The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands

We develop an algorithm to compute an optimal Q(s,S) policy for the joint replenishment problem when demands follow a compound correlated Poisson process. It is a non-trivial generalization of the work by Nielsen and Larsen (2005). We make some numerical analyses on two-item problems where we compare the optimal Q(s,S) policy to the optimal uncoordinated (s,S) policies. The results indicate that the more negative the correlation the less advantageous it is to coordinate. Therefore, in some cases the degree of correlation determines whether to apply the coordinated Q(s,S) policy or the uncoordinated (s,S) policies. Finally, we compare the Q(s,S) policy and the closely connected P(s,S) policy. Here we explain why the Q(s,S) policy is a better choice if item-demands are correlated.joint replenishment problem; compound correlated Poisson process

Coordinated replenishment systems with discount opportunities

Inventory Control;Inventory Models;inkoop

A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process

The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels

Computation of order and volume fill rates for a base stock inventory control system with heterogeneous demand to investigate which customer class gets the best service

We consider a base stock inventory control system serving two customer classes whose demands are generated by two independent compound renewal processes. We show how to derive order and volume fill rates of each class. Based on assumptions about first order stochastic dominance we prove when one customer class will get the best service. That theoretical result is validated through a series of numerical experiments which also reveal that it is quite robust.Base stock policy; service measures; two customer classes; compound renewal processes

On the determination of the control parameters of the optimal can-order policy

Inventory Control

Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Spare Parts And Maintenance Optimization In A Mobile Telephone Company

(WP12/02 Clave pdf) Telecommunication companies depend on high availability of equipment to maintain service quality. In cellular communications electronic cards maintenance is basically reduced to exchanging parts as they fail. These parts are geographically dispersed in unmanned locations. Spares and maintenance policies are thus interrelated and tend to follow multiechelon configurations, following the architecture of the physical network. We describe the optimization of spare parts and maintenance policies performed by the Venezuelan mobile phone operator Movilnet.Mobile phone, MRO, Multi-echelon inventory systems, Spare parts optimization

Cooperation in stochastic inventory models with continuous review

Consider multiple companies that continuously review their inventories and face Poisson demand. We study cooperation strategies for these companies and analyse if there exist allocations of the joint cost such that any company has lower costs than on its own; such allocations are called stable cost allocations. We start with two companies that jointly place an order for replenishment if their joint inventory position reaches a certain reorder level. This strategy leads to a simple expression of the joint costs. However, these costs exceed the costs for non-cooperating companies. Therefore, we examine another cooperation strategy. Namely, the companies reorder as soon as one of them reaches its reorder level. This latter strategy has lower costs than for non-cooperating companies. Numerical experiments show that the gametheoretical distribution rule — a cost allocation in which the companies share the procurement cost and each pays its own holding cost — is a stable cost allocation. These results also hold for situations with multiple companies

Performance Evaluation of Stochastic Multi-Echelon Inventory Systems: A Survey

Globalization, product proliferation, and fast product innovation have significantly increased the complexities of supply chains in many industries. One of the most important advancements of supply chain management in recent years is the development of models and methodologies for controlling inventory in general supply networks under uncertainty and their widefspread applications to industry. These developments are based on three generic methods: the queueing-inventory method, the lead-time demand method and the flow-unit method. In this paper, we compare and contrast these methods by discussing their strengths and weaknesses, their differences and connections, and showing how to apply them systematically to characterize and evaluate various supply networks with different supply processes, inventory policies, and demand processes. Our objective is to forge links among research strands on different methods and various network topologies so as to develop unified methodologies.Masdar Institute of Science and TechnologyNational Science Foundation (U.S.) (NSF Contract CMMI-0758069)National Science Foundation (U.S.) (Career Award CMMI-0747779)Bayer Business ServicesSAP A