Efficient optimization of the dual-index policy using Markov chains

3We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster `emergency' supply source. Unsatistfied emand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to and their optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times

Analysis of a two-echelon inventory system with two supply modes

In this paper, we consider a serial two-echelon periodic review inventory system with two supply modes at the most upstream stock point. As control policy for this system, we propose a natural extension of the dual-index policy, which has three base-stock levels. We consider the minimization of long run average inventory holding, backlogging, and both per unit and fixed emergency ordering costs. We provide nested newsboy characterizations for two of the three base-stock levels involved and show a separability result for the difference with the remaining base-stock level. We use results for the single-echelon system to efficiently approximate the distributions of random variables involved in the newsboy equations and find an asymptotically correct approximation for both the per unit and fixed emergency ordering costs. Based on these results, we provide an algorithm for setting base-stock levels in a computationally efficient manner. In a numerical study, we investigate the value of dual-sourcing in supply chains and show that it is useful to decrease upstream stock levels. In cases with high demand uncertainty, high backlogging cost or long lead times, we conclude that dual-sourcing can lead to significant savings

Modeling Multilevel Supply Chain Systems to Optimize Order Quantities and Order Points Through Mathematical Models, Discrete Event simulation and Physical Simulations

Managing supply chains in today\u27s distributed manufacturing environment has become more complex. To remain competitive in today\u27s global marketplace, organizations must streamline their supply chains. The practice of coordinating the design, procurement, flow of goods, services, information and finances, from raw material flows to parts supplier to manufacturer to distributor to retailer and finally to consumer requires synchronized planning and execution. Efficient and effective supply chain management assists an organization in getting the right goods and services to the place needed at the right time, in the proper quantity and at acceptable cost. Managing this process involves developing and overseeing relationships with suppliers and customers, controlling inventory, and forecasting demand, all requiring constant feedback from every link in the chain. Base Stock Model and (Q, r) models are applied to three tier single-product supply chain to calculate order quantities and reorder point at various locations within the supply chain. Two physical simulations are designed to study the above supply chain. One of these simulations is specifically designed to validate the results from Base Stock model. A computer based discrete event simulation model is created to study the three tier supply chain and to validate the results of the Base Stock model. Results from these mathematical models, physical simulation models and computer based simulation model are compared. In addition, the physical simulation model studies the impact of lean implementation through various performance metrics and the results demonstrate the power of physical simulations as a pedagogical tool for training. Contribution of present work in understanding the supply chain integration is discussed and future research topics are presented

Inventory models with lateral transshipments : a review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satised from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level denition, all in uence the best method of transshipping. Models of many dierent systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these dierences can be understood and gaps within the literature can be identied

The causes and determination of safety stocks in upstream supply chains for mass production of customized products

In an upstream supply chain dedicated to the mass production of customized products, many sources create production instability: the level and structure of production in the final assembly line, variability of lead times, quality issues, packaging and loading constraints on transportation, demand anticipation, and the synchronization of the flows of components sent, received, and produced. For periodic replenishment systems, each member of the supply chain must have two different safety stocks to prevent some sources of fluctuations: a safety stock of produced components to meet the demand of downstream links and a safety stock of supplied components to ensure its own production. Procedures must take the organizational framework of information and products exchanges into account. The relevance of supply and production rules depends on the relevance of structural information broadcast along the supply chain

Integrated optimisation for production capacity, raw material ordering and production planning under time and quantity uncertainties based on two case studies

Abstract This paper develops a supply chain (SC) model by integrating raw material ordering and production planning, and production capacity decisions based upon two case studies in manufacturing firms. Multiple types of uncertainties are considered; including: time-related uncertainty (that exists in lead-time and delay) and quantity-related uncertainty (that exists in information and material flows). The SC model consists of several sub-models, which are first formulated mathematically. Simulation (simulation-based stochastic approximation) and genetic algorithm tools are then developed to evaluate several non-parameterised strategies and optimise two parameterised strategies. Experiments are conducted to contrast these strategies, quantify their relative performance, and illustrate the value of information and the impact of uncertainties. These case studies provide useful insights into understanding to what degree the integrated planning model including production capacity decisions could benefit economically in different scenarios, which types of data should be shared, and how these data could be utilised to achieve a better SC system. This study provides insights for small and middle-sized firm management to make better decisions regarding production capacity issues with respect to external uncertainty and/or disruptions; e.g. trade wars and pandemics.</jats:p