Optimal expediting decisions in a continuous-stage serial supply chain

In this paper, we analyze expediting decisions in a continuous-time, continuous-stage serial supply chain facing a Poisson demand process. For each unit in the chain, one must decide at which speed it should be moved downstream, given the state of the system, so as to minimize total supply chain costs. We decompose the problem into a set of one-dimensional subproblems that can be easily solved and characterize the optimal expediting policy: under quite general assumptions, the optimal speed of a given unit accelerates upstream, and then slows down downstream. We finally provide a case study where we estimate the benefits of expediting compared to a fixed transportation speed and show them to be significant.lead-time management; optimal control; unit-tracking decomposition;

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

A characterization of optimal base-stock levels for a continuous-stage serial supply chain

In this paper, we present a continuous model to optimize multi-echelon inventory management decisions under stochastic demand. Observing that in such continuous system it is never optimal to let orders cross, we decompose the general problem into a set of single-unit sub-problems that can be solved in a sequential fashion. When shipping and inventory holding costs are linear in the stage, we show that it is optimal to move the unit associated with the k-th next customer if and only if the inventory unit is held in an echelon located within a given interval. This optimal policy can be interpreted as an echelon base-stock policy such that the base-stock is initially increasing and then decreasing in the stage. We also characterize the optimal policy when costs are piecewise-constant. Finally, we study the sensitivity of the optimal base-stock levels to the cost structures.multi-echelon; optimal control; unit-tracking decomposition;

Multiple sourcing in single- and multi-echelon inventory systems

This thesis deals with stochastic inventory models that focus on the following two aspects in particular: (i) the coordination of multiple supply sources and (ii) the optimization of the inventory allocation and sizing in multi-echelon systems. Initially, single-echelon inventory models with multiple sourcing and multi-echelon inventory models with single sourcing are analyzed separately. In the former case, the goal is the identification of effective inventory control policies. In the latter case, the focus lies on the development of a new multi-echelon approach, which combines the two major frameworks currently available in the literature. Subsequently, both aspects are integrated into a multi-echelon inventory model with multiple sourcing

A single-unit decomposition approach to multiechelon inventory systems. Working paper

We show the optimality of state dependent echelon base stock policies in uncapacitated serial inventory systems with Markov modulated demand and Markov modulated stochastic leadtimes in the absence of order crossing. Our results cover finite time horizon problems as well as infinite time horizon formulations, with either a discounted or an average cost criterion. We employ a novel approach, based on a decomposition of the problem into a series of single-unit single-customer problems that are essentially decoupled. Besides providing a simple proof technique, this approach also gives rise to efficient algorithms for the calculation of the base stock levels.