Multi-stage Loading Research Articles

Hybrid Heuristics for the Multi-Stage Capacitated Lot Sizing and Loading Problem

Hybrid Heuristics for the Multi-Stage Capacitated Lot Sizing and Loading Problem

Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions

The capacitated lot sizing and loading problem (CLSLP) deals with the issue of determining the lot sizes of product families/end items and loading them on parallel facilities to satisfy dynamic demand over a given planning horizon. The capacity restrictions in the CLSLP are imposed by constraints specific to the production environment considered. When a lot size is positive in a specific period, it is loaded on a facility without exceeding the sum of the regular and overtime capacity limits. Each family may have a different process time on each facility and furthermore, it may be technologically feasible to load a family only on a subset of existing facilities. So, in the most general case, the loading problem may involve unrelated parallel facilities of different classes. Once loaded on a facility, a family may consume capacity during setup time. Inventory holding and overtime costs are minimized in the objective function. Setup costs can be included if setups incur costs other than lost production capacity. The CLSLP is relevant in many industrial applications and may be generalized to multi-stage production planning and loading models. The CLSLP is a synthesis of three different planning and loading problems, i.e., the capacitated lot sizing problem (CLSP) with overtime decisions and setup times, minimizing total tardiness on unrelated parallel processors, and, the class scheduling problem, each of which is NP in the feasibility and optimality problems. Consequently, we develop hybrid heuristics involving powerful search techniques such as simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) to deal with the CLSLP. Results are compared with optimal solutions for 108 randomly generated small test problems. The procedures developed here are also compared against each other in 36 larger size problems.

Exercise therapy in Japan

The purpose of this report is to outline the exercise therapy of diabetes mellitus that has been administered in Japan during the past 10 years, with special emphasis on the results of studies on metabolic and endocrine effects as well as on practical aspects of exercise therapy. The studies on the response to exercise clarified neuroendocrine mechanisms involved in the regulation of carbohydrate and fat metabolism in exercise and provided a basis for the indication of exercise therapy in view of the pre-existing metabolic abnormalities. Concerning the training effects, changes of insulin sensitivity have been chiefly studied in relation to metabolic improvement by physical training using the insulin clamp method. The improvement of glucose and lipid metabolism obtained during the training program, consisting of fast walking or jogging corresponding to 40–60% of predictive VO 2 max for 30–60 min daily, was suggested to be related to improved insulin sensitivity in patients with NIDDM. Intensive studies have been made on exercise programs, and medical checks and guidelines for exercise prescription have been provided. Aerobic exercises with stretching and low-level callisthenics are recommended, and the usefulness of a multi-stage exercise loading test and the necessity of self-monitoring of blood glucose are stressed for the successful management of exercise therapy.

Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress–strain behaviour of clays

This paper describes the recent concept of equivalent time and how it can be used in a revised version of an earlier elastic viscoplastic model for one-dimensional straining of clays. It clarifies how parameters in the model can be determined using data from single-stage or multistage creep tests. The model can describe one-dimensional stress or strain responses under general conditions that include multistage loading with creep straining, continuous loading, and unloading or reloading. It also describes modelling for constant rate of straining tests, constant rate of stressing tests, and relaxation tests. Preconsolidation pressures are shown to depend on unloading–reloading, aging, and other loading processes. Key words : clay, compression, creep, equivalent time, elastic viscoplastic, preconsolidation pressure.

スリーブフラクチャリング法による岩盤応力測定

Sleeve fracturing is very similar to hydraulic fracturing except for the method of loading. Sleeve fracturing is a technique by which radial fractures are induced at any depth without introducing fluid into the rock during the fracturing process, and it is realized by pressurizing a jacketed borehole. Diametral deformation of a borehole is measured to examine the fracturing process of the primary radial fractures, which occur in the direction perpendicular to the minimum in-situ stress in the plane normal to the borehole axis, and the secondary radial fractures which extend perpendicular to the maximum in-situ stress.In this paper, the fracturing process with multi-stage loading is analyzed by the boundary element method and a procedure for determining in-situ rock stresses is presented. Relationships among borehole pressures, length of fractures and in-situ rock stresses on the fracturing process are formulated. It is clarified that the in-situ rock stresses are determined by the length of fractures and the borehole pressures at the stages of the completion of free separation and the re-propagation of fractures, which are evaluated from the curves of pressure-diametral displacement in multi-stage loading test. Furthermore, it is shown that the in-situ rock stresses can be successfully determined by using the presented procedure in practice.

Stress relaxation taking account of single- and multistage loading of a specimen in the elastoplastic region of deformation

Stress relaxation taking account of single- and multistage loading of a specimen in the elastoplastic region of deformation

A modified gradient method for finite element elastoplastic analysis by quadratic programming

The finite analysis problem with piecewise linear constitutive laws is formulated as a linear complementarity and a quadratic programming problem. The solution techniques using the well-known optimization methods of mathematical programming are discussed and a procedure, belonging to the class of gradient methods, is proposed which overcomes the computational difficulties that arise when there is a large number of variables. Through a physical interpretation of the gradient of the objective function, each mathematical step of the proposed optimization technique is translated into a corresponding physical operation on the structure and a mechanical solution procedure with a finite number of steps is derived. Finally, for the incremental analysis problem under non-holonomic constitutive laws the same procedure is adopted combined with the multistage loading technique. Illustrative examples for each of the preceding problems are given.

Cumulative Damage in the Low Cycle Fatigue

The authors proposed a hypothesis of cumulative damage due to the low cycle fatigue and gave the following formula for fatigue fracture criterion for the multi-stage loading test; Σ^^p__(i=1)(niΔWci)(σmaxi)α=C(σmaxp)β where ni and ΔWci are number of cycles and plastic strain energy per cycle in the i-th stage, respectively; σmaxi and σmaxp denote maximum tensile stresses in the i-th and final stages, respectively; α, β and C are material constants. Experimental data on stainless steel show that the above formula approximately holds good. The above formula is transformed into Σ^^p__(i=1)ai(ni/Nfi)=1 for multi-stage constant strain cycling test. Deviations in the experimental value of Σ(ni/Nfi) from Miner's damage rule may be explained by this formula.

The non-linear mechanical behaviour of polypropylene fibres under complex loading programmes

T his paper is concerned with the creep behaviour of a selected polypropylene monofilament under uniaxial loading. Multistage loading programmes have been used to confirm the consistency of the mathematical representation proposed previously (W ard and O nat, 1963). It has been shown that the total elongation in complex loading programmes can be predicted from a knowledge of the creep and recovery in a single stage loading programme, together with the creep in a two-stage loading programme involving the superposition of identical loads. The creep in a two-stage loading programme with non-identical loads is, moreover, fairly close to that predicted by simple addition of the creep observed in two separate one-stage loading programmes at the corresponding load levels. This is true even although the creep and recovery behaviour under single-stage loading is very markedly non-linear. Thus the more sophisticated treatment described in this paper leads to small, but significant, improvements in the fit between measured and predicted creep.