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

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

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

Real-time Allocation Decisions in Multi-echelon Inventory Control

Inventory control is a crucial activity for many companies. Given the recent advances in information technology, there have never been greater opportunities for coordinated inventory control across supply chain facilities. But how do we design efficient control methods and policies that take advantage of the detailed information that is now becoming available? This doctoral thesis investigates these issues within the field of inventory control theory. The objective of the research is: To develop mathematical models and policies for efficient control and increased understanding of stochastic multi-echelon inventory systems, with a focus on allocation decisions and the use of real-time information. This thesis is based on five scientific papers which are preceded by a summarizing introduction. The papers address different types of inventory distribution systems, all consisting of a central stocking facility that supplies an arbitrary number of local stocking facilities (referred to as retailers). The retailers face stochastic end customer demand. The systems are characterized by the presence of real-time inventory information, including continuously updated information on the current inventory levels at different facilities and on the locations of outstanding orders. In Paper I and Paper II we derive and evaluate different decision rules for stock allocation (known as allocation policies) for a central warehouse which applies a time based shipment consolidation strategy. The allocation policy determines how the central warehouse should distribute its stock among different retailers in case of shortages. New allocation policies that utilize real-time information are compared to the commonly used First Come - First Served policy which requires less information. In Paper III we shift focus to the delivery policy at a central warehouse which supplies multiple retailers that order in batches. When the central warehouse cannot satisfy an entire retailer order immediately, the delivery policy determines if the order should be shipped in several parts or in its entirety when all items are available. We investigate the value of using a new delivery policy that uses real-time information on when replenishments will arrive at the central warehouse. The information is used to determine the best course of action for each order placed by the retailers. We also study how to allocate safety stocks to all facilities in the system given this new policy. In Paper IV and Paper V we consider a system where retailers may receive emergency shipments from a support warehouse in combination with regular replenishments from a central warehouse/outside supplier. We investigate how safety stocks should be allocated between the retailers and the support warehouse. Furthermore, we evaluate the benefits of tracking orders in real time and using this information in the decision whether or not to request an emergency shipment

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

The break quantity rule in a 1-warehouse, N-retailers distribution system

In this paper the effect of the break quantity rule on the inventory costs in a 1-warehouse, N-retailers distribution system is analyzed. The break quantity rule is to deliver large orders from the warehouse, and small orders from the nearest retailer, where a so--called break quantity determines whether an order is small or large. Under the assumptions that the stock at the warehouse can only be used to satisfy large orders, and that demand during the leadtimes is normally distributed, an expression for the inventory costs is derived. The objective of this paper is to provide insight into the effect of the break quantity rule on the inventory holding costs, and therefore we present extensive computational results, showing that in many cases the rule leads to a significant cost reduction

A multi-echelon inventory model with fixed reorder intervals

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

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