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.     

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.     

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     

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.     

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...     

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     

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.     

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.     

Modeling rule-based systems by stochastic programmed production systems

A new tool, the stochastic programmed production system (SPPS), is proposed for representing rules and control mechanisms in rule-based systems. This approach is based on the stochastic programmed grammars, and its peculiarity is both its well-formalized semantics and its ability to represent most reasoning and control methods used in expert systems today. Since the proposed method is not limited by the particular heuristic organization of the rule-based system it is modeling, the SPPS is more general than existing knowledge-domain-independent expert-system development languages and may help bring a better understanding of the theory of expert systems.     

Adaptive predictive control policy for nonlinear stochastic systems

The problem of optimal adaptive predictive control for nonlinear stochastic systems is considered. A classification of various suboptimal approaches is given. A new approximation for the probability measure for the extended state of the system is suggested to derive a new suboptimal control law. It is assumed for this approximation that the system operates in closed-loop feedback mode for one part of the extended state vector and in open feedback loop mode for the other part of this vector. The certainty equivalence (CE) assumption is used only for the first part of the extended state vector. An analytical comparison for the suggested control policy shows its superiority in control quality compared with that of the open-loop optimal control policy in the case of an exactly observed first part of the extended state vector. The upper bound of the performance index is determined for this case. The suggested control policy has a simple form for linear systems with unknown parameters. A simulated example is used to demonstrate the potential of the suggested method and its superiority over the usually applied CE policy     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

Optimal observers for continuous time linear stochastic systems

In the past, a major objection to application of the well known solution to the linear stochastic optimal control problem has been that the complexity, or dimension, of the solution exceeds that which is necessary for satisfactory feedback control. For a system described by n first order linear differential equations excited by white noise, the solution requires a filter of dimension n. If non white noise sources excite the system, an even higher dimensional filter is required. This paper presents a technique which alleviates the above objection. A recursive algorithm similar to the Kalman filter algorithm is presented which permits design of a reduced order linear estimator to replace the well known Kalman filter. The new estimator, called an observer, is stochastically optimal subject to its reduced order dimensionality constraint, but its performance is not as good as a full Kalman filter. The observer algorithm is general in that it applies to time variable, multivariable systems. A minimum order = n ? m₁ exists for the observer. Here n = state dimension and m₁ = dimension of the non white measurement. Non white noise sources of any order q may exist and need not contribute to the dimension of the optimal observer. Optimal observers of all orders between n ? m₁ and n ? m₁ + q may be designed, the latter case being a Kalman filter. Detailed examples are given to illustrate the theory.     

Two inventory systems with trapezoidal-type demand rate and time-dependent deterioration and backlogging

The demand rate for seasonable/fashionable products, in general, fluctuates through their life cycle, initially increases during the growth phase, then remains practically constant in the maturity phase, and finally decreases in the decline phase. Consequently, their demand rate can be reasonably depicted by a trapezoidal-type pattern, which includes constant, increasing, decreasing and ramp-type demand patterns as special cases. Recently, inventory models for deteriorating items with trapezoidal-type demand have been developed to minimize the total cost over the planning horizon (see Cheng & Wang, 2009; Skouri & Konstantaras, 2009; Cheng et al., 2011; Lin et al., 2014). However, in these models the purchasing cost is excluded from the total cost. As a result, this implies an underestimation of the lost sales cost. In the present paper, previous studies regarding inventory models with trapezoidal-type demand rate are extended and completed by (1) discussing two inventory systems starting with and without shortages, (2) including the purchasing cost into the total cost, (3) extending the deterioration rate to any time-varying rate, (4) taking into consideration the time value of money (5) maximizing the net present value of total profit. Therefore, many previous inventory models become special cases of the present model.     

On the optimality of output inventory decisions of a firm under imperfect stochastic markets

A class of suboptimal strategies in price, output and inventories is proposed for a firm in imperfectly competitive stochastic markets. When the demand faced is incompletely known and inventories are held partly as a buffer against fluctuations in demand, and partly as active decision variables, the solution is characterized by maximizing expected profits over two periods with an additive error in the demand function having a known prior density. Simulations of the solution profiles show that for the two-period moving horizon model proposed here, the variance of profits and revenues are sharply reduced, a feature that is most attractive for a risk averse firm.     

Observer design for discrete and continuous non-linear stochastic systems

An observer design methodology that is applicable to a general class of non-linear stochastic system and measurement models is given. It is proved that, under the conditions given, discrete- and continuous-time state estimation is possible with guaranteed exponential rate of convergence. The superior performance of the observer is illustrated with two examples.