of the proposed solution strategy.     

A CONTRIBUTION TO THE OPTIMAL DESIGN OF RIDE-RINGS FOR INDUSTRIAL ROTARY KILNS

The design of the ride-rings, or tyres, of industrial rotary kilns is studied as a nonlinear programming problem. The method of monotonicity analysis is employed to obtain results of sufficient generality and utility to the designer. A special-purpose algorithm for the location of the global optimum is presented. A parametric study provides design charts showing the range of criticallity for the various design requirements.

The article represents the type of modeling analysis and subsequent solution, suitable for design problems which must be solved many times with parameter changes larger than those handled with the usual sensitivity analysis.     

DECOMPOSITION ANALYSIS AND OPTIMIZATION OF AN AUTOMOTIVE POWERTRAIN DESIGN MODEL

Decomposition methods in mathematical programming typically apply a coordination strategy based on an identifiable structure in the problem. Decomposition analysis is a rigorous method for discovering how to (i) partition an original model so that the resulting problem structure matches the one required by a general coordination strategy, and (ii) implement the most suitable such strategy. Automated partitioning has received significant attention recently but implementation of coordination strategies based on decomposition analysis is still scarce. This article presents a complete analysis for partitioning and coordinated solution of an automotive powertrain design problem. The model offers a practical approach for accommodating control and geometry variables simultaneously. A variable complexity coordination strategy is proposed and implemented.