An order expediting policy for continuous review systems with manufacturing lead-time

Expedited shipments are often seen in practice. When the inventory level of an item gets dangerously low after an order has been placed, material managers are often willing to expedite the order at extra fixed and/or variable costs. This paper proposes a single-item continuous-review order expediting inventory policy, which can be considered as an extension of ordinary (s,Q)$(s\text{,}Q)$ models. Besides the two usual operational parameters: reorder point s and order quantity Q, it consists of a third parameter called the expedite-up-to level R. If inventory falls below R at the end of the manufacturing lead-time, the buyer can request the upstream supplier to deliver part of an outstanding order via a fast transportation mode. The amount expedited will raise inventory to R, while the remaining order is delivered via a slow (regular) supply mode. Simple procedures are developed to obtain optimal operational parameters. Computational results show that the proposed policy can save large costs for a firm if service level is high, demand variability is large, the extra cost for expediting is small, or the manufacturing lead-time is long.     

A new local search for continuous location problems

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation space search. The local search is applied to the multi-source Weber problem where encouraging results are obtained. This local search is also embedded within Variable Neighbourhood Search producing excellent results.     

A mathematical model for continuous crystallization

J. Banasiak We discuss a mixed‐suspension, mixed‐product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Predicting performance measures for Markovian type of manufacturing systems with product failures

Optoelectronic products are typically assembled and tested in a flow shop environment with multiple processors at each stage. The first few stages are dedicated for assembly and the later stages are dedicated for calibration and testing. Whenever a product (or job) fails at a stage, it is routed back to one of the downstream stages or to the same stage (depending upon the nature of the failure). Consequently, the product could circulate several times between the current stage and the preceding stage(s) before moving to the next stage. Estimating the performance measures (such as WIP and flow time) of such manufacturing systems is not trivial. This paper presents analytical approximations to estimate the performance measures of a manufacturing system with multiple product classes, job circulations due to failures, and some resources being shared among different product classes. The analytical approximations were verified using simulation on several problem instances. The experimental study indicates that these approximations can be used by operations managers to estimate the performance measures of a manufacturing system with product failures.     

A continuous model of the dynamical systems capable to memorise multiple shapes

This paper proposes the novel approach to the mathematical synthesis of continuous self-organising systems capable to memorise and restore own multiple shapes defined by means of functions of single spatial variable or parametric models in two-dimensional space. The model is based on the certain universal form of the integral operator with the kernel representing the system memory. The technique for memorising shapes uses the composition of singular kernels of integral operators. The whole system is described by the potential function, whose minimisation leads to the non-linear dynamics of shape reconstruction by integro-differential non-linear equations with partial derivatives. The corresponding models are proposed and analysed for both parametric and non-parametric shape definitions. Main features of the proposed model are considered, and the results of numerical simulation are shown in case of three shapes memorising and retrieval. The proposed model can be used in theory of smart materials, artificial intelligence and some other branches of non-linear sciences where the effect of multiple shapes memorising and retrieval appears as the core feature.     

Rapid and modular prototyping-based Petri nets and distributed simulation for manufacturing systems

This paper presents an approach to simulate and implement by stepwise refinement the whole manufacturing system (MS) by means of distributed simulation. This approach is based on the use of different classes of Petri nets to model different levels of a manufacturing system. Furthermore these classes may match the abstraction levels of a high-level Petri net used to model the MS. Each level can be simulated on a processor or a cluster of processors which can communicate between themselves using a network. The main contribution is to give the opportunity to combine simulation, performance evaluation and emulation. The emulation means that a part of the system can be run in real time while the other part is simulated. Moreover based on the abstraction levels of high-level Petri nets, subsystems can be integrated step-by-step from the design stage to the implementation one, allowing inter-changeability between simulated components and real-time physical systems. This approach is achieved by defining a simulation engine which involves a local simulator, an emulator and an interface to the physical process. Criteria are defined to use an emulator or a local control software for a physical process as a logical process for the conservative distributed simulation.     

A simulation optimization method that considers uncertainty and multiple performance measures

Simulation optimization provides a structured approach to system design and configuration when analytical expressions for input/output relationships are unavailable. This research focuses on the development of a new simulation optimization technique applicable to systems having multiple performance measures. The aim of this research is to incorporate a simulation end user’s preference towards risk and uncertainty into the search process for the best decision alternative. Automation of the optimization procedure is a necessity. Therefore, this paper proposes a simulation optimization method that involves a preference model, specifically adapted for decision making with simulation models.     

A generic approach to measuring the machine flexibility of manufacturing systems

Despite extensive studies on the flexibility of manufacturing systems over the last two decades, a unified measurement approach has not been developed. To this end, we integrate two domains of machine flexibility models from the literature: operational capability-based machine flexibility and time and cost-based machine flexibility, and propose a generic model to measure machine flexibility with consideration of uncertainties in the system. Furthermore, in our approach we include part characteristics such as processing time and processing cost, the number of operations that a machine can perform, and uncertainties in demand and machine-part assignment. The resulting framework to measure machine flexibility is a two-stage model: a super efficiency Data Envelopment Analysis Model and a flexibility model. The results show that the marginal system machine flexibility does not always increase as the number of operations that a machine can perform increases, and the system machine flexibility depends on the demand uncertainty.     

A scoring model for flexible manufacturing systems project selection

This paper presents a method for identifying, evaluating, and prioritizing manufacturing modernization projects. The paper distinguishes between modernization, which contains significant uncertainty, and capital replacement which contains minimal risk. Extending classical capital budgeting analysis, which prioritizes capital replacement projects by the criterion of utility maximization, the model described herein addresses the complexities of non-economic criteria, project interdependence, and uncertainty. Exploiting results from risk-oriented R & D project selection literature, the model incorporates the scores of five additive terms: technology assessment, equipment evaluation, capacity elasticity, cost-budget analysis, and adjusted net present value. The technology and equipment scores are based on evaluative scales. The paper introduces the workload elasticity of capacity statistic for the analysis of forecasted workload and plant capacity. The model analyses expected costs and budget levels in the cost-budge ratio submodel. Finally, the model explicitly incorporates conditional probabilities into the adjustment of NPV, to address interdependency and uncertainty.     

A sufficient condition for near-optimal stochastic controls and its application to manufacturing systems

This paper presents an asymptotic analysis of control models governed by stochastic ordinary differential equations. A sufficient condition of near-optimal controls is given based on Ekeland's principle. It is shown that, under some concavity assumptions, the-maximum condition in terms of the Hamiltonian implies the -optimality. By applying this result to a general manufacturing system, the common practice of hierarchical controls employed in order to reduce the overall complexity of the system is justified on a rigorous basis. A near-optimal control for the operational level is constructed from a near-optimal control at the corporate level, and an asymptotic error bound is obtained. A stochastic extension of the classical HMMS model is treated as a specific example. The approach of this paper is different from those in the literature, and it allows us to handle some previously unsolved problems with nonlinear state equations as well as nonseparable cost functions.This work was partly supported by NSERC Grant A4619, URIF, and the Manufacturing Research Corporation of Ontario.     

A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study

This study presents a hybrid fuzzy integral decision-making model that integrates factor analysis, interpretive structural modeling, Markov chain, fuzzy integral and the simple additive weighted method for selecting locations of high-tech manufacturing centers in China. The analytical results of this case study demonstrate the feasibility of the proposed model for solving fuzzy multiple attribute decision-making problems, especially when criteria are interdependent. Further, the empirical study brings out some properties that are crucial for high-tech manufacturing centers to invest in China.     

A mathematical model of continuous flotation deinking

A mathematical model is formulated to study the evolution of a continuous flotation process; the model yields a lower bound for the long-time deinking efficiency. Some of the theoretical predictions of the model are analysed using data obtained at a recycle mill.     

A continuous time markov-renewal replacement model for manpower systems

A continuous time Markov-renewal model is presented that generalizes the classical Young and Almond model for manpower systems with given size. The construction is based on the associated Markov-renewal replacement process and exploits the properties of the embedded replacement chain. The joint cumulant generating function of the grade sizes is derived and an asymptotic analysis provides conditions for these to converge in distribution to a multinominal random vector exponentially fast independently of the initial distribution, both for aperiodic and periodic embedded replacement chains. A regenerative approach to the wastage process is outlined and two numerical examples from the literature on manpower planning illustrate the theory.     

A water flow-like algorithm for manufacturing cell formation problems

Available research on the manufacturing cell formation problem shows that most solution approaches are either single- or multiple-solution-agent-based, with a fixed size of solution agents. Frequent problems encountered during the process of solving the cell formation problem include solutions being easily trapped in local optima and bad solution efficiency. Yang and Wang [Yang, F.-C., Wang, Y.-P., 2007. Water flow-like algorithm for object grouping problems. Journal of the Chinese Institute of Industrial Engineers, 24 (6), 475–488] proposed the water flow-like algorithm (WFA) to overcome the shortcomings of single- and multiple-solution -agent-based algorithms. WFA has the features of multiple and dynamic numbers of solution agents, and its mimicking of the natural behavior of water flowing from higher to lower levels coincides exactly with the process of searching for optimal solutions. This paper therefore adopts the WFA logic and designs a heuristic algorithm for solving the cell formation problem. Computational results obtained from running a set of 37 test instances from the literature and newly created have shown that the proposed algorithm has performed better than other benchmarking approaches both in solution effectiveness and efficiency, especially in large-sized problems. The superiority of the proposed WFACF over other approaches from the literature should be attributed to the collaboration of the WFA logic, the proposed prior estimation of the cell size, and the insertion-move. The WFA is a novel heuristic approach that deserves more attention. More attempts on adopting the WFA logic to solve many other combinatorial optimization problems are highly recommended.     

Oscillation for linear non-autonomous systems of difference equations with continuous arguments

In this paper, we establish sufficient conditions for the oscillation of the linear non-autonomous systems of difference equations with continuous arguments

     

A general model for voting systems with multiple alternatives

In this paper, the extension of simple games to the vector case is proposed. Games with multiple qualitative criteria and multi-criteria simple games are introduced as a natural tool for modelling voting systems and related social-choice situations. After formally defining these games, the special class of monotonic multi-criteria simple games is characterized. We show that these games enable the formulation and analysis of several collective decision models proposed in the literature. Furthermore, our model can be applied to group-decision problems which cannot be analyzed in the existing frameworks.     

A continuous covering location model with risk consideration

This paper proposes a continuous covering location model with risk consideration. The investigated model is an extension of the discrete covering location models in continuous space. The objective function consists of installation and risk costs. Because of uncertain covering radius, customer satisfaction degree of covering radius is introduced by fuzzy concept. Since, the uncertainty may cause risk of uncovering customers; the risk cost is added to the objective function. The installation cost is assigned to a zone with a predetermined radius from its center. The model is solved by a fuzzy method named α$\alpha$-cut. After solving the model based on different α$\alpha$-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved to determine the best covering values. This paper, also introduces a risk analysis method based on Response Surface Methodology (RSM) to consider risk management in the location models. Finally, a numerical example is expressed to illustrate the proposed model.     

Using stochastic optimization to determine threshold values for the control of unreliable manufacturing systems

A manufacturing system with two tandem machines producing one part type is considered in this work. The machines are unreliable, each having two states, up and down. Both surplus controls and Kanban systems are considered. Algorithms for approximating the optimal threshold values are developed. First, perturbation analysis techniques are employed to obtain consistent gradient estimates based on a single simulation run. Then, iterative algorithms of the stochastic optimization type are constructed. It is shown that the algorithms converge to the optimal threshold values in an appropriate sense. Numerical examples are provided to demonstrate the performance of the algorithms.The research of these authors was supported in part by grants from URIF, MRCO, National Science Foundation, and Wayne State University. The authors would like to thank Dr. X. R. Cao, Digital Equipment Corporation, for the valuable initial discussion and Dr. X. Y. Zhou, University of Toronto, for his helpful comments.     

Mathematical model for scheduling operations in cascaded continuous processing units

The scenario under consideration involves n cascaded continuous processing units responsible for processing m product lines. Each product line needs to be processed by all the units in the same sequence, and has dedicated finite capacity storage tanks before and after every processing unit. A unit can process only one product line at a time. Inputs for all the product lines arrive continuously and simultaneously on the input side of the first unit in the sequence. There are multiple intermediate due dates for the final products. An optimal schedule for the units calls for a trade-off among spillage costs, upliftment failure penalties and changeover costs. A mathematical model is developed for the purpose and the resulting MINLP is linearized using standard techniques. The MILP has been tested using GAMS for three units and three product lines as encountered in a refinery situation. The model could output optimal schedules for a ten day scheduling horizon within reasonable time.     

Performance evaluation for general queueing networks in manufacturing systems: Characterizing the trade-off between queue time and utilization

Performance evaluation plays a key role in manufacturing system design and productivity improvement. Characterizing performance objectively is the first step. Inspired by the underlying structure of tandem queues, we have derived an approximate model to characterize the system performance. The model decomposes system queue time and variability into bottleneck and non-bottleneck parts while capturing the dependence among workstations. Compared the new model with prior approaches, the new model not only is more accurate but also requires less information. The property of manufacturing system performance is given based on the insight from the model.