On continuous review stochastic (s, S) inventory systems with ordering delays

In this paper a continuous review (s, S) inventory system with ordering delays is considered. Demands for the item arrive according to a Poisson process. When the inventory level drops to s, the order is triggered. However, due to an unavoidable delay, the order is actually placed after a random amount of time. Once the order is placed, it is instantaneously delivered bringing the inventory level back to S. Under a cost structure which includes a setup cost, a holding cost and a penalty cost, an expression for the expected cost per unit time for given control values is obtained. Then some properties of the cost functions are developed to characterize the optimal policy. Based on these properties, an efficient search procedure to find the optimal (s, S) policy is presented.     

A continuous review inventory model with the controllable production rate of the manufacturer

Optimal operating policy in most deterministic and stochastic inventory models is based on the unrealistic assumption that lead‐time is a given parameter. In this article, we develop an inventory model where the replenishment lead‐time is assumed to be dependent on the lot size and the production rate of the manufacturer. At the time of contract with a manufacturer, the retailer can negotiate the lead‐time by considering the regular production rate of the manufacturer, who usually has the option of increasing his regular production rate up to the maximum (designed) production capacity. If the retailer intends to reduce the lead‐time, he has to pay an additional cost to accomplish the increased production rate. Under the assumption that the stochastic demand during lead‐time follows a Normal distribution, we study the lead‐time reduction by changing the regular production rate of the manufacturer at the risk of paying additional cost. We provide a solution procedure to obtain the efficient ordering strategy of the developed model. Numerical examples are presented to illustrate the solution procedure.     

A continuous review inventory model with controllable backorder rate and investments

In this study, we investigate a continuous review inventory model to reduce lead time, yield variability and setup cost simultaneously through capital investments. We assume that the backorder rate is depending on the length of the lead time through the amount of shortages. We also assume that lead time demand's distribution is not known but its first and second moments are known. We apply minimax distribution free procedure to minimise the expected total annual cost. By using logarithmic investment function we describe the relationship between the reduction in lead time, yield variability and setup cost with capital investment. This function was used in many existing models. Our main aim is to determine the optimal capital investment and ordering policies that minimises the expected total annual cost. To find out the optimal solution, an algorithm is given. With the help of this algorithm, optimal capital investment and ordering policies are wrought out. Numerical examples are given to elucidate the model. Our proposed model greatly differs from the model existing in the literature (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])) viz: (1) In the above model, yield variability and setup cost were reduced through capital investment. In our model we reduce yield variability setup cost and also the lead time, which plays a vital role in any business. By reducing lead time we can improve the service level to the customer so as to increase the competitive edge in business. (2) In the model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), it was assumed that lead time demand follows normal distribution. But in our model we take the distribution of lead time demand as distribution free. That is, it can follow any distribution which is more general. (3) In the above model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), shortages are completely backlogged. But we consider partial backlogging and take the backlogging rate as 0 ≤ B ≤ 1. If we set backlogging rate B = 1 we get the above model. That is, the above model is particular case of our model. (4) We also assume that the backorder rate depends on the length of the lead time through the amount of shortages. If the lead time is longer then shortage accumulation is higher. The patience of customers will result in failure in business since some customers may turn to some other supplier. Hence, the backorder rate will be reduced. This assumption is very realistic.     

Multi-item-multi-plant inventory control of production systems with shortages/backorders

A multi-item model of a production-inventory system incorporating deterioration, shortages and capacity/budget constraints is considered. An optimal control policy for the model is developed using linear quadratic (LQ) theory for the case of deterministic demands. The problem of controlling large-scale production-inventory facilities is also considered, and the interaction prediction method is used to develop optimal policies. Results of simulations show that using the developed policy, any desired inventory levels can be maintained while minimizing costs and satisfying demand without violating capacity constraints.     

The production size and inventory policy for a manufacturer in a two-echelon inventory model

This paper proposes a two-echelon inventory model for a periodical commodity, in which the market and manufacturing channels are combined. This model can be used to solve the production policy, the order policies of the raw materials for the manufacturer, and order size for the retailer. By assuming that the retailers’ demand obeys normal distribution and that the retailer makes orders according to the Newsboy Rule, we derive the necessary and sufficient conditions for the optimal solution of production size, wholesale price, and replenishment cycle of raw materials for the manufacturer. Also, the necessary condition is explored in order to gain managerial insights and economic implications based on numerical examples and sensitivity analysis.     

An integrated replenishment and production control policy under inventory inaccuracy and time-delay

Inventory inaccuracy has a significant negative impact on the performance of raw materials replenishment and production control. It usually leads to high inventory holding cost or large backlog penalty. To hedge against it, we investigate a replenishment and production control problems for a multiple machines and multiple product-types production/inventory system with inventory inaccuracy. The objective is to minimize the average production cost, including the inventory holding cost and the backlog penalty. In addition to inventory inaccuracy, the lead-time of raw materials replenishment and the unreliability of machines are also taken into consideration. In light of the principle of dynamic programming, a simplified optimal replenishment and production control policy is constructed based on the assumption that the records of inventories are completely accurate. To overcome the shortcomings of the simplified policy in hedging against inventory inaccuracy, a conditional expectation-based replenishment and production control policy is developed based on the fundamental structure of the simplified optimal replenishment and production control policy, and the conditional probability of the physical inventory level. Numerical experiments are conducted to examine the performance of the proposed policy for hedging against inventory inaccuracy, and sensitivity analysis is carried out to study how the parameters of the production/inventory system and the proposed policy affect the average production cost.     

Multiproduct production/inventory control under random demands

Studies the optimal production/inventory control policy for a single machine multiproduct production system. The machine produces to fill the end-product inventory stock and the demand is satisfied from the inventory when available; unsatisfied demand is backlogged until the product becomes available as the result of production. For each product, the demand follows a Poisson process and the unit processing time is known. When the machine switches production from one product to another, it incurs a set-up time and a set-up cost. The relevant costs include the set-up cost, a cost per unit time while the machine is running, and linear costs for inventory and backlogging. This problem is modeled as a semi-Markov decision process using the criterion of minimizing expected total cost with discounting over an infinite horizon. Procedures for computing near-optimal policies and their error bounds are developed. The error bound given by the authors' procedure is shown to be much tighter than the one given by the “norm-based” approach. Computational test results are presented to show the structure of the near-optimal policy and how its accuracy is affected by the system characteristics such as capacity utilization and set-up time     

可控前置时间的连续盘点联合库存策略研究

鉴于控制前置时间对精益生产系统的重要性,在考虑买方与卖方合作的同时,扩展Goyal生产批量交货的假设,假设需求服从正态分布,以订购数量、运送次数与前置时间为决策变量,建立前置时间可控制的联合库存模型以确定适当的库存水平,使得库存总成本最小化,且可以通过协商在买卖双方之间进行节省成本的分配。进行了数值范例,并将联合库存模型与Banerjee模型、Goyal模型进行了比较。     

The distribution free continuous review inventory system with a service level constraint

The stochastic inventory models require the information on the lead time demand. However, the distributional information of the lead time demand is often limited in practice. We relax the assumption that the cumulative distribution function, say F, of the lead time demand is completely known and merely assume that the first two moments of F are known and finite. The distribution free approach for the inventory model consists of finding the most unfavorable distribution for each decision variable and then minimizing over the decision variable. We apply the distribution free approach to the continuous review inventory system with a service level constraint. We develop an iterative procedure to find the optimal order quantity and reorder level.     

A production/remanufacturing inventory model with price and quality dependant return rate

Inventory management of produced, remanufactured/repaired and returned items has been receiving increasing attention in recent years. The available studies in the literature consider a production environment that consists of two shops. The first shop is for production and remanufacturing/repair, while the second shop is for collecting used (returned) items to be remanufactured in the first shop, where demand is satisfied from producing new and from remanufacturing/repairing returned items. Numerical and analytical results from these developed models suggested that a pure (bang–bang) policy of either no waste disposal (total remanufacturing) or no remanufacturing (pure production and total disposal) is the best strategy, while the mixed strategy (a mixture of production and remanufacturing) is the optimum case under certain limited assumptions. In practice, the quality of the returned items and the purchasing price that reflects this quality is what usually governs a collection (or return) policy of used items. Unlike those available models in the literature, this paper suggests that the flow of returned items is variable, and is controlled by two decision variables, which are the purchasing price for returned items corresponding to an acceptance quality level. Deterministic mathematical models are presented for multiple remanufacturing and production cycles.     

A review of stochastic algorithms with continuous value function approximation and some new approximate policy iteration algorithms for multidimensional continuous applications

We review the literature on approximate dynamic programming, with the goal of better understanding the theory behind practical algorithms for solving dynamic programs with continuous and vector-valued states and actions and complex information processes. We build on the literature that has addressed the well-known problem of multidimensional (and possibly continuous) states, and the extensive literature on model-free dynamic programming, which also assumes that the expectation in Bellman’s equation cannot be computed. However, we point out complications that arise when the actions/controls are vector-valued and possibly continuous. We then describe some recent research by the authors on approximate policy iteration algorithms that offer convergence guarantees (with technical assumptions) for both parametric and nonparametric architectures for the value function.     

Lot-sizing in a class of multistage production inventory systems

In this paper, a mathematical model for a multistage multifacility and multiproduct production inventory system is presented. The basic objective of the model is to determine the economic production quantity (EPQ) for each product-stage-facility combination by minimizing total system cost. The total system cost consists of the set-up cost and the in-process inventory carrying cost. A numerical example is solved to explain the model; a search method has been used for the optimization. The results obtained are compared with the simulation results to validate the mathematical model.     

Optimization models for flow-line production systems with in-process inventory

In this paper, two optimal buffer capacity models are developed for non-mechanical flow lines where the service time variability is described by a defined probability density function. An example is given to illustrate the theory, and sensitivity analysis is also performed to evaluate the effects of changes in the values of the system parameters on buffer capacity. Numerical comparisons are made with the results obtained using approaches developed by other researchers.     

Integrated inventory and production policy for manufacturing with perishable raw materials

Annals of Mathematics and Artificial Intelligence - This research investigates an integrated inventory and production scheduling problem (IIPSP) in a manufacturer that deals with the perishable...     

Optimal ordering and production policy for a recoverable item inventory system with learning effect

This article presents two models for determining an optimal integrated economic order quantity and economic production quantity policy in a recoverable manufacturing environment. The models assume that the unit production time of the recovery process decreases with the increase in total units produced as a result of learning. A fixed proportion of used products are collected from customers and then recovered for reuse. The recovered products are assumed to be in good condition and acceptable to customers. Constant demand can be satisfied by utilising both newly purchased products and recovered products. The aim of this article is to show how to minimise total inventory-related cost. The total cost functions of the two models are derived and two simple search procedures are proposed to determine optimal policy parameters. Numerical examples are provided to illustrate the proposed models. In addition, sensitivity analyses have also been performed and are discussed.     

Production rate control for failure-prone production systems withno backlog permitted

In this paper, we consider systems in which backlog is not allowed. We show that the hedging point policy is still optimal. For systems with backlog, it is usually quite straightforward to show that their optimal cost-to-go functions are convex-a key property that is needed for the hedging point policy to be optimal. With no backlog permitted, it becomes much more difficult to establish the convexity property, and the explicit formulas for the optimal hedging point and the optimal cost-to-go functions have to be obtained, based on which the convexity property can then be verified. The method we use in this paper to derive these explicit formulas is mainly based on an interesting relationship between the inventory process of the system under the hedging point policy and some stochastic processes which are well studied in queueing theory     

Optimal policy for set-up time reduction in a multistage production inventory system

A batch production-inventory system consisting of multiple stages with an optimal policy of set-up time reduction and a fixed increment cost are discussed. The ratio of set-up time reduction as a decision variable under various cases of demand in the batch production-inventory model is considered. The ratio of set-up time reduction and lot size are solved simultaneously to obtain an optimal value of the total annual cost. A numerical example is presented to demonstrate the accuracy of the proposed method.     

Covariance control with variance constraints for continuous perturbed stochastic systems

This paper proposes an approach which deals with the variance constraints for the perturbed stochastic systems. The purpose of this approach is to develop a novel methodology, which is based on the theory of covariance control, to solve the constrained variance design problem for the linear perturbed stochastic systems. Particular attention is paid to the case in which there are only uncertain perturbations in the state dynamic matrix. Moreover, an example is given to illustrate the power of the technique.     

Critical number ordering policy for LIFO perishable inventory systems

This paper considers a stochastic perishable product inventory system characterized by LIFO (Last-In-First-Out) issuing, critical number ordering and a two-period lifetime. Exact and approximate closed form expressions for expected outdates are derived. The approximation, which is straightforward to compute, is shown to be accurate over a wide range of model parameters. The paper concludes by comparing optimal policies and expected costs in the LIFO system with the corresponding policies and costs in a system controlled by FIFO (First-In-First-Out) issuing.     

An inventory model with Weibull demand rate,finite rate of production and shortages

We develop here an inventory model with time-dependent two-parameter Weibull demand rate, allowing shortages in the inventory. The shortages are completely backlogged. The production rate is assumed to be finite and proportional to the demand rate. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. Sensitivity of the optimal solution with respect to changes in the values of the system parameters is also studied. Special features of time-dependent Weibull demand rate are discussed.