Developing a closed-form cost expression for an (R,s,nQ) policy where the demand process is compound generalized Erlang.

We derive a closed-form cost expression for an (R,s,nQ) inventory control policy where all replenishment orders have a constant lead-time, unfilled demand is backlogged and inter-arrival times of order requests are generalized Erlang distributedInventory control; Compound renewal process; Generalized Erlang distribution;

Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times

We investigate a periodic inventory system for a single item with stochastic demand and random yield. Since the optimal policy for such a system is complicated we study the class of stationary linear-inflation policies where orders are only placed if the inventory position is below a critical stock level, and where the order quantity is controlled by a yield inflation factor. We consider two different models for the uncertain supply: binomial and stochastically proportional yield and we allow positive and constant lead times as well as asymmetric demand and yield distributions. In this paper we propose two novel approaches to derive optimal and near-optimal numerical values for the critical stock level, minimizing the average holding and backorder cost for a given inflation factor. First, we present a Markov chain approach, which is exact in case of negligible lead time. Second, we provide a steady state analysis to derive approximate closed-form expressions for the optimal critical stock level. We conduct an extensive numerical study to test the performance of our approaches. The numerical experiments reveal an excellent performance of both approaches. Since our derived formulas are easily implementable and highly accurate they are very valuable for practical application

Inventory management in multi-stage production systems with random yield and positive production times

Random yield occurs if production processes are imperfect and therefore produce defective items. Examples for such imperfect production processes can be found in every industry. Consider for example the production of curved glass for Samsung's cell phones, where the company had to deal with low yield rates of 50 %, meaning that half of all products had to be scrapped. This exemplarily shows that production systems with random yield cannot be neglected and are highly relevant in increasingly complex production processes as well as under high competition and shorter product life cycles. We consider a multi-stage production system where the input of the production system is determined by the order quantity. An order can be placed by the warehouse to replenish stock and be able to satisfy stochastic customer demands. Because the optimal ordering policy is known to be very complex, a common linear inflation policy is used. To make sure that only products meeting the quality requirements are stocked in the warehouse and afterwards sold to the customers, an error-free quality inspection is located after the production process, sorting out all defective items. Defective items are either disposed of and leave the production system or are reworked. If defective items are reworked, they have afterwards the same quality as items that were perfect when first produced. Therefore, reworked items also enter the warehouse and are sold to the customers without any price discount. Different from most of the literature on make-to-stock production systems with random yield we consider positive production times during the production process because they are more realistic especially for highly sophisticated production systems as in the high-tech industry. Positive production times increase the complexity of the problem a lot because the decision maker in the warehouse has to place an order before knowing the exact amount of perfectly produced items leaving the production process in future periods. We show how to set the policy parameters for such a multi-stage make-to-stock production system with random yield, positive lead times and either disposal or rework of defective items. Our approach requires low computation times even for larger production systems and leads to very good results

Dynamic Product Acquisition in Closed Loop Supply Chains

We consider a closed loop supply chain where demands can either be satisfied from manufacturing new products or by buying back used products from customers and upgrading their functionality by remanufacturing. Product life cycles and seasonal aspects are modeled within a continuous time framework. The manufacturing and remanufacturing policies as well as buy back strategies for used products are determined by an optimal control approach

Inventory management in multi-stage production systems with random yield and positive production times

Random yield occurs if production processes are imperfect and therefore produce defective items. Examples for such imperfect production processes can be found in every industry. Consider for example the production of curved glass for Samsung's cell phones, where the company had to deal with low yield rates of 50 %, meaning that half of all products had to be scrapped. This exemplarily shows that production systems with random yield cannot be neglected and are highly relevant in increasingly complex production processes as well as under high competition and shorter product life cycles. We consider a multi-stage production system where the input of the production system is determined by the order quantity. An order can be placed by the warehouse to replenish stock and be able to satisfy stochastic customer demands. Because the optimal ordering policy is known to be very complex, a common linear inflation policy is used. To make sure that only products meeting the quality requirements are stocked in the warehouse and afterwards sold to the customers, an error-free quality inspection is located after the production process, sorting out all defective items. Defective items are either disposed of and leave the production system or are reworked. If defective items are reworked, they have afterwards the same quality as items that were perfect when first produced. Therefore, reworked items also enter the warehouse and are sold to the customers without any price discount. Different from most of the literature on make-to-stock production systems with random yield we consider positive production times during the production process because they are more realistic especially for highly sophisticated production systems as in the high-tech industry. Positive production times increase the complexity of the problem a lot because the decision maker in the warehouse has to place an order before knowing the exact amount of perfectly produced items leaving the production process in future periods. We show how to set the policy parameters for such a multi-stage make-to-stock production system with random yield, positive lead times and either disposal or rework of defective items. Our approach requires low computation times even for larger production systems and leads to very good results

Managing Dynamic Product Recovery : An Optimal Control Perspective

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Stochastic inventory routing with time-based shipment consolidation

Inspired by the retail industry, we consider a stochastic inventory routing problem where retailers are replenished from a central warehouse using a time-based shipment consolidation policy. Such a time-based dispatching policy, where retailers facing stochastic demand are repetitively replenished at fixed times, is essential in practice. It allows for easy incorporation with dependent up- and downstream planning problems such as personal staffing and warehouse operations, and has become a standard part of transportation contracts. We provide a new chance-constrained model that determines an optimal clustering of retailers in groups, their associated routing and shipment interval, and each retailers’ optimal inventory level. A newly developed branch-price-and-cut algorithm solves our model to optimality. Its efficiency comes from a tailored labeling algorithm for solving the pricing problem that relies, among others, on an optimality pruning criterion based on the approximate solution of a 0,1-knapsack problem. Computational experiments show that our exact method can solve instances of up to 60 retailers to optimality. Besides, we accommodate practitioners by providing a fast heuristic that provides excellent solutions with an optimality gap of less than 1%. Finally, we show that incorporating uncertainty already in the planning process is essential for stochastic inventory routing with time-based shipment consolidation, as it results in overall cost-savings of 7.7% compared to the current state-of-the-art