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 Optimization and Demand-Side Management: Models and Algorithms

Inventory management is a fudamental problem in supply chain management. It is widely used in practice, but it is also intrinsically hard to optimize, even for relatively simple inventory system structures. This challenge has also been heightened under the threat of supply disruptions. Whenever a supply source is disrupted, the inventory system is paralyzed, and tremenduous costs can occur as a consequence. Designing a reliable and robust inventory system that can withstand supply disruptions is vital for an inventory system\u27s performance.First we consider a basic type of inventory network, an assembly system, which produces a single end product from one or several components. A property called long-run balance allows an assembly system to be reduced to a serial system when disruptions are not present. We show that a modified version is still true under disruption risk. Based on this property, we propose a method for reducing the system into a serial system with extra inventory at certain stages that face supply disruptions. We also propose a heuristic for solving the reduced system. A numerical study shows that this heuristic performs very well, yielding significant cost savings when compared with the best-known algorithm.Next we study another basic inventory network structure, a distribution system. We study continuous-review, multi-echelon distribution systems subject to supply disruptions, with Poisson customer demands under a first-come, first-served allocation policy. We develop a recursive optimization heuristic, which applies a bottom-up approach that sequentially approximates the base-stock levels of all the locations. Our numerical study shows that it performs very well.Finally we consider a problem related to smart grids, an area where supply and demand are still decisive factors. Instead of matching supply with demand, as in the first two parts of the dissertation, now we concentrate on the interaction between supply and demand. We consider an electricity service provider that wishes to set prices for a large customer (user or aggregator) with flexible loads so that the resulting load profile matches a predetermined profile as closely as possible. We model the deterministic demand case as a bilevel problem in which the service provider sets price coefficients and the customer responds by shifting loads forward in time. We derive optimality conditions for the lower-level problem to obtain a single-level problem that can be solved efficiently. For the stochastic-demand case, we approximate the consumer\u27s best response function and use this approximation to calculate the service provider\u27s optimal strategy. Our numerical study shows the tractability of the new models for both the deterministic and stochastic cases, and that our pricing scheme is very effective for the service provider to shape consumer demand

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

Evaluation of cost balancing policies in multi-echelon stochastic inventory control problems

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 67-68).We study a periodic-reviewed, infinite horizon serial network inventory control problem. The demands in different periods are independent of each other and follow an identical Poisson distribution. Unsatisfied demands are backlogged until they are satisfied by supply units. In each period, there is a per-unit holding cost is incurred for each unit of supply that stays in the system and a per-unit backorder cost is incurred for each unsatisfied unit of demand. The objective of the inventory control policy is to minimize the long-run expected average cost over an infinite horizon. The goal of the thesis is to evaluate the empirical performance of the dual balancing policy and several other variants of cost balancing policies through numerical simulations. The dual-balancing policy is based on two novel ideas: the marginal cost accounting scheme, which assigns to each decision all the costs that are made inevitable after that decision is made; and the cost balancing idea to balance opposing costs.(cont.) The dual-balancing policy can be modified in several ways to get other cost balancing policies. It has been proven that the dual-balancing policy has a worst-case guarantee of 2 but this does not indicate the empirical performance. An approximately optimal policy is considered as the benchmark to test the quality of the cost balancing policies. In the computational experiments, the dual-balancing policy shows an average error of 7.74% compared to the approximately optimal policy, much better than the theoretical worst-case guarantee. The three variants of cost balancing policies have made significant improvement on the performance of the dual-balancing policy. The accuracy of the dual-balancing policy is also affected by the system parameters. In addition, with high demand rate and long lead times, we have observed several scenarios when the cost balancing policies dominate the approximately optimal policy.by Qian Yu.S.M

Strategic inventory placement in multi-echelon supply chains : three essays

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 2008.Includes bibliographical references (p. 134-137).A central question in supply chain management is how to coordinate activities and inventories over a large number of stages and locations, while providing a high level of service to end customers. One theoretically and practically important methodology for addressing this problem is the guaranteed service (GS) framework, in which the stages of the supply chain operate according to base stock policies, and prove guaranteed service to one another. Demand is assumed to be bounded. Previous work on GS models has established very effective algorithms for finding optimal safety stock placement. In the first essay of the thesis, we show how these methods can be generalized to handle problems with capacity constraints. Furthermore, we investigate orders that are censored (reduced so as to prevent deliveries greater than what can be processed). We find safety stock reductions, sometimes even below what was needed in the no-constraint situation. In the second essay, we investigate a situation in which different parts of the supply chain are controlled by different parties, each of which selfishly applies its own GS optimization. We find that provided that the parties can agree on the right service time between them, it will be in their own interests to maintain the globally optimal solution (i.e., the system is incentive compatible). This suggests that the GS framework is better suited for coordination, than are other frameworks analyzed in the coordination literature. Finally, in the third essay, we apply the GS framework to a setting where orders are driven by forecasts and schedules, rather than by past demand as in previous GS work. We show precisely how the demand bound can be replaced by a bound on forecast errors, and that existing optimization methods can be used.(cont.) In a case study, we obtained data from the supply chain of an electronic test system, as well as characterized the forecasting process. We found that incorporating the forecast process led to 25% reduction of safety stocks.by Tor Schoenmeyr.Ph.D

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