A numerical study of expressions for fill rate for single stage inventory system with periodic review.

Fill rate is one of the most important measurements for inventory systems in the supply chain management. The primary goal of this thesis is to give a comprehensive review of existing analytical expressions for the system fill rate, and provide numerical comparison for all relevant expressions in terms of their accuracy against (simulated) fill rate from the Monte Carlo simulation. We prove relationships between several expressions. Although majority of the expressions discussed herein are designed for standard periodic review system, we conduct numerical simulations for the general periodic review system. Under this general periodic review setting, numerical results indicate that all else being equal, replenishment lead time has larger effect on the system\u27s fill rate than does the review interval. In addition, numerical comparison suggests that Johnson et al.\u27s approach, Zhang and Zhang\u27s approach, Hadley and Whitin\u27s approach dominate the traditional approach, exponential approximation and Silver\u27s modified approach. The dominance is especially true for cases with high demand variability. For general periodic review system, our numerical results indicate that scaling is necessary for Silver\u27s modified, Johnson et al.\u27s and Johnson et al.\u27s modified approaches

Stock allocation in general multi-echelon distribution systems with (R, S) order-up-to-policies

In this paper we analyze stock allocation policies in general N-echelon distribution systems, where it is allowed to hold stock at all levels in the network. The goal is to achieve differentiated target customer service levels (fill rates). Various allocation rules and accompanying numerical methods that have already been developed for smaller networks are extended and compared in an extensive numerical experiment. We conclude that the extension of Balanced Stock rationing (see Van der Heijden (1996)) is the most accurate method, in particular in cases of relatively high imbalance. If the imbalance is not too high, the extension of Consistent Appropriate Share rationing (see De Kok et al., 1994; Verrijdt and De Kok, 1996) performs good as well

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

A simulation approach to determine the probability of demand during lead-time when demand distributed normal and lead-time distributed gamma

Globalization and advances in information and production technologies make inventory management can be very difficult even for organizations with simple structures. The complexities of inventory management increase in multi-stage networks, where inventory appears in multiple tiers of locations. Due to massive practical applications in the reality of the world, an efficient inventory system policy whether single location or multi-stage location will avoid falling into overstock inventory or under stock inventory. However, the optimality of inventory and allocation policies in a supply chain is still unknown for most types of multi-stage systems. Hence, this paper aims to determine the probability distribution function of demand during lead-time by using a simulation model when the demand distributed normal and the lead-time distributed gamma. The simulation model showed a new probability distribution function of demand during lead-time in the considered inventory system, which is, Generalized Gamma distribution with 4 parameters. This probability distribution function makes the mathematical expression more difficult to build the inventory model especially in multistage or multi-echelon inventory model

A replenishment control system with uncertain returns and random opportunities for disposal

We consider a replenishment control system in which product returns play an important role in inventory planning. We focus on the inventory of an individual item that is stored at a single location to meet a constant demand over time. We assume that the total amount of returns accumulated over a period of time can be represented by a compound Poisson process. We further assume that opportunities for inventory disposals or relocation arise occasionally in accordance with a Poisson process. We not only seek to resolve the issues of when to order and how much to order, we also consider the question of when to dispose of excess inventory and by how much. Inventory reductions occur when the opportunity for a disposal arises and the inventory position is deemed too high. After each disposal the inventory position is restored to a specified base-stock level. We develop a cost model of this system and highlight its properties through an extensive numerical study

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies

Virtual transshipments and revenue-sharing contracts in supply chain management

This dissertation presents the use of virtual transshipments and revenue-sharing contracts for inventory control in a small scale supply chain. The main objective is to maximize the total profit in a centralized supply chain or maximize the supply chain\u27s profit while keeping the individual components\u27 incentives in a decentralized supply chain. First, a centralized supply chain with two capacitated manufacturing plants situated in two distinct geographical regions is considered. Normally, demand in each region is mostly satisfied by the local plant. However, if the local plant is understocked while the remote one is overstocked, some of the newly generated demand can be assigned to be served by the more remote plant. The sources of the above virtual lateral transshipments, unlike the ones involved in real lateral transshipments, do not need to have nonnegative inventory levels throughout the transshipment process. Besides the theoretical analysis for this centralized supply chain, a computational study is conducted in detail to illustrate the ability of virtual lateral transshipments to reduce the total cost. The impacts of the parameters (unit holding cost, production cost, goodwill cost, etc.) on the cost savings that can be achieved by using the transshipment option are also assessed. Then, a supply chain with one supplier and one retailer is considered where a revenue-sharing contract is adopted. In this revenue-sharing contract, the retailer may obtain the product from the supplier at a less-than-production-cost price, but in exchange, the retailer must share the revenue with the supplier at a pre-set revenuesharing rate. The objective is to maximize the overall supply chain\u27s total profit while upholding the individual components\u27 incentives. A two-stage Stackelberg game is used for the analysis. In this game, one player is the leader and the other one is the follower. The analysis reveals that the party who keeps more than half of the revenue should also be the leader of the Stackelberg game. Furthermore, the adoption of a revenue-sharing contract in a supply chain with two suppliers and one retailer under a limited amount of available funds is analyzed. Using the revenue-sharing contract, the retailer pays a transfer cost rate of the production cost per unit when he obtains the items from the suppliers, and shares the revenue with the suppliers at a pre-set revenue-sharing rate. The two suppliers have different transfer cost rates and revenue-sharing rates. The retailer will earn more profit per unit with a higher transfer cost rate. How the retailer orders items from the two suppliers to maximize his expected profit under limited available funds is analyzed next. Conditions are shown under which the optimal way the retailer orders items from the two suppliers exists