Random Lead Time Research Articles

Modeling and Analyzing a Joint Optimization Policy of Block-Replacement and Spare Inventory With Random-Leadtime

We consider a generalized joint optimization policy of block replacement & periodic review spare inventory with random lead time. According to the relationship between geometric area in the graph of inventory level over time, and holding or shortage costs, a model analyzing four mutually exclusive & exhaustive possibilities is developed for the expected average cost per unit time, and is based on the stochastic behavior of the assumed system. The model reflects the cost of inventory holding, spare shortage, replacement, and ordering. And for the first time known to the authors, we deliver the sufficient and necessary conditions of the existence and uniqueness of the minimum in the joint models of this type. Because the model and its analysis are general, one existing result is shown to be subsumed by this model with some modifications. Some numerical cases verify the deduction, and give a general searching solution procedure. Finally, we introduce some discussions related to the models. The models mentioned in the paper can be readily applied in many fields such as economical fields, financial engineering, armament administration, and even medical fields, with some modifications. And the mathematical deduction in the paper will be a guideline for analyzing related stochastic models.

On stochastic lot-sizing problems with random lead times

We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in the scenario tree size, when orders do not cross in time.

Supply chain coordination: A game-theory approach

In a supply chain organized as a network of autonomous enterprises, the main objective of each partner is to optimize his production and supply policy with respect to his own economic criterion. Conflicts of interests and the distributed nature of the decision structure may induce a global loss of efficiency. Contracts can then be used to improve global performance and decrease risks. The purpose of the paper is to evaluate the efficiency of different types of contracts between the industrial partners of a supply chain. Such an evaluation is made on the basis of the relationship between a producer facing a random demand and a supplier with a random lead-time. The model combines queuing theory for evaluation aspects and game theory for decisional purposes.

Continuous review inventory model in mixed fuzzy and stochastic environment

In this paper, we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting. Since demand plays an important role in such type of inventory systems, we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand. After fuzzifying the random lead-time demand we consider the annual average demand as a fuzzy random variable. We provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value. Since the expected value of a fuzzy random variable is a fuzzy quantity, a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution. A numerical example is presented to illustrate the proposed model.

Queueing systems with inventory management with random lead times and with backordering

We investigate M/M/1/∞-systems with inventory management, continuous review, exponentially distributed lead times and backordering. We compute performance measures and derive optimality conditions under different order policies. For performance measures, which are not explicitly at hand, we present an approximation scheme for all possible parameter combinations. Although we cannot completely determine analytically the steady state probabilities for the system we are able to derive functional relations between interesting probabilities and show surprising insensitivity properties of several performance measures. For the approximations we develop an algorithm adapted to the system structure which suggests easy adaption to other systems.

Minimizing the bullwhip effect in a supply chain using genetic algorithms

This paper presents a computational intelligence approach, which addresses the bullwhip effect in supply chains (SCs). A genetic algorithm (GA) is employed to reduce the bullwhip effect and cost in the MIT beer distribution game. The GA is used to determine the optimal ordering policy for members of the SC. The paper shows that the GA can reduce the bullwhip effect when facing deterministic and random customer demand combined with deterministic and random lead times. The paper then examines the effect of sales promotion on the ordering policies and shows that the bullwhip effect can be reduced, even when sales promotions occur in the SC.

Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand

This article considers the mixture inventory model involving variable lead time with backorders and lost sales. We first fuzzify the random lead-time demand to be a fuzzy random variable and obtain the total cost in the fuzzy sense. Then, we further fuzzify the total demand to be the triangular fuzzy number and derive the fuzzy total cost. By the centroid method of defuzzification, we derive the estimate of total cost in the fuzzy sense. Also, we find the optimal solution for order quantity and lead time in the fuzzy sense such that the total cost has a minimum value. A numerical example is provided to illustrate the results of proposed model.

On (s, S) inventory system with random lead time and repeateddemands

We consider an (s, S) inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the level s, an order is placed to bring the level to S. The quantity ordered is M = S − s. Demands to the system are served immediately if there is a positive inventory. Otherwise it will go to a pool of unsatisfied customers called orbit. After a random amount of time, that demand is retried for service. We assume a Markovian setup for the time between consecutive arrivals, replenishments, and retrials. We obtained the condition for ergodicity of the system, steady state system size probabilities, expected length of the busy period of the system, expected inventory level, expected number of customers waiting in the orbit, expected waiting times, and so forth. A control problem is studied and some numerical illusrtations are provided.

A two-commodity perishable inventory system

We present a two-commodity perishable stochastic inventory system under continuous review at a service facility with a finite waiting room. The maximum storage capacity for the i–th item is fixed as Si (i = 1, 2). We assume that a demand for the i–th commodity is of unit size. The arrival instants of customers to the service station constitutes a Poisson process with parameter lambda. The customer demands for these commodities are assumed to be in the ratio p1:p2. An individual customer is issued a demanded item after a random time of service with a negative exponential distribution. The items are perishable in nature and the life time of items of each commodity is assumed to be exponentially distributed. Both commodities are supposed to be substitutable in the sense that at the instant of any zero-stock, the other item may be used to meet the demand. A joint reordering policy is adopted with a random lead time for orders with exponential distribution. The joint probability distribution of the number of customers in the system and the inventory levels are obtained in both the transient and steady states. We also derive some stationary performance measures. The results are illustrated by means of a numerical example.

Generalized spare ordering policies with allowable inventory time

In this paper, a generalized ordering policy of a one-unit system with age-dependent minimal repair and random lead time is considered. We treat the general order-replacement model with two decision variables: ordering time and allowable inventory time. The allowable inventory period is measured from the time instant that the ordered spare is delivered. By introducing costs due to ordering, repairs, shortage, and holding, we derive the expected cost per unit time in the long run as a criterion of optimality, and seek the optimum policy by minimizing that cost. And we can prove under some mild conditions that there exists a finite and unique optimum policy. Various special cases are discussed.

Quantifying the Value of Leadtime Information in a Single-Location Inventory System

This article studies a single-location inventory model with random leadtimes. Inventory is replenished by a single supplier who, at the time a replenishment order is received, knows exactly when the order will be delivered. In other words, the supplier knows the leadtime for every replenishment order. Suppose the single-location inventory system is managed by a retailer. The objective of this article is to quantify the value of the information about leadtimes to the retailer. This is achieved by considering and comparing the performances of two scenarios whether or not the supplier shares his leadtime information with the retailer. Numerical evidence suggests that the value of leadtime information can be significant.

Optimal age-replacement policy of a system subject to shocks with random lead-time

This paper considers a generalized age-replacement policy of a system subject to shocks with random lead-time. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. The minimum-cost policy time is described and discussed. Various special cases are considered. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.

TWO-LEVEL INVENTORY OPTIMIZATION UNDER PROBABILITY EVENT CHAIN

The paper introduces the concept of effective inventory level, which is used to evaluate the impact of upstream shortage on downstream inventory, models the inventory at warehouse and retailer under random lead time and demand, and makes the global optimization of the safety factor to minimize channel inventory cost. It is shown that optimization and coordination of the safety factor lead to inventory cost savings at two sites, especially under large lead time variability and stock value-adding rate. Presented also is the coordination mechanism of the global optimization of the safety factor, i.e., cost-sharing contract, which allows both supplier and buyer to benefit from the program. Finally, this paper makes sensitivity analyses on the key parameters of the global optimization scheme. The numerical results obtained in our work differ from those of Lee and Billington (1995) that only consider demand variability and Bookbinder and others (1999) that only consider supply variability. JMDMES Vol.2(1) 2003: 39-53

The effectiveness of investment in lead time reduction for a make-to-stock product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.

A multi-echelon integrated JIT inventory model using the time buffer and emergency borrowing policies to deal with random delivery lead times

This paper proposes a multi-echelon integrated just-in-time (JIT) inventory model with random delivery lead times for a serial supply chain in which members exchange information to jointly make purchase, production, and delivery decisions. The performance of the whole supply chain depends on whether or not uncertain delivery can be handled properly. In this paper, a time buffer and emergency borrowing policies are used simultaneously to deal effectively with random delivery lead times and to protect a JIT system against shortages of goods. To construct easily the proposed multi-echelon integrated JIT inventory (MEIJITI) model, a duplication methodology is created. Since optimizing the proposed model is equivalent to solving an extremely complex mixed nonlinear integer programming problem, three propositions used to reduce the solution space and simplify the solution procedure are derived. Accordingly, a proposed search method for finding the optimal solution and a simulated annealing algorithm used successfully to obtain a near-optimal solution are developed. Two phases of an experiment were conducted, and some important observations are drawn.

Multiple-input heavy-traffic real-time queues

A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered--earliest deadline first and first-in, first-out. The set of current lead times of the K streams is modeled as a K-dimensional vector of random counting measures on $\mathbb{R}$, and the limit of this vector of measure-valued processes is obtained under heavy traffic conditions.

Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times

We study a single-product assembly system in which the final product is assembled to order whereas the components (subassemblies) are built to stock. Customer demand follows a Poisson process, and replenishment lead times for each component are independent and identically distributed random variables. For any given base-stock policy, the exact performance analysis reduces to the evaluation of a set of M/G/∞ queues with a common arrival stream. We show that unlike the standard M/G/∞ queueing system, lead time (service time) variability degrades performance in this assembly system. We also show that it is desirable to keep higher base-stock levels for components with longer mean lead times (and lower unit costs). We derive easy-to-compute performance bounds and use them as surrogates for the performance measures in several optimization problems that seek the best trade-off between inventory and customer service. Greedy-type algorithms are developed to solve the surrogate problems. Numerical examples indicate that these algorithms provide efficient solutions and valuable insights to the optimal inventory/service trade-off in the original problems.

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.

Optimal age-replacement policy with age-dependent minimal-repair and random-leadtime

A generalized age-replacement policy with age-dependent minimal repair and random leadtime is considered. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. Determination of the minimum-cost policy time is described and illustrated with a numerical example. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.

Continuous review inventory models where random lead time depends on lot size and reserved capacity

The processing time of large orders is, in many industries, longer than that of small orders. This renders supply lead times in such settings to be increasing in the order size. Yet that pattern is not reflected in existing inventory control models, especially those allowing for random lead times. This work aims at rectifying the situation. Our setting is an order-quantity/reorder-point model with backordering, where the shortage penalty is incurred per unit per unit time. The processing time of each unit is random; the processing time of a lot is correlated with its size. For the case where lead time is proportional to the lot size, we obtain a closed-form solution. That is, unlike the classical ( Q, r) model (where lead time is independent of lot size), no iterations are required here. We also analyze a case where the processing time exhibits economies of scale in the lot size. Finally, we consider a situation where a customer can secure shorter processing times by reserving capacity at the supplier's manufacturing facility.