Exact Methods for Multi-echelon Inventory Control : Incorporating Shipment Decisions and Detailed Demand Information

Recent advances in information technologies and an increased environmental awareness have altered the prerequisites for successful logistics. For companies operating on a global market, inventory control of distribution systems is often an essential part of their logistics planning. In this context, the research objective of this thesis is: To develop exact methods for stochastic inventory control of multi-echelon distribution systems incorporating shipment decisions and/or detailed demand information.The thesis consists of five scientific papers (Paper I, II, III, IV and V) preceded by a summarizing introduction. All papers study systems with a central warehouse supplying a number of non-identical local warehouses (retailers) facing stochastic demand. For given replenishment policies, the papers provide exact expressions for evaluating the expected long-run system behavior (e.g., distributions of backorders, inventory levels, shipment sizes and expected costs) and present optimization procedures for the control variables. Paper I and II consider systems where shipments from the central warehouse are consolidated to groups of retailers and dispatched periodically. By doing so, economies of scale for the transports can be reached, reducing both transportation costs and emissions. Paper I assumes Poisson customer demand and considers volume-dependent transportation costs and emissions. The model involves the possibility to reserve intermodal (train) capacity in combination with truck transports available on demand. For this system, the expected inventory costs, the expected transportation costs and the expected transport emissions are determined. Joint optimization procedures for the shipment intervals, the capacity reservation quantities, the reorder points and order-up-to levels in the system are provided, with or without emission considerations. Paper II analyses the expected costs of the same system for compound Poisson demand (where customer demand sizes may vary), but with only one transportation mode and fixed transportation costs per shipment. It also shows how to handle fill rate constraints. Paper III studies a system where all stock points use installation stock (R,Q) ordering policies (batch ordering). This implies that situations can occur when only part of a requested retailer order is available at the central warehouse. In these situations, the models in existing literature predominantly assume that available units are shipped immediately (partial delivery). An alternative is to wait until the entire order is available before dispatching (complete delivery). The paper introduces a cost for splitting the order and evaluates a system where optimal choices between partial and complete deliveries are made for all orders. In a numerical study it is shown that significant savings can be made by using this policy compared to systems which exclusively use either partial or complete deliveries. Paper IV shows how companies can benefit from detailed information about their customer demand. In a continuous review base stock system, the customer demand is modeled with independent compound renewal processes at the retailers. This means that the customer inter-arrival times may follow any continuous distribution and the demand sizes may follow any discrete distribution. A numerical study shows that this model can achieve substantial savings compared to models using the common assumption of exponential customer inter-arrival times. Paper V is a short technical note that extends the scope of analysis for several existing stochastic multi-echelon inventory models. These models analyze the expected costs without first determining the inventory level distribution. By showing how these distributions can be obtained from the expected cost functions, this note facilitates the analysis of several service measures, including the ready rate and the fill rate

Multilocation Inventory Systems With Centralized Information.

The management of multi-echelon inventory systems has been both an important and challenging research area for many years. The rapid advance in information technology and the emphasis on integrated supply chain management have new implications for the successful operation of distribution systems. This research focuses on the study of some fundamental issues related to the operation of a multilocation inventory system with centralized information. First, we do a comparative analysis to evaluate the overall performance of individual versus centralized ordering policies for a multi-store distribution system where centralized information is available. This study integrates the existing research and clarifies one of the fundamental questions facing inventory managers today: whether or not ordering decisions should be centralized. Next, we consider a multi-store distribution system where emergency transshipments are permitted among these stores. Based on some simplifying assumptions, we develop an integrated model with a joint consideration of inventory and transshipment components. An approximately optimal (s, S) policy is obtained through a dynamic programming technique. This ordering policy is then compared with a simplified policy that assumes free and instantaneous transshipments. We also examine the relative performance of base stock policies for a centralized-ordering distribution system. Numerical studies are provided to give general guidelines for use of the policies

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

Multi-echelon Inventory Control with Integrated Shipment Decisions

Rising fuel prices and increasing environmental awareness emphasizes the importance of the transportation aspect in logistics. This calls for new improved inventory control methods that consider the effects of shipment strategies in a more realistic manner. This thesis, consisting of an introduction and three scientific papers, studies how shipment decisions can be included in the inventory control of distribution systems. The systems studied in the papers consist of a central warehouse that supplies goods to a number of retailers that face stochastic customer demand. The first two papers consider a system where shipments from the central warehouse are consolidated to groups of retailers periodically. This means that replenishment orders of one or several items from different retailers are consolidated and dispatched at certain time intervals. By doing so, transportation cost savings can be realized and emissions can be reduced. This is achieved by filling the vehicles or load carriers to a higher extent and by using cheaper and more environmentally friendly, transportation modes. The first paper explicitly focuses on how to include more realistic transportation costs and emissions. This is done by obtaining the distribution of the size of an arbitrary shipment leaving the central warehouse (directly affected by the shipment frequency). It is thereby easy to evaluate any system where the transportation costs and emissions are dependent on the size of the shipment. The paper also provides a detailed analysis of a system where there is an opportunity to reserve shipment capacity on an intermodal truck-train-truck solution to at least one of the retailer groups. For this system it is shown how to jointly optimize the shipment intervals, the reserved capacities on the intermodal transportation modes and the reorder points in the system. The presented optimization procedure is applicable in three scenarios; (i) the emissions are not considered, (ii) there is a fixed cost per unit of emission, and (iii) there is a constraint on the maximum emissions per time unit. The second paper extends the analysis of a similar time-based shipment consolidation system to handle compound Poisson demand (instead of pure Poisson demand). This system has a simpler transportation cost structure, but the more general demand structure makes the model applicable for a broader array of products. The paper also extends the model to handle fill rate constraints, which further improves the practical applicability. The cost analysis is performed with a new methodology, based on the nominal inventory position. This variable is a helpful tool for analyzing the dynamics of distribution systems. Another system where this tool can be used is studied in the third paper. In this paper all stock points use installation stock (R,Q) ordering policies (batch ordering). This implies that situations can occur when only part of a requested retailer order is available at the central warehouse. The existing literature predominantly assumes that the available units are shipped immediately and the remaining units are shipped as soon as they arrive to the central warehouse, referred to as partial delivery. An alternative is to wait until the entire order is available before dispatching, referred to as complete delivery. The paper introduces a cost for splitting the order and evaluates three delivery policies; the PD policy (only partial deliveries are used), the CD policy (only complete deliveries are used), and the state-dependent MSD policy (an optimization between a partial and a complete delivery is performed for each delivery). The MSD policy is proven to perform better than both the PD and the CD policy. In a numerical study it is shown that significant savings can be made by using the MSD policy

Tactical design of production-distribution networks : safety stocks, shipment consolidation and production planning

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A multi-echelon inventory model with fixed reorder intervals

Includes bibliographical references (p. 30-31).by Stephen C. Graves

Effective Multi-echelon Inventory Systems for Supplier Selection and Order Allocation

Successful supply chain management requires an effective sourcing strategy to counteract uncertainties in both the suppliers and demands. Therefore, determining a better sourcing policy is critical in most of industries. Supplier selection is an essential task within the sourcing strategy. A well-selected set of suppliers makes a strategic difference to an organization\u27s ability to reduce costs and improve the quality of its end products. To discover the cost structure of selecting a supplier, it is more interesting to further determine appropriate levels of inventory in each echelon for different suppliers. This dissertation focuses on the study of the integrated supplier selection, order allocation and inventory control problems in a multi-echelon supply chain. First, we investigate a non-order-splitting inventory system in supply chain management. In particular, a buyer firm that consists of one warehouse and N identical retailers procures a type of product from a group of potential suppliers, which may have different prices, ordering costs, lead times and have restriction on minimum and maximum total order size, to satisfy stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the proposed model. The model is solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained with sensitivity analysis. In the next place, we extend the study to consider the multi-echelon system with the order-splitting policy. In particular, the warehouse acquisition takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. This consideration is important since it could pool lead time risks by splitting replenishment orders among multiple suppliers simultaneously. We develop an exact analysis for the order-splitting model in the multi-echelon system, and formulate the problem in a Mixed Integer Nonlinear Programming (MINLP) model. To demonstrate the solvability and the effectiveness of the model, we conduct several numerical analyses, and further conduct simulation models to verify the correctness of the proposed mathematical model