Dynamic warehouse size planning with demand forecast and contract flexibility

This paper develops a dynamic warehouse planning model incorporating demand forecast and contract flexibility, and addresses how demand forecast and contract flexibility affect warehouse size planning. In this model, a manager announces a nominal size of the warehouse space to rent before the planning horizon begins (strategic decision), and determines the ordering quantity and actual warehouse size during the horizon (operational decision). In particular, the manager can adjust the actual warehouse size within a range according to dynamically updating demand forecast during the horizon, which reflects the contract flexibility. We start with the characterisation of the operational decision. For any given nominal size, we show the monotonicity of optimal inventory replenishment and warehousing decisions w.r.t. demand forecast and contract flexibility. However, this monotonicity does not necessarily hold for the strategic choice of the nominal size. Finally, a case study is presented to investigate the interaction between demand forecast information and contract flexibility. We find that the value of demand forecast can be enhanced as the contract flexibility improves. However, more forecasted demands do not imply higher value of contract flexibility.     

REPLACEMENT OF TECHNOLOGY WHEN A NEW TECHNOLOGICAL BREAKTHROUGH IS EXPECTED

A replacement problem is presented in which two technologies are involved. One technology is immediately available while the second, considered a technological breakthrough, is expected at some uncertain time in the future. The technological environment is dynamic. Therefore, special attention is given to the availability and reliability of data. Decision horizon stopping rules are suggested when long time horizons are considered. The algorithm is different from currently known standard procedures. It does not rely on the monotonicity properties of the optimal solution that occur when the horizon is extended, nor on action elimination considerations based on non-homogeneous Markov decision analysis. Rather, a special procedure is suggested in which an auxiliary problem binds the solution of the original problem. Interrelationships between the two problems lead to the desired horizon results. The procedure detects much shorter forecast horizons than the Bess and Sethi (1988) procedure without increasing the computational effort needed.     

Quantifier elimination supported proofs in the numerical treatment of fluid flows

During the analysis of numerical methods for fluid flows some properties of numerical methods as stability or monotonicity can be stated as quantified problems and proved by quantifier elimination. A case study demonstrating such proofs is presented. The study shows that the stability region of the central scheme for advection-diffusion equation with Runge–Kutta time discretization is much bigger than classical stability region.     

Aggregate and detailed production planning integrating procurement and distribution plans in a multi-site environment

A monolithic mixed integer linear goal programming (MILGP) model that is developed in this paper produces a time and capacity aggregated production plan, a detailed production plan, a detailed procurement plan and a detailed distribution plan simultaneously to overcome the drawbacks of the hierarchical/sequential planning approaches of not yielding a feasible and/or an optimal plan. The model uses different time-grids and planning horizons for aggregate and detailed planning to reduce the computational burden. The limitations of storage space, raw material availability and production capacity at plants and a requirement of maintaining a minimum level of inventory buffer or forward cover have been modelled. Two heuristics that are proposed to solve the MILGP model gave good quality solutions with an average and the worse case optimality gap of 1.17% and 4.4% respectively when applied to one hundred randomly generated industry size problem instances.     

A simulation-based heuristic solution procedure for analyzing human postural balance

Human postural movements can be simulated by a biomechanical model. Biomechanical models, however, involve differential equations and do not admit conventional optimization techniques for solution. Introducing the notion of dynamic grid-sizing, this paper presents an easy-to-implement simulation-based heuristic procedure for solving biomechanical models. We adopt the four-segment sagittal model for human postural analysis from [Iqbal K, Pai YC (2000) Predicted region of stability for balance recovery: motion at the knee joint can improve termination of forward movement. J Biomech 33:1,619–1,627] for illustration and solve it to predict a region of stability for the model. The size and the feasibility of the stability region predicted by the proposed scheme in comparison with results reported in (Iqbal K, Pai YC (2000) Predicted region of stability for balance recovery: motion at the knee joint can improve termination of forward movement. J Biomech 33:1,619–1,627) demonstrate that the proposed scheme is fairly efficient and effective and further suggest its practical usage in analyzing human postural balance.     

A rolling horizon simulation approach for managing demand with lead time variability

This paper proposes a rolling horizon (RH) approach to deal with management problems under dynamic demand in planning horizons with variable lead times using system dynamics (SD) simulation. Thus, the nature of dynamic RH solutions entails no inconveniences to contemplate planning horizons with unpredictable demands. This is mainly because information is periodically updated and replanning is done in time. Therefore, inventory and logistic costs may be lower. For the first time, an RH is applied for demand management with variable lead times along with SD simulation models, which allowed the use of lot-sizing techniques to be evaluated (Wagner-Whitin and Silver-Meal). The basic scenario is based on a real-world example from an automotive single-level SC composed of a first-tier supplier and a car assembler that contemplates uncertain demands while planning the RH and 216 subscenarios by modifying constant and variable lead times, holding costs and order costs, combined with lot-sizing techniques. Twenty-eight more replications comprising 504 new subscenarios with variable lead times are generated to represent a relative variation coefficient of the initial demand. We conclude that our RH simulation approach, along with lot-sizing techniques, can generate more sustainable planning results in total costs, fill rates and bullwhip effect terms.     

A COMPUTATIONAL STUDY OF EMPIRICAL DECISION HORIZONS IN INFINITE HORIZON, MULTIPERIOD NETWORK FLOW PROBLEMS

The minimum cost, multiperiod network flow model is an important optimization model for solving problems in many application areas including resource scheduling, planning and distribution. This network model describes decision making problems over time. In earlier work, we discussed the development, implementation and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method exploits the natural decomposition of multiperiod network problems, by limiting its pivoting activity to the date of the last few time periods. Both the solution CPU time and pivot count are linear in the number of time periods. For standard network optimization codes, the pivot count is linear while the solution time is approximately quadratic in the number of periods.

Here we present a computational study of the natural decomposition of, or empirical decision horizons for, an “infinite” horizon, multiperiod network model. We demonstrate the existence of such horizons for a model for which there is no guarantee of having an exact, or theoretical, decision horizon. When a problem having a sufficiently large number of time periods is solved, there is no effect on the decisions to be made for the first few time periods. Thus, the early periods' solution to a problem having an infinite number of time periods may be considered solved.     

A multi-objective optimisation model to integrating flexible process planning and scheduling based on hybrid multi-objective simulated annealing

Process planning and production scheduling play important roles in manufacturing systems. In this paper we present a mixed integer linear programming (MILP) scheduling model, that is to say a slot-based multi-objective multi-product, that readily accounts for sequence-dependent preparation times (transition and set up times or machine changeover time). The proposed scheduling model becomes computationally expensive to solve for long time horizons. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimisation problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for this, the hybrid multi-objective simulated annealing algorithm (MOHSA) is proposed by fully utilising the capability of the exploration search and fast convergence. Two numerical experiments have been performed to demonstrate the effectiveness and robustness of the proposed algorithm.     

The collocation solution of Poisson problems based on approximate Fekete points

The aim of this work is to show how the collocation method may be used for the approximate solution of Poisson problems on planar domains with a smooth boundary in a stable and efficient way. The most important aspect of this work consists in the use of approximate Fekete points recently developed by Sommariva and Vianello. Numerical experiments concerning the collocation solution of Poisson problems defined on the unit disc and an eccentric annulus with the homogeneous Dirichlet boundary conditions are presented. Two sets of trial functions, consisting of algebraic polynomials, satisfying and not satisfying the prescribed boundary conditions are considered. As the presented results show, these easily computable collocation points, giving well-conditioned collocation matrices, open new horizons for the collocation solution of elliptic partial differential equations considered on planar and higher-dimensional domains.     

ASRWM: an arid/semiarid region water management model

Water shortage resulting from both natural conditions and human activities has been proved to be a bottleneck that chokes development in arid and semiarid regions. Systems analysis provides an effective way of clarifying conflicts between water supply and demand. In this study, an arid/semiarid region water management (ASRWM) model is developed for sound planning of a water resources system. The proposed model is founded on interval-fuzzy multiobjective programing (IFMOP) for effectively reflecting complexities of the study system and expediently facilitating solution of the model. Member-ship functions for modeling objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. To evaluate the applicability of the proposed model, a case study for the Luopu County in northwestern China has been undertaken. The modeling outputs generated through scenario analyses are based on in-depth examination of several sensitive issues including farming, horticulture, stockbreeding, spring water allocation, pasture expansion, and land exploitation. The obtained results lead to two alternatives that provide an useful basis for formulating desired policies of sustainable development in the region. Through the case study, the proposed model is proved to have reasonable computational requirements and to be applicable to large-scale practical planning problems.     

Comparative analysis of lot-sizing models for multi-stage systems: a simulation study

In the past few years researchers have given considerable attention to various aspects of lot-sizing for single-stage and multi-stage systems in material requirements planning (MRP). Numerous models have been developed and tested on problems with finite horizons and deterministic time-varying demand. A real production system is, however, so complex that no model can capture all the elements under consideration. Instead of the static horizon commonly assumed by researchers, real planning is usually carried out on rolling horizons with different lengths. Such performance measures may include minimization of the total cost, inventory level, and schedule instability caused by rolling horizon and the number of setups. For large and complex product structures, the conventional approach is to apply a single-stage lot-sizing rule once to every stage of the multi-stage system. The Wagner–Whitin (WW) algorithm does provide a solution to this problem, but the length of the necessary calculations precludes its use in practice. As a result, many researchers have proposed numerous other lot-sizing procedures. The purpose of this paper is to examine the performance of various multi-stage lot-sizing procedures under rolling horizon environment using simulation. Cost and schedule instability were used as the performance criteria and product structure, demand variabillity, cost structure and planning horizon were considered as independent variables. It has been shown that Silver–Meal (SM) procedure outperforms other procedures such as WW and incremental approach (ICA) in most of the cases. The performance of ICA and SM are better than their respective counterparts Gaither’s rule (GA) and modified Silver-Meal (MSM). The results also indicate that there are differences in the performance of various lot-sizing procedures when applied to two different product structures.     

Influence of local fracture energy distribution on maximum fracture load of three-point-bending notched concrete beams

The maximum fracture load of a notched concrete beam has been related to the local fracture energy at the cohesive crack tip region analytically in this paper, and then the correlation between the size effects on the maximum fracture loads and the RILEM specific fracture energy is established. Two extreme conditions have been established, namely zero crack-tip bridging with zero local fracture energy and maximum crack-tip bridging with the maximum size-independent fracture energy. It is concluded that the local fracture energy at the crack tip region indeed varies with the initial crack length and the size of specimen. The tri-linear model for the local fracture energy distribution is confirmed by using the proposed simple analytical solution.     

Anode Streamer Branching

An analytical investigation of the problem on stability of a locally flat ionization front corresponding to some region of the streamer surface is performed using complete electrodynamic relations on the streamer surface. Electrodynamic boundary conditions, which allow for the continuity of the total electric current (displacement current and conduction current) on the boundary, are derived. The solution of the problem on stability of the initial stationary state for the chosen region, which may be both the streamer head and its side surface, is constructed in a local coordinate system. A characteristic equation is obtained which, in addition to generalization of previously known results, includes new effects and makes it possible to find the limits of the region of streamer surface instability. The hypothesis is formulated that the observed instability of the streamer surface results in streamer branching, and the criterion of the emergence of branching is derived. This criterion makes it possible to explain some experimentally observed features of the branching process. It is shown that a short streamer is stable; however, when the critical size is reached, secondary formations may branch out from the streamer which correspond to the branching process.     

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

钢铁工业中的自由边值问题

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture.The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region. overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin "intermediate region" at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

A compliant track link model for high‐speed,high‐mobility tracked vehicles

Several modelling methods have recently been developed for the dynamic analysis of low‐speed tracked vehicles. These methods were used to demonstrate the significant effect of the force of the interaction between the track links and vehicle components, even when low speeds are considered. It is the objective of this investigation to develop compliant track link models and investigate the use of these models in the dynamic analysis of high‐speed, high‐mobility tracked vehicles. There are two major difficulties encountered in developing the compliant track models discussed in this paper. The first is due to the fact that the integration step size must be kept small in order to maintain the numerical stability of the solution. This solution includes high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. The characteristics of the compliant elements used in this investigation to describe the track joints are measured experimentally. A numerical integration method having a relatively large stability region is employed in order to maintain the solution accuracy, and a variable step size integration algorithm is used in order to improve the efficiency. The second difficulty encountered in this investigation is due to the large number of the system equations of motion of the three‐dimensional multibody tracked vehicle model. The dimensionality problem is solved by decoupling the equations of motion of the chassis subsystem and the track subsystems. Recursive methods are used to obtain a minimum set of equations for the chassis subsystem. Several simulations scenarios including an accelerated motion, high‐speed motion, braking, and turning motion of the high‐mobility vehicle are tested in order to demonstrate the effectiveness and validity of the methods proposed in this investigation. Copyright © 2000 John Wiley & Sons, Ltd.     

Effects of forecast errors on optimal utilisation in aggregate production planning with stochastic customer demand

The hierarchical structure of production planning has the advantage of assigning different decision variables to their respective time horizons and therefore ensures their manageability. However, the restrictive structure of this top-down approach implying that upper level decisions are the constraints for lower level decisions also has its shortcomings. One problem that occurs is that deterministic mixed integer decision problems are often used for long-term planning, but the real production system faces a set of stochastic influences. Therefore, a planned utilisation factor has to be included into this deterministic aggregate planning problem. In practice, this decision is often based on past data and not consciously taken. In this paper, the effect of long-term forecast error on the optimal planned utilisation factor is evaluated for a production system facing stochastic demand and the benefit of exploiting this decision’s potential is discussed. Overall costs including capacity, backorder and inventory costs, are determined with simulation for different multi-stage and multi-item production system structures. The results show that the planned utilisation factor used in the aggregate planning problem has a high influence on optimal costs. Additionally, the negative effect of forecast errors is evaluated and discussed in detail for different production system environments.     

Trefftz boundary elements—multi‐region formulations

This paper is concerned with an effective numerical implementation of the Trefftz boundary element method, for the analysis of two‐dimensional potential problems, defined in arbitrarily shaped domains. The domain is first discretized into multiple subdomains or regions. Each region is treated as a single domain, either finite or infinite, for which a complete set of solutions of the problem is known in the form of an expansion with unknown coefficients. Through the use of weighted residuals, this solution expansion is then forced to satisfy the boundary conditions of the actual domain of the problem, leading thus to a system of equations, from which the unknowns can be readily determined. When this basic procedure is adopted, in the analysis of multiple‐region problems, proper boundary integral equations must be used, along common region interfaces, in order to couple to each other the unknowns of the solution expansions relative to the neighbouring regions. These boundary integrals are obtained from weighted residuals of the coupling conditions which allow the implementation of any order of continuity of the potential field, across the interface boundary, between neighbouring regions. The technique used in the formulation of the region‐coupling conditions drives the performance of the Trefftz boundary element method. While both of the collocation and Galerkin techniques do not generate new unknowns in the problem, the technique of Galerkin presents an additional and unique feature: the size of the matrix of the final algebraic system of equations which is always square and symmetric, does not depend on the number of boundary elements used in the discretization of both the actual and region‐interface boundaries. This feature which is not shared by other numerical methods, allows the Galerkin technique of the Trefftz boundary element method to be effectively applied to problems with multiple regions, as a simple, economic and accurate solution technique. A very difficult example is analysed with this procedure. The accuracy and efficiency of the implementations described herein make the Trefftz boundary element method ideal for the study of potential problems in general arbitrarily‐shaped two‐dimensional domains. Copyright © 1999 John Wiley & Sons, Ltd.     

Heuristic solution approaches to operational forest planning problems

Operational forest planning problems are typically very difficult problems to solve due to problem size and constraint structure. This paper presents three heuristic solution approaches to operational forest planning problems. We develop solution procedures based on Interchange, Simulated Annealing and Tabu search. These approaches represent new and unique solution strategies to this problem. Results are provided for applications to two actual forest planning problems and indicate that these approaches provide near optimal solutions in relatively short amounts of computer time.     

共沉淀法制备硅酸锆包裹炭黑及其高温稳定性

以正硅酸乙酯和氧氯化锆为原料, 采用溶胶共沉淀法制备了硅酸锆包裹炭黑复合粉体。利用XRD、SEM、色度计和粒度分析仪等手段对样品进行了表征。采用正交试验考察了前驱体pH值、煅烧温度、矿化剂种类和用量等工艺条件对复合粉体高温稳定性的影响。结果表明, 矿化剂和煅烧温度是最重要的影响因素。最佳的工艺条件是前驱溶液pH为5、矿化剂为5wt%LiF、煅烧温度为1150℃。该工艺条件下形成的球形镶嵌结构能够有效防止炭黑被氧化。获得的硅酸锆包裹炭黑粉体具有较好的高温稳定性, 粒度分布符合陶瓷色料的要求。该粉体用于熔块釉中, 1000℃烧成仍然具有较好的发色效果。