A new algorithm for computing optimal (s, S) policies in a stochastic single item/location inventory system

It has been shown that a class of (s, S) policies is optimal to the single item/location inventory system. However, the computational complexity of finding the optimal (s, S) policy has restricted applications of this inventory system. This paper proposes a new algorithm to search for the optimal pair of s and S. We introduce a dummy cost factor and an auxiliary function into our algorithm. The algorithm searches for the optimal dummy cost through continuously evaluating the auxiliary function. It differs from the approach of Zheng and Federgruen (1991) in several aspects and has certain advantages. First, as it revises the dummy cost based on the sign of the auxiliary function, the primary goal of the search is not to compute the optimal s and S during each iteration. Second, by identifying the non-prospective sets of S, the algorithm further reduces the search effort. Numerical tests show that on the average, the proposed algorithm saves more than 30% of evaluation effort compared with Zheng and Federgruen's method.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

The trans-shipment problem in a two-echelon,multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R,?s,?S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s,?S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.     

Continuous review (s,S) policies for inventory systems incorporating a cutoff transaction size

In this paper, a mathematical model is developed for the analysis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff transaction size of w units is specified such that customer demands with sizes exceeding w units will be filtered out of the inventory system and treated as special orders to be satisfied by special deliveries. Customer demands with sizes > units will be met From stock. The control discipline is the (s, S) inventory policy with continuous review and the nature of the demands is approximated by a stuttering Poisson distribution. Recursive formulae are developed for the determination of the probabilities of the lead time demand and the available inventory position. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.     

Tangential contact problem for a transversely isotropic elastic layer bonded to an elastic foundation

A system consisting of an elastic layer made of a transversely isotropic material bonded to an elastic half-space made of a different transversely isotropic material is considered. An arbitrary tangential displacement is prescribed over a domain S of the layer, while the rest of the layer’s surface is stress-free. The tangential contact problem consists of finding a complete field of stresses and displacements in this system. The generalized-images method developed by the author is used to get an elementary solution to the problem. It is also shown that an integral transform can be interpreted as a sum of generalized images. The case of a circular domain of contact is considered in detail. The results are valid for the case of isotropy as well.     

Modelling and solving spare parts supply chain network design problems

Spare parts are key operational assets in order to minimise unexpected equipment downtimes that may significantly impact a company’s results. The spare parts supply chain network supports the entire spare parts operations management and it is essential to achieve the planned goals. However, most of the traditional literature on spare parts management has not focused on the underlying supply chain network. Thus, this paper studies the integration of supply chain network design and control with traditional spare parts management. In particular, a generic network optimisation modelling structure is proposed, with simultaneous optimisation of warehouse locations and inventory control decisions, allowing minimising the total costs associated with the spare parts supply chain network. The generic model is specified based on three inventory control policies widely employed in the industry, which are suitable for managing a great variety of spare parts, i.e. (s, Q), (R, s, S) and (S-1, S). Furthermore, a solution approach is proposed based on Generalised Benders Decomposition. Finally, numerical results from a real-world application case in the process industry are shown and discussed.     

LQG optimal controller synthesis with robust optimization in multivariable systems

Abstract

This paper presents an algorithm to synthesize a controller for treating the problem of robustness optimization in an LQG (linear‐quadratic‐Gaussian) control system. The controller not only maximizes the excess stability margin in perturbed system but also minimizes the cost functional J in LQG problems by specifying two frequency dependent weighting matrices Q(s) and R(s) in the cost functional.

Our approach is based on Wiener‐Hopf's technique (frequency domain approach), and two weighting matrices in cost functional are shaped by inverse LQG method. The feature of this paper is that the plant of the system has no stable, proper, square, and minimum phase constraints.     

Centralised vs. decentralised control decision in card-based control systems: comparing kanban systems and COBACABANA

Kanban systems are simple yet effective means of controlling production. Production control is decentralised or exercised locally on the shop floor, i.e. a downstream station signals to an upstream station that an item is needed. If items are always the same and known, then demands can be satisfied instantaneously from stock; but if items differ and are unknown, demands must first be propagated backwards from station to station before being satisfied. The former is defined as an inventory control problem and the latter as an order control problem. Handling the order control problem via kanban involves a decentralised card acquisition process (during which information is propagated from station to station) that is separated from the actual production process. COBACABANA (control of balance by card-based navigation), an alternative card-based solution, shares kanban’s control structure but centralises the card acquisition process. Evaluating the two systems therefore provides a unique opportunity to compare decentralised and centralised control. Using simulation, we demonstrate that it is specifically the centralised card acquisition process that allows COBACABANA to balance the workload across resources and thus to outperform kanban in an order control problem. This has major implications for research and practice.     

Tele-maintenance “intelligent” system for technical plants result management

The management of technical plant for productivity and safety is generally a complex activity, particularly when many plants distributed in the territory are considered (i.e. the more and more frequent case of outsourced plants maintenance by specialized companies), granted quality and cost results are required (i.e. the case of some rather innovative contract solutions) and the technology involved is heterogeneous and innovative (i.e. electro-mechanical plants).In order to efficiently achieve the above aims an “intelligent” maintenance-management system for the distant monitoring and controlling by a remote control center has been developed. The so-called GrAMS (granted availability management system) system is conceived to give to organizations involved in technical-industrial plants management the possibility to tend to a “well-known availability” and “zero-failures” management.In particular, this study deals with the diagnostic aspects and safety level of technical plants (such as elevators, thermo-technical plants, etc.), and with the involvement of ad hoc designed software analysis tools based on neural networks and reliability indicators.Part of the research dealing with the tele-maintenance intelligent system has been financed by the Italian High Institute for Safety (ISPESL) and led to the development of a pre-industrial prototype whose realization and testing is here described.     

Evaluation of divergent N-echelon (s,nQ)-policies under compound renewal demand

In this paper, decentralized inventory control in a divergent multi-echelon network is considered. All stockpoints are controlled by continuous review (s,nQ)-installation stock policies. Due to the fact that orders from a stockpoint to its predecessors may have to wait, this delay must be incorporated into the lead time of an arbitrary replenishment. We develop analytical approximations for the first two moments of this waiting time. These results enable us to accurately approximate the relevant performance characteristics at each stockpoint, given its (s,nQ)-policy. The performance measure considered in this paper are fill rate and average physical inventory. The analysis can easily be extended for other performance measures. The main contribution of this paper is the fact that the results apply to arbitrary divergent multi-echelon systems, with stochastic transportation times, arbitrary lot sizes and compound renewal demand. Correspondence to: Gudrun P. Kiesmüller     

An efficient method for solving implicit and explicit stiff differential equations

When the s‐stage fully implicit Runge–Kutta (RK) method is used to solve a system of n ordinary differential equations (ODE) the resulting algebraic system has a dimension ns. Its solution by Gauss elimination is expensive and requires 2s³n³/3 operations. In this paper we present an efficient algorithm, which differs from the traditional RK method. The formal procedure for uncoupling the algebraic system into a block‐diagonal matrix with s blocks of size n is derived for any s. Its solution is s²/2 times faster than the original, nondiagonalized system, for s even, and s³/(s−1) for s odd in terms of number of multiplications, as well as s² times in terms of number of additions/multiplications. In particular, for s=3 the method has the same precision and stability properties as the well‐known RK‐based RadauIIA quadrature of Ehle, implemented by Hairer and Wanner in RADAU5 algorithm. Unlike RADAU5, however, the method is applicable with any s and not only to the explicit ODEs My′=f(x, y), where M=const., but also to the general implicit ODEs of the form f(x, y, y′)=0. The block‐diagonal form of the algebraic system allows parallel processing. The algorithm formally differs from the implicit RK methods in that the solution for y is assumed to have a form of the algebraic polynomial whose coefficients are found by enforcing y to satisfy the differential equation at the collocation points. Locations of those points are found from the derived stability function such as to guarantee either A‐ or L‐stability properties as well as a superior precision of the algorithm. If constructed such as to be L‐stable the method is a good candidate for solving differential‐algebraic equations (DAEs). Although not limited to any specific field, the application of the method is illustrated by its implementation in the multibody dynamics described by both ODEs and DAEs. Copyright © 2000 John Wiley & Sons, Ltd.     

Construction of double sampling s‐control charts for agile manufacturing

Double sampling (DS) ‐control charts are designed to allow quick detection of a small shift of process mean and provides a quick response in an agile manufacturing environment. However, the DS ‐control charts assume that the process standard deviation remains unchanged throughout the entire course of the statistical process control. Therefore, a complementary DS chart that can be used to monitor the process variation caused by changes in process standard deviation should be developed. In this paper, the development of the DS s‐charts for quickly detecting small shift in process standard deviation for agile manufacturing is presented. The construction of the DS s‐charts is based on the same concepts in constructing the DS ‐charts and is formulated as an optimization problem and solved with a genetic algorithm. The efficiency of the DS s‐control chart is compared with that of the traditional s‐control chart. The results show that the DS s‐control charts can be a more economically preferable alternative in detecting small shifts than traditional s‐control charts. Copyright © 2002 John Wiley & Sons, Ltd.     

Properties of the Markov‐Dependent Attribute Control Chart with Estimated Parameters

The performance of attribute control charts that monitor Markov‐dependent data is usually evaluated under the assumption of known process parameters, that is, known values of a the probability an item is nonconforming given the previous item is conforming and b the probability an item is conforming given the previous item is nonconforming. In practice, these parameters are usually not known and are calculated from an in‐control Phase I‐data set. In this paper, a comparison of the in‐control ARL (average run length) properties of the attribute chart for Markov‐dependent data with known and estimated parameters is presented. The probability distribution of the estimators is developed and used to calculate the in‐control ARL and standard deviation of the run length of the chart with estimated parameters. For particular values of a and b, the in‐control ARL values of the charts with estimated parameters may be very different than those with known parameters. The size of the Phase‐I data set needed for charts with estimated parameters to exhibit the same in‐control ARL properties as those with known parameters may vary widely depending on the parameters of the process, but in general, large samples are needed to obtain accurate estimates. As the Phase‐I sample size increases, the in‐control ARL values of the charts with estimated parameters approach that of the known parameter case but not in a monotonic fashion as in the case of the X‐bar chart. Copyright © 2015 John Wiley & Sons, Ltd.     

Additivity hypothesis and effects of stress on phase transformations in steel

Theoretical analysis shows that the fraction of pearlite formed from nucleation is additive and that from growth is not. A modified additivity model is established with two continuous cooling experiments. Calculations of Ae₃ temperature for proeutectoid ferrite formation under stress and nucleation rate as well as incubation period of ferrite or pearlite transformation under stress are successfully made. Kinetics equations for ferrite and pearlite transformations under stress are expressed from modification of J–M–A equation with addition of a stress item. The acceleration effect of stress on bainite formation is mainly attributed to the increase of diffusivity of solute atoms and even iron. By consideration of the grain size effect, Patel and Cohen’s equation expressing the effect of stress on M_s is modified. Calculations of M_s for fcc → bcc(bct) and fcc → hcp under stress are introduced. An equation showing the relationship between strain and nucleation of martensite which can well explain the morphology of martensite formed under stress is mentioned. Appearance and mechanism of mechanical stabilization of austenite in martensitic transformation, i.e., the lowering of M_s, resulted from the work hardening of austenite, are different from retardation of bainite formation under stress, i.e., after B_s raising, occurring the retardation of bainite growth resulted from hindrance by defects.     

A bi-objective robust inspection planning model in a multi-stage serial production system

In this paper, we present a bi-objective mixed-integer linear programming (BOMILP) model for planning an inspection process used to detect nonconforming products and malfunctioning processors in a multi-stage serial production system. The model involves two inter-related decisions: (1) which quality characteristics need what kind of inspections (i.e. which-what decision) and (2) when the inspection of these characteristics should be performed (i.e. when decision). These decisions require a trade-off between the cost of manufacturing (i.e. production, inspection and scrap costs) and the customer satisfaction. Due to inevitable variations in manufacturing systems, a global robust BOMILP (RBOMILP) is developed to tackle the inherent uncertainty of the concerned parameters (i.e. production and inspection times, errors type I and II, misadjustment and dispersion of the process). In order to optimally solve the presented RBOMILP model, a meta-heuristic algorithm, namely differential evolution (DE) algorithm, is combined with the Taguchi and Monte Carlo methods. The proposed model and solution algorithm are validated through a real industrial case from a leading automotive industry in France.     

Optimization of geometrically non‐linear symmetric systems with coincident critical points

A new formulation is presented for optimum design of an elastic symmetric structure for specified non‐linear buckling load factor. It is shown that the method of sensitivity analysis of bifurcation load factor developed in Ohsaki and Vetani (Int. J. Numer. Methods Engng. 1996; 39 : 1707–1720) can also be applied for the case where the structure reaches coincident critical points including a limit point. Based on the method of sensitivity analysis, an algorithm is presented for finding optimum designs for specified coincident critical points. The well‐known danger of designing a structure that exhibits coincident buckling is discussed in detail. It is shown in the examples of trusses that the structural volume may be successfully reduced as a result of optimization even if the reduction of the maximum load factor due to possible asymmetric initial imperfection is considered. Copyright © 2000 John Wiley & Sons, Ltd.     

An Integrated Optimization Model for Inventory and Quality Control Problems

In this paper, we develop an integrated economic model for inventory and quality control problems, extending the work of Rahim ( IIE Transactions 1994; 26(6): 2–11) and Rahim and Ben-Daya (IJPR 1998; 36(1): 277–289). The production process is subject to an assignable cause which shifts the process from an in-control state to an out-of-control state. We consider the shifts in both the process mean and the process variance. When a signal for an assignable cause is triggered, a search is initiated and is terminated upon finding the cause within a pre-specified target time. The process is then brought back to an in-control state by repair. However, if the assignable cause is not discovered within the pre-specified time, production is allowed to continue until the next sampling or warning, whichever occurs first. In this case, either the alarm is considered to be false with a probability of Type I error, or the assignable cause has not been eliminated with a probability of Type II error. In the latter case, the process produces products in an out-of-control state until the next sampling or warning, whichever occurs first. However, this state does not indicate any severe damage to the system. Joint X and R charts are used for monitoring both process mean and variance. Under these conditions, a generalized economic model for the joint determination of production quantity, an inspection schedule, and the design of the X and R control charts are developed. A direct search optimization method is used to determine the optimal decision variables of the economic model.     

Angular Characteristics of a Laser Light Interference Modulator

In the present work the optical characteristics of a multilayer laser light modulator at oblique incidence are studied. The modulator is a Fabry-Perot type interference filter with metal-dielectric multilayers as mirror subsystems deposited directly on both sides of a plane-parallel electro-optical plate. Some general polarization dependences as a result of the combined action of isotropic and anisotropic layers of the system are discussed. The conditions for calculation of the optical characteristics by the 2 x 2 matrix method are considered. The transmittance coefficients (T _s, T _p), angular (Δθ_s, Δθ_p) and voltage U _1/2 half-widths for both polarizations are calculated and measured and their angular dependences are estimated. The conditions when the system operates as a laser light modulator are presented. The characteristics described should be important when the system proposed is used as an optical multistable element.     

Adaptive isogeometric analysis based on a combined r-h strategy

In the present work, an r-h adaptive isogeometric analysis is proposed for plane elasticity problems. For performing the r-adaption, the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points. While preserving the boundary control points, relocation of only the interior control points is made by adopting a successive relaxation approach to achieve the equilibrium of spring system. To suit the noninterpolatory nature of the isogeometric approximation, a new point-wise error estimate for the h-refinement is proposed. To evaluate the point-wise error, hierarchical B-spline functions in Sobolev spaces are considered. The proposed adaptive h-refinement strategy is based on using De-Casteljau’s algorithm for obtaining the new control points. The subsequent control meshes are thus obtained by using a recursive subdivision of reference control mesh. Such a strategy ensures that the control points lie in the physical domain in subsequent refinements, thus making the physical mesh to exactly interpolate the control mesh and thereby allowing the exact imposition of essential boundary conditions in the classical isogeometric analysis (IGA). The combined r-h adaptive refinement strategy results in better convergence characteristics with reduced errors than r- or h-refinement. Several numerical examples are presented to illustrate the efficiency of the proposed approach.     

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.