A four-input three-stage queuing network approach to model an industrial system

An industrial system is represented as a four-input, three-stage queuing network in this paper. The four-input queuing network receives orders from clients, and the orders are waiting to be served. Each order comprises (i) time of occurrence of the orders, and (ii) quantity of items to be delivered in each order. The objective of this paper is to compute the optimal path which produces the least response time for the delivery of items to the final destination along the three stages of the network. The average number of items that can be delivered with this minimum response time constitute the optimum capacity of the queuing network. After getting serviced by the last node (a queue and its server) in each stage of the queuing network, a decision is made to route the items to the appropriate node in the next stage which can produce the least response time. Performance measures such as average queue lengths, average response times, average waiting times of the jobs in the four-input network are derived and plotted. Closed-form expressions for the equivalent service rate, equivalent average queue lengths, equivalent response and waiting times of a single equivalent queue with a server representing the entire four-input queuing network are also derived and plotted.     

A closed queuing network model with single servers for multi-threaded architecture

In this paper, a closed queuing network model with single servers for each queue is proposed to model dataflow in a multi-threaded architecture. Multi-threading is useful in reducing the latency by switching among a set of threads in order to improve the processor utilization. Two sets of processors, synchronization and execution processors exist. Synchronization processors handle load/store operations and execution processors handle arithmetic/logic and control operations. A closed queuing network model is suitable for large number of job arrivals. The normalization constant is derived using a recursive algorithm for the given model. State diagrams are drawn from the closed queuing network model, and the steady-state balance equations are derived from it. Performance measures such as average response times and average system throughput are derived and plotted against the total number of processors in the closed queuing network model. Other important performance measures like processor utilizations, average queue lengths, average waiting times and relative utilizations are also derived.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

Performance evaluation of a single queue capable of handling two like jobs as a single entity

In this paper, we model an open queuing network and analyze performance measures with and without feedback as two individual cases. The model comprises a single queue with a dedicated processor capable of handling two like jobs as a single job. Two different job arrivals with different processing times are considered with an internal timer. Performance measures such as average queue length, average response time, average waiting time of the jobs are computed and plotted. The joint density function for the inter arrival time and arrival rate are derived. The probability mass function has been derived for all possible cases that may arise in a duration (0, t], considering n job arrivals during that period of time and an integer programming problem is formulated to obtain optimal sequence patterns which would maximize the efficiency of the model.     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

Performance analysis and design of supply chains: a Petri net approach

In this paper, we investigated a dynamic modelling technique for analysing supply chain networks using generalised stochastic Petri nets (GSPNs). The customer order arrival process is assumed to be Poisson and the service processes at the various facilities of the supply chain are assumed to be exponential. Our model takes into account both the procurement process and delivery logistics that exist between any two members of the supply chain. We compare the performance of two production planning and control policies, the make-to-stock and the assemble-to-order systems in terms of total cost which is the sum of inventory carrying cost and cost incurred due to delayed deliveries. We formulate and solve the decoupling point location problem in supply chains as a total relevant cost (sum of inventory carrying cost and the delay costs) minimisation problem. We use the framework of integrated GSPN-queuing network modelling—with the GSPN at the higher level and a generalised queuing network at the lower level—to solve the decoupling point location problem.     

Unreliable newsboy problem with a forecast update

In this paper, we derive an optimal ordering policy for an unreliable newsboy who can place two sequential orders before the start of a single selling season by using a demand forecast update. Supply yield is modeled using a uniform distribution considering both the minimum order guarantee and the maximum yield. Our results indicate that a firm should focus on increasing the minimum order guarantee from a first stage supplier to reduce its total supply chain cost.     

Equivalent single-queue–single-server model for a Pentium processor

In this paper, a Pentium processor is represented as a queuing network. The objective of this paper is to deduce an equivalent single-queue–single-server model for the original queuing network. Closed-form expressions for the equivalent service rate, equivalent queue lengths, equivalent response and waiting times of the equivalent single-queue–single-server model are derived and plotted. For large values of arrival rate, queue lengths increase faster than the response times and waiting times for both the cases. Performance measures like, queue lengths, response times and waiting times are higher for lower service rates and lower for higher service rates (which is expected) of the different servers in the original queuing network. Also, the reliability in estimating performance measures for homogeneous workloads is much better than that for heterogeneous workloads.     

An exact algorithm for a cross-docking supply chain network design problem

This paper proposes a branch-and-price algorithm as an exact algorithm for the cross-docking supply chain network design problem introduced by one of the authors of this paper. The objective is to optimally locate cross-docking (CD) centres and allocate vehicles for direct transportation services from the associated origin node to the associated CD centre or from the associated CD centre to the associated destination node so as to satisfy a given set of freight demands at minimum cost subject to the associated service (delivery) time restriction. A set-partitioning-based formulation is derived for the problem for which some solution properties are characterized. Based on the properties, a branch-and-price algorithm is derived. The properties can also be used in deriving any efficient local search heuristics with the move operation (neighbourhood search operation) of modifying assignment of some freight demands from current CD centres to other CD centres. Computational experiments show that the branch-and-price algorithm is effective and efficient and also that the solution properties contribute to improve the efficiency of the local search heuristics.     

Integrated pricing and lot-sizing decisions in a serial supply chain

In this article, we consider a serial supply chain controlled by a decision-maker who is responsible for deciding the amount of raw material to order from the selected suppliers, the amount of product to transfer between consecutive stages in order to avoid any inventory shortages, and the final product's selling price so that the profit per time unit is maximized. Coordinating all these decisions simultaneously is a topic that has been neglected in literature. This integrated process is modeled as a mixed-integer nonlinear programming model. In addition, the model requires the order quantity received from each selected supplier to be an integer multiple of the order quantity delivered to the following stage, which means that a different multiplicative factor can be assigned to each supplier. This coordination mechanism shows an improvement in the objective function compared to existing models that assign the same multiplicative factor to each selected supplier. Moreover, we develop a heuristic algorithm that generates near optimal solutions in a timely manner. Two numerical examples are presented to illustrate the proposed model and the heuristic algorithm.     

Production planning with load dependent lead times: an update of research

Lead times impact the performance of the supply chain significantly. Although there is a large body of literature concerning queuing models for the analysis of the relationship between capacity utilization and lead times, and another body of work on control and order release policies that take lead times into consideration, there have been relatively few aggregate planning models that recognize the (nonlinear) relationship between the planned utilization of capacity and lead times. In this paper we provide an in-depth discussion of the state-of-the art in this area, with particular attention to those models that are appropriate at the aggregate planning level. An earlier version of this paper appeared in 4OR 3, 257–302, 2005.     

随机需求条件下不同合作方式的供应链利润分配研究

考虑由一个制造商和一个分销商组成的二级供应链,引入共享契约作为利润再分配的手段,建立了随机需求条件下供应链的Stackberg博弈和张伯伦利润分配模型,研究表明:核心企业制造商可以通过调整利润分配参数使供应链各节点实现共赢,同时在供应链节点企业竞争地位不对等的情况下,采用张伯伦模型的合作方式会使节点利润更优.     

The research on optimization of auto supply chain network robust model under macroeconomic fluctuations

Considering the uncertainty of the macroeconomic environment, the robust optimization method is studied for constructing and designing the automotive supply chain network, and based on the definition of robust solution a robust optimization model is built for integrated supply chain network design that consists of supplier selection problem and facility location–distribution problem. The tabu search algorithm is proposed for supply chain node configuration, analyzing the influence of the level of uncertainty on robust results, and by comparing the performance of supply chain network design through the stochastic programming model and robustness optimize model, on this basis, determining the rational layout of supply chain network under macroeconomic fluctuations. At last the contrastive test result validates that the performance of tabu search algorithm is outstanding on convergence and computational time. Meanwhile it is indicated that the robust optimization model can reduce investment risks effectively when it is applied to supply chain network design.     

Production planning with load dependent lead times

Lead times impact the performance of the supply chain significantly. Although there is a large literature concerning queuing models for the analysis of the relationship between capacity utilization and lead times, and there is a substantial literature concerning control and order release policies that take lead times into consideration, there have been only few papers describing models at the aggregate planning level that recognize the relationship between the planned utilization of capacity and lead times. In this paper we provide an in-depth discussion of the state-of-the art in this literature, with particular attention to those models that are appropriate at the aggregate planning level. Received: September 2005 / Revised version: November 2005 AMS classification: 46N10 All correspondence to: Stefan Vo?     

碳减排政策下多周期供应链网络均衡决策

为研究碳减排政策对多周期供应链网络均衡决策的影响,分析了供应链网络结构中各层的最优条件,建立了多周期碳减排供应链网络均衡模型.首先将其转化为等价的变分不等式问题,然后利用变分不等式的投影收缩算法进行求解.并通过模型仿真分析了在不同周期下不同碳限额、单位碳排放量对供应链网络均衡的影响结果发现企业在环境绩效和经济绩效之间存在冲突,适当的控制碳税和调整产品的单位碳排放量可以缓解这种冲突.同时,政府对于碳限额的值过于宽松,对于碳减排的实施起不到明显作用.     

Decentralized Dual-Based Algorithm for Computing Optimal Flows in a General Supply Chain

This paper addresses the issue of the optimal flow allocation in general supply chains. Our basic observation is that a distribution channel involving several reselling steps for a particular product can be viewed as a route in a supply chain network. The flow of goods or services along each route is influenced by the customer's demand, described by the corresponding utility functions, and prices charged at each node. We develop an optimization algorithm based on the primal-dual framework and the Newton's step that computes optimal prices at each node (dual problem) and then computes the optimal flow allocation (primal problem) based on these prices. Our main contribution is a discovery that the Newton's step leads to a partially decentralized algorithm which is a first step toward a decentralization schema for computing optimal prices.     

Optimizing inventory decisions in a two-level supply chain with order quantity constraints

A fundamental assumption in traditional inventory models is that all of the ordered items are of perfect quality. A two-level supply chain is considered consists of one retailer and a collection of suppliers that operate within a finite planning horizon, including multiple periods, and a model is formulated that simultaneously determines both supplier selection and inventory allocation problems in the supply chain. It is supposed that the ordered products dependent on the suppliers include a certain percentage of imperfect quality products and have different prices. In this paper, we study the impact of the retailer’s financial constraint. On the other hand, suppliers have restricted capacities and set minimum order quantity (MOQ) policy for the retailer’s order amount happened in each period. So, the problem is modeled as a mixed integer nonlinear programming. The purpose of this model is to maximize the total profit. The nutrients, fishery and fruitage industries give good examples for the proposed model. A numerical example is presented to indicate the efficiency of the proposed model. Considering the complexity of the model, a genetic algorithm (GA) is presented to solve the model. We demonstrate analytically that the proposed genetic algorithm is suitable in the feasible situations.     

M-G-P型复杂网络中有寿命节点的进入退出机制

现实中复杂网络结构复杂,形式多样,处在高度动态变化的过程.为了更好地理解真实网络的演化,基于复杂网络的特性进行分析,建立了Poissotn连续时间增长节点具有寿命的M-G-P型复杂网络模型,模型中包括:新节点加入、节点老化和老节点退出等,基于齐次马尔可夫链对模型的度分布进行计算,得出M-G-P型网络的度分布符合幂律分布,模型和BA模型一样能产生指数γ=3的无标度网络,验证了导致无标度网络度分布特征起关键性作用的是链接的偏好特性.     

Equilibrium analysis and corporate social responsibility for supply chain integration

This paper evaluates the profit of coordination between manufacturers on corporate social responsibility (CSR) under network equilibrium. A three-tier supply chain network with multiple manufacturers, distributors, and retailers is considered, and several mathematical models are established to investigate behavior and profits in a decentralized supply chain network, a centralized supply chain network, and a supply chain network with CSR. The system-optimal solution of a supply chain network problem is usually not achievable or stable since each member always tries to maximize its own profit. In order to make such a system-optimal solution in a stable state and ensure the maximization of total profits, a strategy of coordination between manufacturers on CSR is proposed. The amount of payment in CSR of each manufacturer is clearly defined. A hybrid diagonalization method with a super-network representation is proposed and tested with numerical examples. The results show that by taking CSR, the total profits of the whole supply chain network can increase with or without coordination.