The stochastic machine replenishment problem

Abstract. We study the stochastic machine replenishment problem, which is a canonical special case of closed multiclass queuing systems in Markov decision theory. The problem models the scheduling of processor repairs in a multiprocessor system in which one repair can be made at a time and the goal is to maximize system utilization. We analyze the performance of a natural greedy index policy for this problem. We first show that this policy is a 2 approximation by exploring linear queuing structure in the index policy. We then try to exploit more complex queuing structures, but this necessitates solving an infinite-size, non-linear, non-convex, and non-separable function-maximization program. We develop a general technique to solve such programs to arbitrary degree of accuracy, which involves solving a discretized program on the computer and rigorously bounding the error. This proves that the index policy is in fact a 1.51 approximation. The main non-trivial ingredients of the proof are two folds: finding a way to analyze the complex queuing structure of the index policy, and bounding the error in discretization when numerically solving the nonlinear function-maximization. We believe that this framework is general enough to be useful in the analysis of index policies in related problems. As far as we are aware, this is one of the first non-trivial approximation analysis of an index policy a multi-class queuing problem, as well as one of the first non-trivial example of an approximation ratio that is rigorously proven by numerical optimization via a computer

Integrated Production-Distribution Planning with Considering Preventive Maintenance

The preventive maintenance activity is important thing in production system especially for a continuous production process, for example in fertilizer industry. Therefore, it has to be considered in production-distribution planning. This paper considers the interval of production facility’s preventive maintenance in production-distribution planning of multi echelon supply chain system which consists of a manufacturer with a continuous production process, a distribution center, a number of distributors and a number of retailers. The problem address in this paper is how to determine coordinated productiondistribution policies that considers the interval of production facility’s preventive maintenance, and customer demand only occurred at retailers and it fluctuates by time. Based on model of Santoso, et al. (2007), using the periodic review inventory model and a coordinated production and replenishment policies that are decided by central planning office and it must be obeyed by all entities of multi-echelon supply chain, the integrated production-distribution planning model is developed to determine the production and replenishment policies of all echelon in the supply chain system in order to minimize total system cost during planning horizon. Total system cost consists of set-up/ordering cost, maintenance cost, holding cost, outsourcing cost and transportation cost at all of entities. With considering preventive maintenance and there is one production run over the planning horizon, the replenishment cycle at distribution center, distributors and retailers that are found out are greater than the basic model. Also, the multiplication of replenishment cycle at distribution center in production cycle that is found out is greater than the basic model but the multiplication of replenishment cycle at retailers in its distributor are smaller than the basic model

Coordinated replenishment systems with discount opportunities

Inventory Control;Inventory Models;inkoop

A Neuroevolutionary Approach to Stochastic Inventory Control in Multi-Echelon Systems

Stochastic inventory control in multi-echelon systems poses hard problems in optimisation under uncertainty. Stochastic programming can solve small instances optimally, and approximately solve larger instances via scenario reduction techniques, but it cannot handle arbitrary nonlinear constraints or other non-standard features. Simulation optimisation is an alternative approach that has recently been applied to such problems, using policies that require only a few decision variables to be determined. However, to find optimal or near-optimal solutions we must consider exponentially large scenario trees with a corresponding number of decision variables. We propose instead a neuroevolutionary approach: using an artificial neural network to compactly represent the scenario tree, and training the network by a simulation-based evolutionary algorithm. We show experimentally that this method can quickly find high-quality plans using networks of a very simple form

Scheduling of non-repetitive lean manufacturing systems under uncertainty using intelligent agent simulation

World-class manufacturing paradigms emerge from specific types of manufacturing systems with which they remain associated until they are obsolete. Since its introduction the lean paradigm is almost exclusively implemented in repetitive manufacturing systems employing flow-shop layout configurations. Due to its inherent complexity and combinatorial nature, scheduling is one application domain whereby the implementation of manufacturing philosophies and best practices is particularly challenging. The study of the limited reported attempts to extend leanness into the scheduling of non-repetitive manufacturing systems with functional shop-floor configurations confirms that these works have adopted a similar approach which aims to transform the system mainly through reconfiguration in order to increase the degree of manufacturing repetitiveness and thus facilitate the adoption of leanness. This research proposes the use of leading edge intelligent agent simulation to extend the lean principles and techniques to the scheduling of non-repetitive production environments with functional layouts and no prior reconfiguration of any form. The simulated system is a dynamic job-shop with stochastic order arrivals and processing times operating under a variety of dispatching rules. The modelled job-shop is subject to uncertainty expressed in the form of high priority orders unexpectedly arriving at the system, order cancellations and machine breakdowns. The effect of the various forms of the stochastic disruptions considered in this study on system performance prior and post the introduction of leanness is analysed in terms of a number of time, due date and work-in-progress related performance metrics