Spare parts inventory control for an aircraft component repair shop

We study spare parts inventory control for a repair shop for aircraft components. Defect components that are removed from the aircraft are sent to such a shop for repair. Only after inspection of the component, it becomes clear which specific spare parts are needed to repair it, and in what quantity they are needed. Market requirements on shop performance are reflected in fill rate requirements on the turn around times of the repairs for each component type. The inventory for spare parts is controlled by independent min-max policies. Because parts may be used in the repair of different component types, the resulting optimization problem has a combinatorial nature. Practical instances may consist of 500 component types and 4000 parts, and thus pose a significant computational challenge. We propose a solution algorithm based on column generation. We study the pricing problem, and develop a method that is very efficient in (repeatedly) solving this pricing problem. With this method, it becomes feasible to solve practical instances of the problem in minutes

A General Framework for Cooperation under Uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with these situations are totally balanced and, hence, have non-empty cores. Finally, we consider several example situations, which can be studied using this general framework.Two-stage stochastic programming;cooperative game theory;core

Inventory Control at AQ Electric Suzhou

This report details the process and result of developing a mathematical inventory control model to be use by AQ Electric Suzhou. The mathematical model was written in Microsoft Excels inherent programming language Visual Basic and utilizes printouts such as sales history, bill of materials, component data etc. from AQ Electric Suzhous ERP system Monitor to derive a demand history for each component. Each component is then given a compound Poisson lead time demand distribution with an optimization of reorder point in a (R,Q) continuous review inventory system with regards to service level and maximum inventory constraints. The results were that AQ Electric Suzhou would find it difficult to achieve the target on time delivery and target inventory turn rate simultaneously without changing input parameters such as minimum order quantities and lead times

Dynamic Product Assembly and Inventory Control for Maximum Profit

We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw materials for assembly. The plant operates in slotted time, and every slot it makes decisions about re-stocking materials and pricing the existing products in reaction to (possibly time-varying) material costs and consumer demands. We develop a dynamic purchasing and pricing policy that yields time average profit within epsilon of optimality, for any given epsilon>0, with a worst case storage buffer requirement that is O(1/epsilon). The policy can be implemented easily for large M, K, yields fast convergence times, and is robust to non-ergodic system dynamics.Comment: 32 page

Optimization of Inventory and Capacity in Large-Scale Assembly Systems Using Extreme-Value Theory

High-tech systems are typically produced in two stages: (1) production of components using specialized equipment and staff and (2) system assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic investments in excess production capacity and in buffer inventories of components. To optimize these, it is crucial to characterize the relation between component shortage risk and capacity and inventory investments. We suppose that component production capacity and produce demand are normally distributed over finite time intervals, and we accordingly model the production system as a symmetric fork-join queueing network with N statistically identical queues with a common arrival process and independent service processes. Assuming a symmetric cost structure, we subsequently apply extreme value theory to gain analytic insights into this optimization problem. We derive several new results for this queueing network, notably that the scaled maximum of N steady-state queue lengths converges in distribution to a Gaussian random variable. These results translate into asymptotically optimal methods to dimension the system. Tests on a range of problems reveal that these methods typically work well for systems of moderate size

A central limit theorem for temporally non-homogenous Markov chains with applications to dynamic programming

We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally non-homogeneous Markov chains, and the principal innovation is that here the summands are permitted to depend on both the current state and a bounded number of future states of the chain. We show through several examples that this added flexibility gives one a direct path to asymptotic normality of the optimal total reward of finite horizon Markov decision problems. The same examples also explain why such results are not easily obtained by alternative Markovian techniques such as enlargement of the state space.Comment: 27 pages, 1 figur

Operations research models and methods for safety stock determination: A review

In supply chain inventory management it is generally accepted that safety stocks are a suitable strategy to deal with demand and supply uncertainty aiming to prevent inventory stock-outs. Safety stocks have been the subject of intensive research, typically covering the problems of dimensioning, positioning, managing and placement. Here, we narrow the scope of the discussion to the safety stock dimensioning problem, consisting in determining the proper safety stock level for each product. This paper reports the results of a recent in-depth systematic literature review (SLR) of operations research (OR) models and methods for dimensioning safety stocks. To the best of our knowledge, this is the first systematic review of the application of OR-based approaches to investigate this problem. A set of 95 papers published from 1977 to 2019 has been reviewed to identify the type of model being employed, as well as the modeling techniques and main performance criteria used. At the end, we highlight current literature gaps and discuss potential research directions and trends that may help to guide researchers and practitioners interested in the development of new OR-based approaches for safety stock determination.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020, and by the European Structural and Investment Funds in the FEDER component, through the Operational Competitiveness and Internationalization Program (COMPETE 2020) [Project no. 39479, Funding reference: POCI-01-0247-FEDER-39479]

Certainty Equivalent Planning for Multi-Product Batch Differentiation: Analysis and Bounds

We consider a multi-period planning problem faced by a firm that must coordinate the production and allocations of batches to end products for multiple markets. Motivated by a problem faced by a biopharmaceutical firm, we model this as a discrete-time inventory planning problem where in each period the firm must decide how many batches to produce and how to differentiate batches to meet demands for different end products. This is a challenging problem to solve optimally, so we derive a theoretical bound on the performance of a Certainty Equivalent (CE) control for this model, in which all random variables are replaced by their expected values and the corresponding deterministic optimization problem is solved. This is a variant of an approach that is widely used in practice. We show that while a CE control can perform very poorly in certain instances, a simple re-optimization of the CE control in each period can substantially improve both the theoretical and computational performance of the heuristic, and we bound the performance of this re-optimization. To address the limitations of CE control and provide guidance for heuristic design, we also derive performance bounds for two additional heuristic controls -- (1) Re-optimized Stochastic Programming (RSP), which utilizes full demand distribution but limits the adaptive nature of decision dynamics, and (2) Multi-Point Approximation (MPA), which uses limited demand information to model uncertainty but fully capture the adaptive nature of decision dynamics. We show that although RSP in general outperforms the re-optimized CE control, the improvement is limited. On the other hand, with a carefully chosen demand approximation in each period, MPA can significantly outperform RSP. This suggests that, in our setting, explicitly capturing decision dynamics adds more value than simply capturing full demand information.http://deepblue.lib.umich.edu/bitstream/2027.42/116386/1/1296_Ahn.pd