Continuous Review Inventory System Research Articles

Leadtime reduction in a [formula omitted] inventory system: An agency perspective

We examine the problem of designing and implementing a continuous-review ( Q , r ) inventory system from an agency perspective, in which the agent's effort influences the item's replenishment leadtime. Our results are as follows: if the agent is risk-neutral, a linear or quadratic contract achieves first-best. For a risk-averse agent with an exponential utility function, assuming a normal leadtime distribution, we determine the optimal linear contract. Extensive numerical experiments suggest that ignoring the possible influence of the agent on the replenishment leadtime can be costly, but that the cost penalty of ignoring agency can be significantly reduced by a simple contract.

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.

Numerical analysis of(s, S) inventory systems with repeated attempts

This paper deals with a continuous review (s,S) inventory system where arriving demands finding the system out of stock, leave the service area and repeat their request after some random time. This assumption introduces a natural alternative to classical approaches based either on lost demand models or on backlogged models. The stochastic model formulation is based on a bidimensional Markov process which is numerically solved to investigate the essential operating characteristics of the system. An optimal design problem is also considered.

BATCH DETERMINISTIC AND STOCHASTIC PETRI NETS: MODELLING, ANALYSIS AND APPLICATION TO INVENTORY SYSTEMS

We recently introduced a new stochastic Petri net model called “batch deterministic and stochastic Petri nets” (BDSPNs) capable of describing the synchronization of discrete and batch token flows in discrete batch processes. It is a powerful formal model for the study of inventory systems and supply chains where materials are processed or ordered in finite discrete quantities (batches) and many operations such as inventory replenishment, manufacturing and distribution are usually performed in a batch way because of the batch nature of customer orders and/or in order to take advantages of the economies of scale. In this paper, the modelling and analysis powers of the model are demonstrated through inventory systems. We show particularly how to model and evaluate the performance of a continuous review (s, S) inventory system with stochastic and batch demand using BDSPNs.

A multi-product continuous review inventory system with stochastic demand, backorders, and a budget constraint

Common characteristics of inventory systems include uncertain demand and restrictions such as budgetary or storage space constraints. Several authors have examined budget constrained multi-item stochastic inventory systems controlled by continuous review policies without considering marginal shortage costs. Existing models assume that purchasing costs are paid at the time an order is placed, which is not always the case since in some systems purchasing costs are paid when orders arrive. In the latter case the maximum investment in inventory is random since the inventory level when an order arrives is a random variable. Hence payment of purchasing costs on delivery yields a stochastic budget constraint for inventory. This paper models a multi-item stochastic inventory system with backordered shortages when estimation of marginal backorder cost is available, and payment is due upon order arrival. The budget constraint can easily be converted into a storage constraint.

Inventory System Subject to Disaster with General Interarrival Times

We discuss a single commodity continuous review (s, S) inventory system in which commodities get damaged due to external disaster. Shortages are not permitted and lead time is assumed to be zero. The interarrival times of demands constitute a family of i.i.d. random variables with a common arbitrary distribution. The quantity demanded at a demand epoch is arbitrarily distributed which depends only on the time elapsed since the last demand epoch. Transient and steady state probabilities of the inventory levels are derived by identifying suitable semi-regenerative process. In the case when the demand is for unit item and the disaster affects only an exhibiting item, the steady state probability distribution is obtained as uniform. An optimization problem is discussed and numerical examples are provided.

A Two-Commodity Stochastic Inventory System with Lost Sales

This paper considers a two commodity continuous review inventory system with fixed individual and joint reorder level. The maximum storage capacity for the ith commodity is fixed as S i (i = 1, 2). It is assumed that demand for ith commodity is of unit size and has Poisson distribution with parameter λ i (i = 1, 2). The independent reorder level for ith commodity is fixed as r i and whenever the inventory level of ith commodity falls on r i an order for P i (=S i − r i ) i = 1, 2 items is placed for that commodity irrespective of the inventory level of the other commodity. A joint inventory level s (<min(r 1, r 2)(x + y = s, x = 0, 1,…, s, y = 0, 1,…, s) is fixed for both commodities whenever the inventory level drops to a prefixed level s, an order for and items is placed for both commodities. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illustrated with numerical examples.

Optimal design of a heuristic inventory model

This study proposes the stochastic inventory mathematical model for the continuous review inventory systems under simultaneously taking account to the controllable lead time and time value of money. In the model, the shortages are allowed and the total amount of stockout during the stockout period is considered to be a mixture of backorders and lost sales. In this paper, we consider the case of the lead time demand follows a normal distribution, and then use the DCF approach procedure to solve the optimal solution. We also develop an algorithm to obtain the optimal ordering strategy for each case (the lead time demand follows normal distribution or distribution free). Furthermore, for all models proposed in this paper, the effects of parameters are also included.

A continuous review inventory model with order expediting

In this paper we consider a continuous review inventory system in which the lead time L includes a part of fixed duration, T, and a part whose duration can be either T a or T e , where T a > T e . When the net inventory reaches the reorder point r, an order of size Q is released. If the net inventory at time T after the order release is equal to or smaller than r e , the order is expedited at a cost comprising a fixed cost and a cost per unit and the lead time is L= T+ T e , otherwise the lead time is L= T+ T a . Therefore, the decision variables considered are the order quantity Q, the reorder point r and the order expediting point r e . Our aim is to find the inventory policy variables Q, r and r e that minimize the average cost rate. We present an algorithm to obtain the policy variables with global minimal costs when the inventory policy decision variables are integers. We also discuss the case in which the decision variables are real valued.

A replenishment model for the supply-uncertainty problem

We consider a continuous-review inventory system with compound Poisson demand, hyperexponentially distributed lead time, and lost sales where the supply process may be randomly interrupted depending on the availability of a supplier. It is assumed that the supplier's availability can be modeled as an alternating renewal process in which the on and off periods are independent random variables following general and hyperexponential distributions, respectively. We present an exact formulation of the long-run average cost rate function based on deriving the stationary distribution of the on-hand inventory, and provide some numerical results.

Optimal ordering policies and capital investment in setup reduction for continuous review inventory system with random yields

In existing production/inventory models with random yields, the setup cost is given and fixed. However, in many practice situations, they can be reduced by investment in modern production technology. In this study, we attempt to determine the optimal capital investment in setup cost reduction for (Q, r) inventory system, jointly with the optimal ordering policies. We assume that the setup cost is the function of capital expenditure. Furthermore, we show that the expected total annual cost function with capital investment is convex. With the convexity, an algorithm is developed to determine the optimal order quantity and reorder point, and then to find the optimal setup cost. Finally, numerical results are presented to illustrate the algorithm procedure and compared to the results without considering capital investment. Our results evidently show that substantial cost saving might be obtained through capital investment in setup reduction.

Multiple replenishment orders in a continuous-review inventory system with lost sales

For a continuous-review inventory system with lost sales, non-unit-sized demand, multiple replenishment orders outstanding, and split deliveries, we derive the stationary distribution of the on-hand inventory using a level-crossing methodology. This distribution is then used to formulate an exact expression for the long-run average cost per unit time. Some numerical results are also presented.

Supply interruptions in a lost-sales inventory system with random lead time

This paper presents an analytical model for computing the stationary distribution of the on-hand inventory in a continuous-review inventory system with compound Poisson demand, Erlang distributed lead time, and lost sales, where the supplier can assume one of the two “available” and “unavailable” states at any point in time according to a continuous-time Markov chain. Exact analytical expressions are derived for the special case where demand sizes are exponentially distributed, and some cost minimization numerical results are presented. Scope and purpose One of the main factors that greatly influence the efficiency of every production and/or inventory control operation in a highly competitive environment is the reliability of its supply process. Many organizations, due to various reasons ranging from equipment breakdowns to political crises, are often faced with the challenge of managing their inventories in the presence of randomly occurring supply interruptions. The significance of modeling such interruptions is undoubtedly due to the severity of their potential negative impacts on the customer service level and the operating cost of virtually every supply chain in today's business market. The problem has motivated a considerable body of research in recent years. However, within the context of inventory control theory, very little has appeared in the literature that focuses on the issue of random supply interruptions in inventory systems with non-zero replenishment lead times, owing to the inherent analytical complexity of such systems. The main purpose of this work is to expand some of our earlier research findings in lost-sales inventory systems with variable lead times to address the supply interruption problem in a similar setting.

Stocking Decisions for Low-Usage Items in a Multilocation Inventory System

This research shows that organizations with a number of “sister” plants, warehouses, or other stocking points can profit from the concept of proactive use of transshipments as an element of their inventory control policy. For certain types of parts, employing transshipments can significantly reduce the total inventory needed throughout the entire collection of stocking points. The study is motivated by a real-life situation involving a large utility company having 29 power-generating plants in five Southeastern states where there are thousands of parts that are commonly used at multiple plants. At present, each plant operates independently and maintains enough stock to meet its own requirements. Transshipments take place between plants whenever there is an emergency requirement for a part, but no explicit consideration is given to this effect while deciding on stocking levels at different plants. In the case we examined, by setting stocking levels to explicitly take account of transshipments, total system cost could be reduced by about 70% over the company's decentralized policy. In general, this work considers a single-echelon, N-location, continuous-review inventory system in which complete pooling of stock is permitted among the locations. A model is developed for slow-moving, expensive, and consumable parts that are common to two or more locations. A one-for-one ordering policy and queueing theory allow development and solution of a system of equations for the probability distribution of net inventory at each location. A heuristic procedure is also developed to determine cost-effective stocking levels. Actual data from the utility company are used to demonstrate the applicability of the model. Savings achieved as a result of pooling are reported.

Computing the Optimal Replenishment Policy for Inventory Systems with Random Discount Opportunities

The paper considers the optimal control of a single-item continuous-review inventory system with random demand and discount opportunities. Items can always be purchased with the regular order setup and variable costs. However, when a discount opportunity occurs, they can also be purchased with a different setup cost and a lower variable cost. Demands for individual items and discount opportunities occur according to independent Poisson processes. The paper proposes an algorithm to compute the parameters of the optimal replenishment policy, which has been shown to be an (r, R, d, D) policy where r &lt; R, r ≤ d, and d &lt; D. Under an (r, R, d, D) policy, when the inventory position drops to the level r, an order is placed with the regular costs to increase the inventory position to R; and when a discount opportunity occurs at or below d, an order is placed with the discount costs to increase the inventory position to D. The algorithm is based on a bisection search procedure to minimize the long-run average cost and is finitely convergent.

A Stochastic Inventory Model for Deteriorating Items with Random Supply Quantity

In this paper, we consider a continuous review (s,S) inventory system with stochastic demand for deteriorating item. The replenishinent quantity is assumed to be random. To accommodate more general situations the demand is assumed to be dependent on the inventory level. Explicit expressions for the steady state probabilities and the system measures, are derived. The optimal values of the decision variables, i.e., S and s, are obtained. Numerical examples are provided to illustrate the theoretical development.

Analysis of two commodity Markovian inventory system with lead time

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity is fixed asSi (i = 1,2). The net inventory level at timet for the i-th commodity is denoted byIi(t),i = 1,2. If the total net inventory levelI(t) =I1(t) +I2(t) drops to a prefixed level\(s[ \leqslant \tfrac{{(S_1 - 2)}}{2}or\tfrac{{(S_2 - 2)}}{2}]\), an order will be placed for (Si −s) units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.

A multi-item continuous review inventory system with compound Poisson demands

In this paper, we consider a multi-item continuous review inventory system with compound Poisson demands under a general cost structure. Excess demand is backlogged and a fixed delivery lag is assumed. A new algorithm for computing an exact optimal policy is derived based upon the policy iteration method (PIM) using properties of the optimal policy. This algorithm reduces substantially computation times in both the policy evaluation and the policy improvement routines of the PIM. In fact, numerical examples show that the computation times of the new algorithm are less than three percent of those of the PIM. Moreover, three joint ordering policies – the (s, c, S), the (R, T) and the (Q, S) policies – are compared with the optimal ordering policy computed by the new algorithm. It is shown that the (Q, S) policy is almost best among the three joint ordering policy and gives more than ten percent higher expected cost rate than the optimal ordering policy.

Order splitting under periodic review inventory systems

Most research on order splitting have focused on the reduction of safety stock in the multiple sourcing setting. Moreover, all works study the use of order splitting for the continuous review inventory systems. In this paper, we investigate the possibility of the multiple-delivery arrangement in the sole sourcing environment. In addition, we concentrate on the reduction of cycle stock for periodic review systems. We show that splitting an order into multiple deliveries can significantly reduce the total cost especially if the cost of despatching an order for an item is not small. Although the use of information technology such as EDI decreases the ordering cost and thus shortens the period length, order splitting remains a cost-effective approach as long as the cost of despatching an order is not close to zero.

An improved ordering policy for continuous review inventory systems with arbitrary inter-demand time distributions

In this paper, we revisit the optimality of (s,S) policies in continuous review inventory models where demand forms a renewal process. We explain why when orders are placed at demand epochs, (s,S) policies are not optimal in general, and propose a simple but practical ordering policy by introducing a delay in order placement as a policy parameter. Under our proposed policy, the operating characteristics of such systems can be evaluated using the existing results in the literature. In order to demonstrate the effectiveness of our policy, we restrict our analysis to a special class of inventory systems where demand follows a counting process, fixed ordering costs are negligible and leadtimes are constant. We derive expressions for the operating characteristics of such systems under our policy and present insights on the behavior of the policy parameters which minimize the average total cost rate under our policy. Using these results, we develop an efficient heuristic for computing the policy parameters. Finally, we investigate the effectiveness of our policy in comparison to policies which place orders only at demand epochs. The results of our numerical experiment indicate that our policy can result in a significant savings.