Control of multiproduct bulk server diffusion/oxidation processes. Part 2: multiple servers

We investigate how knowledge of future arrivals can be used to control bulk server diffusion and oxidation processes in semiconductor manufacturing to reduce the average waiting time of lots. While past research has dealt with the control of bulk server queueing systems, only a few studies have addressed the use of knowledge of future arrivals, and those studies were limited to a single server system. We extend prior strategies for the single product-single server case to a multiple product-multiple server case, and devise a control strategy that is tested through the use of simulation. The performance of the new policy is compared to that of the optimal control strategy ignoring future arrivals (i.e., a Minimum Batch Size strategy). Results indicate that the new strategy performs well under a wide variety of circumstances. To demonstrate the control strategy performance in a realistic setting, a detailed simulation model of the diffusion area of an existing wafer fab was developed. The model was run with several start rates and the results compared to those from a Minimum Batch Size strategy. Results indicate that the new strategy performs well over a wide range of start rates.     

An analytical method for the calculation of the number of units at the arrival instant in a discrete time G/G/1-queueing system with batch arrivals

In this paper, we analyze a G/G/1-queueing system with batch arrivals in the discrete time domain. On the basis of the waiting time distribution, we present an analytical approach for the calculation of the number of units in the queue at the arrival instant. This approach is exact within an ε-environment. In addition, the computing times are low such that a huge set of computations can be performed in a short time. We close our paper with a set of numerical experiments. Our research is motivated through various applications in the field of logistics, where it is of important interest to know the distribution of the number of units waiting to be proceeded at the moment of a new arrival.     

An analytical method for the calculation of the waiting time distribution of a discrete time G/G/1-queueing system with batch arrivals

This paper presents an analytical method to calculate the waiting time distribution for the G/G/1-queueing system with batch arrivals. Using the discrete time scale, it is possible to calculate the distribution of the waiting times and the idle times of a G/G/1-queueing system based on the Wiener–Hopf factorization. The influence of batch arrivals on the waiting time distribution is analyzed. The waiting time distribution is calculated for batch arrivals with both constant and stochastic batch sizes. The effect of stochastic batch sizes on the waiting process is highlighted. With the developed methods, it is possible to obtain congestion measures of high precision for logistic systems. The analytical results are evaluated by simulation. Several numerical examples are presented to emphasize the quality of the introduced methods.     

The impact of delayed differentiation in make-to-order environments

To cope with the challenges of product proliferation, many firms are shifting their supply chain structures from make-to-stock (MTS) to make-to-order (MTO). An MTO strategy comes at a price however, as customers must wait longer for their configured products. Incorporating delayed differentiation (DD) in an MTO environment offers the potential of reducing the customer's waiting time, since the generic part/component of the products is made available before receiving customer orders. In this paper, we quantify the trade-offs involved in implementing DD in an MTO environment using both customer waiting time and system cost as performance metrics. We show that under common conditions, the introduction of DD results in shorter waiting times and higher cost over a pure MTO strategy. These results are as expected. However, we also derive conditions where DD results not only in shorter customer waiting time but also lower cost, thus dominating a pure MTO strategy. Through a simulation experiment, we test the robustness of our results for the case where the customer arrivals and production times are generally distributed. For firms with the capability of estimating the customer waiting cost, we derive the optimal base-stock level of the generic component to minimise the total cost.     

Blocking Probabilities for a Class of Two-Station Tandem Queueing Models

We study a two-station tandem queueing system with a finite buffer of maximum size M (M≥0) between the stations. The first service station has L≥1(homogeneous) parallel servers with an unlimited waiting space, while at the second there are N≥1 (homogeneous) parallel servers. Assuming Poisson arrivals and exponential service times, we derive exact results for the blocking probabilities for some special cases, and we present a unified approach for the analysis of this class of models under saturation conditions. Practical applications of the model are also discussed.     

A stochastic model for joint inventory and outbound shipment decisions

In this paper, we consider a vendor realizing a sequence of random order arrivals in random sizes. The vendor has the autonomy to hold/consolidate small orders until an economical dispatch quantity accumulates. Consequently, the actual inventory requirements at the vendor are in part determined by the parameters of the shipment release policy in use. In this context, we investigate the impact of shipment consolidation on the expected long-run average cost by simultaneously computing the optimal order quantity for inventory replenishment at the vendor and the optimal dispatch quantity for outbound shipments. Since we consider the case where demand follows a general stochastic bulk arrival process, obtaining exact analytical expressions for some key operating characteristics of the cost function is intractable. Hence, we provide easy-to-compute approximations which enable efficient numerical solutions for the problem. We also investigate: (i) the cases where consolidated shipments are preferred over immediate deliveries; (ii) the sensitivity of optimal integrated policy variables to demand/cost parameters; (iii) the potential savings that can be obtained by shipment consolidation; and (iv) the tradeoffs between the waiting time induced by shipment consolidation and costs saved. Our results provide insights into the impact of outbound transportation operations on inventory replenishment decisions and outbound distribution system design. Moreover, numerical testing suggests that significant cost savings (up to 57%) are possible with shipment consolidation.     

Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism

In this paper we study a production system consisting of a group of parallel machines producing multiple job types. Each machine has its own queue and it can process a restricted set of job types only. On arrival a job joins the shortest queue among all queues capable of serving that job. Under the assumption of Poisson arrivals and identical exponential processing times we derive upper and lower bounds for the mean waiting time. These bounds are obtained from so-called flexible bound models, and they provide a powerful tool to efficiently determine the mean waiting time. The bounds are used to study how the mean waiting time depends on the amount of overlap (i.e. common job types) between the machines.

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Received: February 8, 2000 / Accepted: November 28, 2000     

Heuristic control of multiple batch processors with incompatible job families and future job arrivals

We analyse the problem of minimising the mean cycle time of a batch processing stage containing K?>?1 batch processors in parallel with incompatible job families and future job arrivals. We provide an integer linear programming formulation and a dynamic program formulation for small problem instances. For larger problem instances, we propose an online heuristic policy MPC_REPEAT. At each instance a decision has to be made, MPC_REPEAT decomposes the problem of simultaneously assigning multiple batches to multiple processors into sequentially assigning multiple batches to multiple processors. When job families are uncorrelated, we show via simulation experiments that MPC_REPEAT has significantly lower mean cycle time than a previously proposed look-ahead method except when: (MPC_REPEAT ignores some job families AND the traffic intensity is high.) Our experiments also reveal that increasing the job family correlation of consecutive job arrivals results, with a few exceptions, in a mean cycle-time reduction, for both policies evaluated. This reduction in cycle time generally increases with: increasing number of job families, decreasing number of processors, and increasing time between job arrivals. Our findings imply that controlling the upstream processors, such that job families of consecutive job arrivals are correlated, can reduce the cycle time at the batch processing stage. Furthermore, the expected mean cycle time reduction due to this strategy can be substantially larger than that expected from switching to a more complex batch processing stage policy, under less stringent conditions.     

Optimization of express line performance: numerical examination and management considerations

Improving the waiting process at checkouts in stores is an important goal of operations management in the era of time-based competition. The paper presents a method for evaluating the effect of express lines on the waiting process. An optimization model is developed which minimizes the average waiting time in line with respect to the maximum number of items allowed in the express lines. The research is based on a real case of a do-it-yourself superstore, but the methodology applied at the store can be used generally. The optimization model includes sensitivity analyses. Sensitivity analyses show how the optimal value of the limit parameter changes if major parameters of the model change. The results of these analyses help managers make decisions about short and medium-term operations of express lines.     

CONTROL OF MULTIPRODUCT BULK SERVICE DIFFUSION/OXIDATION PROCESSES

This paper demonstrates how knowledge of future arrivals can be used to control bulk service diffusion and oxidation processes. The objective of the research reported herein is to reduce the average time that lots spend waiting to be processed. A review of the current literature reveals that several researchers have dealt with the control of bulk service queueing systems; however, only one has addressed the use of knowledge of future arrivals and it only considered the case of a single product and a single server. This research reexamines the single product-single server case, and men explores the multiple products-single server case. For both cases, a control strategy is devised and evaluated through the use of systems simulation. The steady-state performance of each control strategy is then compared to the steady-state performance of the theoretical optimal control strategy not considering the timing of any future arrivals (i.e. a Minimum Batch Size strategy). The experimental results indicate that the control strategies developed in this paper perform well under most circumstances.     

The double ended queue with mixed-Erlangian arrival distribution and limited waiting space

The steady state solution of the double-ended queue involving taxis and customers at a taxi stand has been considered under the assumption that there is limited waiting space both for taxis and for customers. Taxis arrive according to mixed Erlangian input, the mean times of stay in the various phases which comprise the arrival channel not being the same. The arrivals of customers are assumed to be Poisson distributed. We obtain an expression for the probabilities that there aren units in the queue. The cases of exponential and 2-Erlang arrival distributions for taxis have been considered as particular cases. For the 2-Erlang arrival distribution for taxis, we have evaluated the probabilities that the waiting space for customers or taxis is full; their values are also shown by means of graphs. Paper presented at the Fourth Annual Convention of Operational Research Society of India, 2nd–4th, March 1972, held at Madras.     

Synchronization of yard truck scheduling and storage allocation in container terminals

Yard truck scheduling and storage allocation, as two separate subproblems in port operations, have been extensively studied in the past decades. However, from the operational point of view, they are highly interdependent. This article proposes an integer programming model in which yard truck scheduling and storage allocation problems are formulated as a whole for heterogeneous import containers. Different stacking times at yard blocks is modelled as well. The objective of the proposed model is to reduce the congestion and waiting time of yard trucks in the terminal so as to decrease the makespan of discharging containers. Owing to the inherent computational complexity, a genetic algorithm and a greedy heuristic algorithm have been designed. Computational experiments show that the proposed genetic algorithm and greedy algorithm are both effective in solving the studied problem.     

基于地域性设计理念的甘蔗收获机造型设计

根据地域性设计的实质及其表现形式,分析探讨了产品地域性设计的方法,并结合甘蔗收获机的开发设计实践及其所处的自然环境和人文环境,论述了甘蔗收获机地域性设计中的限定性和非限定性因素,进而分析了这些因素对甘蔗收获机造型的影响。在此基础上,对甘蔗收获机外观形态及色彩进行了地域性设计,以壮族蛙崇拜和蛙图腾作为设计的创意切入点和创新点,对蛙图腾的形态进行提炼创新,将收获机的基本形态与之契合,获得多个具有实际参考价值的创新性收获机造型方案。     

Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times

This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.     

Inventory reservation and real-time order promising in a Make-to-Stock system

In this paper we consider a Make-to-Stock order fulfillment system facing random demand with random due date preferences from two classes of customers. We develop an integrated approach for reserving inventory in anticipation of future order arrivals from high priority customers and for order promising in real-time. Our research exhibits three distinct features: (1) we explicitly model uncertain due date preferences of the customers; (2) we consider multiple receipts in the planning horizon that can be utilized to fulfill customer orders; and (3) we choose to utilize a service level measure for reserving inventory rather than estimating short- and long-term implications of order promising with a penalty cost function. We propose an algorithm that exploits the time structure in order arrivals and time-phased material receipts to determine inventory reservations for high priority orders. Numerical experiments are conducted to investigate the performance and the benefits of the inventory reservation and order promising approach under varying system parameters.     

Enhancing performance in order picking processes by dynamic storage systems

Increasing productivity and reducing labour cost in order picking processes are two major concerns for most warehouse managers. Particularly picker-to-parts order picking methods lead to low productivity as order pickers spend much of their time travelling along the aisles. To enhance order picking process performance, an increasing number of warehouses adopt the concept of dynamic storage where only those products needed for the current order batch are dynamically stored in the pick area, thereby reducing travel time. Other products are stored in a reserve area. We analyse the stability condition for a dynamic storage system with online order arrivals and develop a mathematical model to derive the maximum throughput a DSS can achieve and the minimum number of worker hours needed to obtain this throughput, for order picking systems with a single pick station. We discuss two applications of dynamic storage in order picking systems with multiple pick stations in series. In combination with simulation modelling, we are able to demonstrate that dynamic storage can increase throughput and reduce labour cost significantly.     

Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

In this paper, we study process completion time and propose an accurate approximation for the mean waiting time in queues with servers experiencing autocorrelated times to failure, which include only busy periods from a repair completion until the next failure. To do this, we employ a three-parameter renewal approximation that represents the stream of autocorrelated times to failure. The approximation gives rise to a renewal interruption process with two-state Hyper-exponential (H2) times to failure. Then we compute the mean waiting time exactly in a queue experiencing H2 times to failure when the job arrival process is Poisson. This model provides an approximation for the mean waiting time of the original queue having an autocorrelated disruption process. We also propose an accurate approximation for queues with renewal job arrival processes when the server interruption process is general.     

Real-time scheduling for twin RMGs in an automated container yard

This paper proposes heuristic-based and local-search-based real-time scheduling methods for twin rail-mounted gantry (RMG) cranes working in a block at an automated container terminal. The methods reschedule the cranes in real time for a given fixed-length look-ahead horizon whenever an RMG finishes a job. One difficulty with this problem is that sometimes additional rehandling of containers needs to be carried out in order to complete a requested job, especially when other containers are stacked on top of the target container. These rehandlings are the main cause of the delay of the crane operations, leading to extended waiting of automated guided vehicles (AGVs) or external trucks that co-work with the cranes. By treating the rehandling operations as independent jobs in our solution methods, we can greatly facilitate the cooperation between the two RMGs. Through this cooperation, the workload of the two RMGs can be better balanced and interference can be more easily avoided, thereby maximizing crane utilization. Simulation experiments show that the waiting times of AGVs and external trucks are significantly reduced due to the increased utilization through cooperation.