On multi-stage production/inventory systems under stochastic demand

This paper was presented at the 1992 Conference of the International Society of Inventory Research in Budapest, as a tribute to professor Andrew C. Clark for his inspiring work on multi-echelon inventory models both in theory and practice. It reviews and extends the work of the authors on periodic review serial and convergent multi-echelon systems under stochastic stationary demand. In particular, we highlight the structure of echelon cost functions which play a central role in the derivation of the decomposition results and the optimality of base stock policies. The resulting optimal base stock policy is then compared with an MRP system in terms of cost effectiveness, given a predefined target customer service level. Another extension concerns an at first glance rather different problem; it is shown that the problem of setting safety leadtimes in a multi-stage production-to-order system with stochastic lead times leads to similar decomposition structures as those derived for multi-stage inventory systems. Finally, a discussion on possible extensions to capacitated models, models with uncertainty in both demand and production lead time as well as models with an aborescent structure concludes the paper

Joint Inventory and Scheduling Control in a Repair Facility

We study inventory and repair scheduling decisions of a maintenance service provider for repairable capital goods. Due to high downtime costs, the service provider keeps spare parts on stock to replace broken parts quickly. The service provider should determine the inventory level of spare parts for each component and the repair scheduling policy. Furthermore, in case of a stock-out, the service provider should decide whether to backorder the demand or execute an emergency repair, which is an urgent but expensive repair operation for abroken part followed by a fast form of installation. The objective is to minimize the long-run average inventory holding, backorder, and emergency repair costs. We formulate the repairable network as a closed queueing system and consider an asymptotic regime in which the repair facility is in the conventional heavy-traffic regime. Then, we formulate and solve a Brownian control problem (BCP). From the optimal BCP solution, we derive a simple and intuitive decision rule stating if the emergency repairs are necessary to achieve a close-to-optimal system performance. Moreover, we propose a simple, intuitive, and easy-to-implement heuristic control policy and demonstrate its close-to-optimal performance via numerical experiments

Optimal data pooling for shared learning in maintenance operations

This paper addresses the benefits of pooling data for shared learning in maintenance operations. We consider a set of systems subject to Poisson degradation that are coupled through an a-priori unknown rate. Decision problems involving these systems are high-dimensional Markov decision processes (MDPs). We present a decomposition result that reduces such an MDP to two-dimensional MDPs, enabling structural analyses and computations. We leverage this decomposition to demonstrate that pooling data can lead to significant cost reductions compared to not pooling

Improving Ambulance Dispatching with Machine Learning and Simulation

As an industry where performance improvements can save lives, but resources are often scarce, emergency medical services (EMS) providers continuously look for ways to deploy available resources more efficiently. In this paper, we report a case study executed at a Dutch EMS region to improve ambulance dispatching. We first capture the way in which dispatch human agents currently make decisions on which ambulance to dispatch to a request. We build a decision tree based on historical data to learn human agents’ dispatch decisions. Then, insights from the fitted decision tree are used to enrich the commonly assumed closest-idle dispatch policy. Subsequently, we use the captured dispatch policy as input to a discrete event simulation to investigate two enhancements to current practices and evaluate their performance relative to the current policy. Our results show that complementing the current dispatch policy with redispatching and reevaluation policies yields an improvement of the on-time performance of highly urgent ambulance requests of 0.77% points. The performance gain is significant, which is equivalent to adding additional seven weekly ambulance shifts.</p

Simulation Supported Bayesian Network Approach for Performance Assessment of Infrastructure Systems

We present a simulation supported Bayesian Network modeling approach to evaluate the performance of bridge networks with respect to both infrastructure owner's cost and users' travel time based on bridge level maintenance decisions. By combining system decomposition, simulation and Bayesian Networkm (BN) modelling, our approach enables the construction of a BN model of bridge networks where probabilistic information resulting from simulation are used to populate the conditional probability tables. Our approach is therefore useful when access to actual conditions of bridges and their monitoring is difficult, and the conditional dependencies accross different networks elements are not easily quantifiable. Once built, the BN can be used by infrastructure managers as a scenario analysis tool to assess how maintenance decisions on individual bridges affect maintenance costs and travel time for the whole network. The approach is presented on a small-scale bridge network for demonstration purposes

A two-echelon spare parts network with lateral and emergency shipments: A product-form approximation

We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high down time costs. The inventory system consists of a central warehouse and multiple local warehouses, from where customers are served, and a central repair facility at an external supplier. When a part fails at a customer, his request for a ready-for-use part is immediately fullled by his local warehouse if it has a part on stock. At the same time, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part on stock. Otherwise, it is sent via a lateral transshipment from another local warehouse or the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a base-stock policy for the inventory control.\ud Because our inventory system is too complex to solve for a steady-state distribution in closed form, we approximate it by a network of Erlang loss queues with so-called hierarchical jump-over blocking. We show that this network has a steady-state distribution in product-form. Further, this steady-state distribution and several relevant performance measures only depend on the distributions for the repair and replenishment lead times via their means (i.e., they are insensitive for the underlying probability distributions). The steady-state distribution in product-form enables an ecient heuristic for the optimization of base-stock levels, resulting in good approximations of the optimal costs

Integrated planning of asset-use and dry-docking for a fleet of maritime assets

In maritime industry, moving assets (e.g., naval ships, dredgers, pilot vessels) are subject to obligatory inspections based on calendar time. These inspections consist of exhaustive operations that need the assets to be towed into specialized facilities referred to as dry-docks. In addition, there are maintenance operations needed as a result of usage-related deterioration of the assets, also requiring the assets to be dry-docked. In practice, a common approach for a fleet of assets is to synchronize these inspection and maintenance operations to avoid unnecessary dry-dockings. However, when and how these operations, some of which are calendar-based and some of which are usage-based, should be synchronized, and whether synchronizing them is always optimal remain as important questions. Since how an asset is used influences when it requires maintenance, answering these questions requires solving an integrated planning problem that combines the planning of asset-use and the planning of dry-docking. Operational constraints such as the locations of assets, limited dry-docking capacity, and the requirement to meet the demand for asset-use in each location make the problem even more challenging. This real-life problem is formulated as a mixed integer linear programming model which minimizes the total discounted cost for a finite time horizon and ensures the full satisfaction of the demand in every time period. The resulting optimal policy is compared with a sequential planning approach to quantify the economic benefit of integrated planning for asset-use and dry-docking. Additionally, two alternative planning approaches are presented for large problem instances. Results of the numerical analysis show that integrated planning can save up to 28.5% of the total cost

Joint queue length distribution of multi-class, single server queues with preemptive priorities

In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an $M/M/1$ queueing system with non-preemptive priorities between customer classes.Comment: 15 pages, 5 figures -- version 3 incorporates minor textual changes and fixes a few math typo

Maintenance optimization for a Markovian deteriorating system with population heterogeneity

We develop a partially observable Markov decision process model to incorporate population heterogeneity when scheduling replacements for a deteriorating system. The single-component system deteriorates over a finite set of condition states according to a Markov chain. The population of spare components that is available for replacements is composed of multiple component types that cannot be distinguished by their exterior appearance but deteriorate according to different transition probability matrices. This situation may arise, for example, because of variations in the production process of components. We provide a set of conditions for which we characterize the structure of the optimal policy that minimizes the total expected discounted operating and replacement cost over an infinite horizon. In a numerical experiment, we benchmark the optimal policy against a heuristic policy that neglects population heterogeneity