Analysis of a generalized shortest queue system by flexible bound models

Motivated by a practical situation for the production/assembly of Printed Circuit Boards, we study a generalized shortest queue system. This system consists of parallel servers, which all have their own queue. The system serves several types of jobs, which arrive according to Poisson processes. Because of technical reasons, most or all types of arriving jobs can only be served by a restricted set of servers. All jobs have the same exponential service time distribution, and, in order to minimize its own service time, each arriving job joins (one of) the shortest queue(s) of all queue(s) where the job can be served. The behavior of the resulting queueing system may be described by a multi-dimensional Markov process. Since an analytical solution for this Markov process is hard to obtain, we present flexible bound models in order to find the most relevant performance measures, viz. the waiting times for each of the job types separately and for all job types together. The effectiveness of the flexible bound models is shown by some numerical results

Robust location-transportation problems with integer-valued demand

A Location-Transportation (LT) problem concerns designing a company's distribution network consisting of one central warehouse with ample stock and multiple local warehouses for a long but finite time horizon. The network is designed to satisfy the demands of geographically dispersed customers for multiple items within given delivery time targets. The company needs to decide on the locations of local warehouses and their basestock levels while considering the optimal shipment policies from central or local warehouses to customers.\u3cbr/\u3e\u3cbr/\u3eIn this paper, we deal with integer uncertain demands in LT problems to design a robust distribution network. We prove two main characteristics of our LT problems, namely convexity and nondecreasingness of the optimal shipment cost function. Using these characteristics, we show for two commonly used uncertainty sets (box and budget uncertainty sets) that the optimal decisions on the location and the basestock levels of local warehouses can be made by solving a polynomial number of deterministic problems. For a general uncertainty set, we propose a new method, called Simplex-type method, to find a locally robust solution. The numerical experiments show the superiority of our method over using the integer-valued affine decision rules, which is the only available method for this class of problems

Joint optimization of condition-based maintenance and production lot-sizing

Due to the development of sensor technologies nowadays, condition-based maintenance (CBM) programs can be established and optimized based on the data collected through condition monitoring. The CBM activities can significantly increase the uptime of a machine. However, they should be conducted in a coordinated way with the production plan to reduce the interruptions. On the other hand, the production lot size should also be optimized by taking the\u3cbr/\u3eCBM activities into account. Relatively fewer works have been done to investigate the impact of the CBM policy on production lot-sizing and to propose joint optimization models of both the economic manufacturing quantity (EMQ) and CBM policy. In this paper, we evaluate the average long-run cost rate of a degrading manufacturing system using renewal theory. The optimal EMQ and CBM policy can be obtained by minimizing the average long-run cost rate that\u3cbr/\u3eincludes setup cost, inventory holding cost, lost sales cost, predictive maintenance cost and corrective maintenance cost. Unlike previous works on this topic, we allow the use of continuous time and continuous state degradation processes, which broadens the application area of this model. Numerical examples are provided to illustrate the utilization of our model

Cost optimization in the (S-1,S) lost sales inventory model with multiple demand classes

For the (S − 1, S) lost sales inventory model with several demand classes that have different lost sale penalty cost, three accurate and efficient heuristic algorithms are presented that, at a given base stock level, aim to find optimal values for the critical levels, i.e., values that minimize inventory holding and penalty cost

Dynamic control in multi-item production/inventory systems

We consider a production/inventory system consisting of one production line and multiple products. Finished goods are kept in stock to serve stochastic demand. Demand is fulfilled immediately if there is an item of the requested product in stock and otherwise it is backordered and fulfilled later. The production line is modeled as a non-preemptive single server and the objective is to minimize the sum of the average inventory holding costs and backordering costs. We investigate the structure of the optimal production policy, propose a new scheduling policy, and develop a method for calculating base stock levels under an arbitrary but given scheduling policy. The performance of the various production policies is evaluated in extensive numerical experiments

On a method to improve your service BOMs within spare parts management

For advanced capital goods with high system availability requirements, it is common that all customers have service contracts with the Original Equipment Manufacturer (OEM). These service contracts include service level agreements on spare parts supply. The OEM operates a service network to support these logistic contracts. To determine spare parts stock levels the OEM needs to forecast spare parts demand. An important input for this forecast is the service Bill Of Material (BOM) per installed machine in the field, which specifies the applicable spare parts for a machine, and is usually derived from the machine configuration. Because of a growing installed base, increasing machine complexity, and an increasing number of machine variants, companies face a challenge in defining and maintaining machine configurations, which is why the service BOM is not always in line with the actual installed machine. An incorrect service BOM results in either a too low or a too high forecast for spare parts demand, and will result in under- or overstock.\u3cbr/\u3e\u3cbr/\u3eIn this paper we study the service BOMs at ASML, a large OEM in the semiconductor industry. We develop a method to generate alerts for possible errors. This method builds on multiple sources of machine information. Our method was tested in a pilot study, and found to be very effective. 95% of the generated alerts were correctly triggered and did result in actions that improved the service BOM. As a result, the method has been implemented by ASML. By this method, ASML reduced spare part non-availabilities by approximately 4-5 percent per year

The compensation approach applied to a 2x2 switch

In this paper we analyze an asymmetric 2 x 2 buffered switch, fed by two independent Bernoulli input streams. We derive the joint equilibrium distribution of the numbers of messages waiting in the two output buffers. This joint distribution is presented explicitly, without the use of generating functions, in the form of a sum of two alternating series of product-form geometric distributions. The method used is the so-called compensation approach, developed by Adan,Wessels and Zijm. Keywords: buffered switch, Markov chain, equilibrium distribution, product form