Comparison of two methods for customer differentiation

In response to customer specific time guarantee requirements, service providers can offer differentiated ser- vices. However, conventional customer differentiation methods often lead to high holding costs and may have some practical drawbacks. We compare two customer differentiation policies: stock reservation and pipeline stock priority for high priority customers. We derive exact analytical expressions of the waiting time distri- bution of both types of customers for a stock reservation policy. We then provide accurate approximation methods for a pipeline stock priority policy. By comparison, we offer insights concerning which method should be used under different service level requirements

Enabling customer satisfaction and stock reduction through service differentiation with response time guarantees

In response to customer specific service time guarantee requirements, service providers can offer differentiated services. However, conventional customer differentiation models based on fill rate constraints do not take full advantage of the stock reduction that can be achieved by differentiating customers based on agreed response times. In this paper we focus on the (S − 1, S, K) model with two customer classes, in which low priority customers are served only if the inventory level is above K. We employ lattice paths combinatorics to derive the exact distribution of the response time (within leadtime) for the lower priority class and provide a simple and accurate approximation for the response time of the high priority class. We show that the stock levels chosen based on agreed response times can be significantly lower than the ones chosen based on fillrates. This indicates that response time guarantees are an efficient tool in negotiating after-sale contracts, as they improve customer satisfaction and reduce investment costs

Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf

Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self-financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61323/1/20322_ftp.pd

Approximation Algorithms for Stochastic Inventory Control Models

Approximation Algorithms for Stochastic Inventory Control Model

Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem

The principal challenge of inventory control in supply chains is that the interacting autonomous enterprises have to plan their production and logistics under information asymmetry, driven by different, often conflicting objectives. In this paper, four different computational approaches are investigated to cope with this challenge: decomposition, integration, coordination, and bilevel programming. The four approaches are applied to solving the same two-stage economic lot-sizing problem, and compared in computational experiments. The prerequisites of the approaches are analyzed, and it is shown that the profits realized and the costs incurred at the different parties largely depend on the solution approach applied. This research also resulted in a novel coordination mechanism, as well as a new algorithm for the bilevel optimization approach to the investigated lot-sizing problem. A specific goal of this study is to highlight the so far less recognized application potential of the coordination and the bilevel optimization approaches for controlling inventories in a supply chain. © 2012 Elsevier B.V. All rights reserved