Simulation of Allocation Policies for a Serial Inventory System Under Advance Demand Information

It is important to share demand information among the members in supply chains. In recent years, production and inventory systems with advance demand information (ADI) have been discussed, where advance demand information means the information of demand which the decision maker obtains before the corresponding actual demand arrives. Appropriate production and inventory control using demand information leads to the decrease of inventory and backlog costs. For a single stage system, the optimal base stock and release lead time have been discussed in the literature. In practical production systems the manufacturing system has multiple processes. The multiple stage production and inventory system with ADI, however, has been analyzed by simulation or assuming exponential processing time. That is, their theoretical analysis and optimization of release lead time and base stock level have little been obtained because of its difficulty. In this paper, theoretical analysis of a two-stage production inventory system with advance demand information is developed, where the processing time is assumed deterministic and identical; demand arrival process is Poisson, and an order base stock policy is adopted. Using the analytical results, optimal release lead time and optimal base stock levels for minimizing the average cost on the holding and backlog costs are explicitly derived.

Customers with positive demand lead times place orders in advance of their needs. A portfolio of customers with different demand lead times gives rise to what we call advance demand information. We develop effective inventory policies for a distribution system to account for this information. In particular, we study a centralized system with one warehouse serving multiple retailers under advance demand information. The inventory manager replenishes the warehouse from an outside supplier. Units arriving to the warehouse are allocated to the retailers. To control this system, we develop a lower bound and proposed a close-to-optimal heuristic for which the optimality gap is on average 1.92%. We also provide a closed-form solution to approximate the system-wide inventory level. Using this explicit solution, the model and the heuristic, we investigate (1) the benefit of advance demand information, and its impact on allocation decisions, (2) the joint role of risk pooling and advance demand information, and (3) the system performance with respect to supplier and retailer lead times. We illustrate how advance demand information can be a substitute for lead times and inventory, and how it enhances the outcome of delayed differentiation.

This article models a single-stage hybrid production system, which can be regarded as a Make To Order (MTO) production system with safety stocks or a Make To Stock (MTS) production system with advance demand information. In an environment with multiple products and variable customer due dates, optimality conditions for safety stocks (base stocks) and safety lead times (work-ahead window) that minimize inventory and backorder costs are derived. For a simplified M/M/1 system with exponentially distributed customer required lead time, an explicit comparison between MTO and MTS is conducted. A pure MTO policy gets relatively more favorable to a pure MTS policy if inventory holding costs increase, backorder costs decrease, the mean customer required lead time increases, or the processing rate increases. In a numerical study, the influence of variance, the behavior of optimal parameters, and the cost reduction potential of this hybrid policy are shown.

It can be difficult to set the reorder point in an inventory system because often one does not have much knowledge of the lead-time demand (LTD)distribution. A frequent practice is to assume a “standard” distribution, such as the Normal. The reorder point is then taken as the p-th fractile of that standard distribution, where (1 −p) is the specified probability of stockout during a replenishment cycle. When the desired service level p is high and the “true” LTD distribution is skewed, previous research has shown that the reorder point and inventory costs are strongly affected by the shape of the assumed LTD distribution. Ideally, no assumptions about this distribution should be necessary. One such “distribution-free” approach is the bootstrap procedure. Beginning with a single sample W = {x1x2,…,xn} of lead-time demand, the bootstrap repeatedly samples with replacement from W, A family of bootstrap samples of size n is thereby created, each sample furnishing an estimate Xp∗ of the p-th fractile of the LTD distribution. The probability mass function of these values yields the bootstrap estimate of the reorder point [[Xcirc]p = E(Xp)]. We employ the bootstrap procedure to determine the reorder point s in an (s,Q) system for desired service levels p = 0.8, 0.9 and 0.95. The bootstrap and normal approaches are compared using LTD data simulated from a number of populations with varying tail shapes. Analyses of variance are performed to compare the estimated reorder points across various levels of distribution form, coefficient of variation, sample size and service level. The relative performance of the bootstrap and normal approaches is also discussed in terms of a cost model. We found it preferable to use the bootstrap procedure in any situation where a “non-standard’ LTD distribution, e.g. a bimodal one, is suspected. If the distribution actually is a standard shape, such as normal or lognormal, the bootstrap estimate is often as good as the normal. Situations are also identified where the bootstrap procedure should not be used, and suggestions are made for further research.

This paper investigates the benefits of integrating advance demand information (ADI) with pull-kanban type production and inventory control systems (PICS). Since efficient analytical models for performance evaluation studies of these systems are unavailable, we use simulation experiments for the study. In particular, we investigate the impact of several PICS design parameters such as kanban card limits, target finished goods inventory levels, amount of demand information available, and the quality of ADI on performance measures such as system throughput, inventory holding costs and customer service levels. Our study shows that in many situations, integrating ADI with pull systems provides opportunities for efficiencies that might be significantly greater that that available using pull systems alone. Further more, we show that the performance of systems operating under pull-type PICS with ADI could be fairly robust to the quality of information being shared. 1

We consider an inventory system under continuous review with two demand classes that are different in terms of service level required (or penalty cost incurred for backordering of demand). Prior literature has proposed the critical level rationing (CLR) policy under which the demand from the lower priority class is backordered once inventory falls below the critical level. While this reduces the penalty cost for the higher demand class, the fill rate achieved for the lower priority demand class gets compromised. In this study, we propose a new class of two‐bin (2B) policy for the problem. The proposed 2B policy assigns separate bins of inventory for the two demand classes. The demand for each class is fulfilled from its assigned bin. However, when the bin intended for the higher demand class is empty, the demand from the higher class can still be fulfilled with the inventory from the other bin. The advantage of the 2B policy is that better fill rates are achieved, especially for the lower demand class. Computational results show that the proposed policy is able to provide a much higher service level for the lower priority class demand without increasing the total cost too much and without affecting the service level for the higher priority class. When a service level constrained optimization problem is considered, the 2B policy dominates the CLR policy when the service level difference for the two classes is not too high or the service levels required for both the classes are relatively lower.

Dynamic repair priority rule based on remaining useful life predictions

To improve the inventory management system in spare-part business. The author studied how to improve inventory management in automotive spare-part business. Seven steps of inventory management system for this research are conducted to solve problems in ABC Company as poor storage space utilization, large number of stocks and high inventory costs. Warehouse management and inventory record system improvement are required for solving warehouse problems and more accuracy of stocks. Then, inventory policy is set to decide which part and when they should start to stocks. Trend of spare parts is another point to study trend of demand for demand forecasting. This research also presents how to select the suitable techniques for forecasting, and example of forecast demand in the next year. Optimal order quantity is also computed for appropriated replenishment order. Finally, dead stocks and sleeping stocks will be managed to improve storage space area and reduce inventory cost. From the proposed systems, the result for inventory management system involves total inventory costs reduction of the example spare parts around 64.7% from actual system with trends of spare part demands analysis and more storage space area is also benefit from the system.

On the tradeoff between optimal order-base-stock levels and demand lead-times

A retailer or distributor of finished goods, or the manager of a spare-parts inventory system, must generally forecast the major portion of demand. A specific customer-service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum-cost investment in inventory. The pth fractile of lead-time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order-statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order-statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order-statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order-statistic method. © 1994 John Wiley & Sons, Inc.

Import companies operating in the globalized market and in a multi-item context are frequently faced with the need of aggregating their orders to benefit from scale economies associated to the use of containers for freight shipping. We introduce the problem of optimal replenishment order placement, namely the problem of scheduling and aggregating a fixed number of replenishment orders, along a given planning horizon, with the aim of minimizing the total inventory and backorder costs. For this problem, a continuous optimization formulation is provided, which is characterized by a nonconvex piecewise affine objective function. We introduce an ad hoc algorithm, based on the coordinate search approach, for the approximate numerical solution of the continuous model, and present the numerical results obtained on a set of randomly generated instances. In order to evaluate the quality of solutions returned by the algorithm, a discrete formulation of the problem is also provided, which falls into the well-known class of uncapacitated location models of the p-median type, whose exact solution on the same instance set can be obtained by means of an integer programming commercial solver.

Traditional inventory systems treat all demands of a given item equally. This approach is optimal if the penalty costs of all customers are the same, but it is not optimal if the penalty costs are different for different customer classes. Then, demands of customers with high penalty costs must be filled before demands of customers with low penalty costs. A commonly used inventory policy for dealing with demands with different penalty costs is the critical level inventory policy. Under this policy demands with low penalty costs are filled as long as inventory is above a certain critical level. If the inventory reaches the critical level, only demands with high penalty costs are filled and demands with low penalty costs are backordered. In this article, we consider a critical level policy for a periodic review inventory system with two demand classes. Because traditional approaches cannot be used to find the optimal parameters of the policy, we use a multidimensional Markov chain to model the inventory system. We use a sample path approach to prove several properties of this inventory system. Although the cost function is not convex, we can build on these properties to develop an optimization approach that finds the optimal solution. We also present some numerical results. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

This paper discusses an inventory rationing system with a threshold in a relatively stable inventory demand environment. There are two different demand classes in this inventory system, prior demand and secondary demand, distinguished by different shortage cost. The inventory system functions as follow. When the inventory level is above the threshold, demands come from both classes are filled. Once the inventory level falls below the threshold, all demands come from secondary demand class are backordered, only prior demand would be served. Heuristic approach was used to solve the model in this paper, and the optimal order quantity, single inventory cycle time and inventory threshold were given. Compare between inventory system with and without inventory threshold shows the cost advantage of the first system. Sensitivity analysis was performed to give a better understanding of two crucial parameter, inventory threshold and cost saving rate.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

An inventory system is operated as a base stock system under a compound Poisson demand process. Besides having inventory and backorder costs, also a cost is incurred for each order that is delivered in several pieces to the customer (irrespective of whether some items in the order are delivered on time, or whether they are all delivered late but at different times). The possible split deliveries are assumed to happen automatically, meaning that there cannot at the same time be a positive on-hand inventory and a positive backlog. We develop a mathematical cost expression for this system to be optimized, denoted Model 1. We compare Model 1 to another model, denoted Model 2, where it is forbidden to make any of these split deliveries; thus at the same time, there can be a positive on-hand inventory and a positive backlog. We compare Model 2 to the standard textbook model, denoted Model 0, where split deliveries occur automatically and are costless. Thereby, we address a claim made by Zipkin (Foundations of inventory management. McGraw-Hill, Boston, 2000). We also examine the threshold value for the delivery split cost, which makes Model 1 and 2 perform equally well, and we examine how this threshold value depends on the other common parameters of the models.