Random Lead Time Research Articles

An emergency supply policy for an inventory replenishment model with returns and partial backorders

AbstractThis paper studies a continuous-review inventory replenishment model with a limited storage capacity S in an uncertain environment. We assume that the demands and returns follow independent Poisson processes. We further assume a ra1079 shelf life, a random lead time, and early loss. The storage is managed according to the base-stock (S, s) policy for $$s<S,S>0.$$ s < S , S > 0 . In case of overstock, each returned item exceeding S is transferred to a foreign facility. If during the lead time a demand reaches zero stock, we consider two alternatives: either allow partial backordering up to $$L_{B}$$ L B items, beyond which the unsatisfied demand is lost, or call for an immediate and costly emergency supply up to level $$0<Q_{B}^{e}\le S$$ 0 < Q B e ≤ S . Our objective is to study how the thresholds s, S, $$L_{B},$$ L B , and $$Q_{B}^{e}$$ Q B e are impacted by the system’s parameters, such as returns, demands, and costs. Using a Markovian framework, we derive the steady-state probabilities for the inventory level, and construct closed-form expressions for the average cost functions. Then, we numerically investigate the impact of the different parameters on the best policy and on the threshold levels. We compare the two alternatives and identify situations in which calling for an emergency supply is economically profitable.

Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

A nonparametric approach for setting safety stock levels

In practice, lead time demand (LTD) can be skewed, multi‐modal or highly variable, and these factors compromise the validity of typical approaches used for setting safety stock levels. Motivated by encountering this problem at our industry partner, we develop an approach for setting safety stock levels using the bootstrap, a widely used statistical procedure. Existing bootstrap approaches for inventory management either operate directly on observed LTD or assume deterministic lead times, permitting direct application of the bootstrap approach for univariate quantile estimation. As LTD is a convolution of multiple random demands over a random lead time, a multivariate bootstrap approach is required. As we demonstrate, when lead times are stochastic, our multivariate approach provides improved safety stock estimates. We develop a multivariate central limit theorem for the bootstrap mean and bootstrap quantile—components of the safety stock calculation—highlighting why the generalization of these bootstrap methods is critical for inventory management. These results provide a theoretical underpinning for the bootstrap estimator of safety stock and permit the construction of confidence intervals for safety stock estimates, allowing decision makers to understand the reliability with which the desired service level will be achieved. Building on our theoretical results, and supported by numerical experiments, we provide insights on the behavior of the bootstrap for various LTD distributions, which our results demonstrate are critical when employing the bootstrap method. Implementation of our approach with our industry partner resulted in an inventory investment reduction of $1.17 million combined with an overall increase in service level. Our approach is general and can be implemented without modification in other settings.

Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M, and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (positive and negative) linear rates governed by a Markov chain, and retailers arriving according to a Markov arrival process and bringing a (positive and negative) random number of items. The PW is managed according to a triple-parameter band policy (M,S,s),0≤s<S≤M, under a lost sales assumption. Under this policy, as soon as the stock level at the PW falls below s, a refilling to S is performed by a distributor after a random lead-time. However, if the stock exceeds level S when the distributor arrives, no refilling is carried out, and only maintenance services are performed. Items that exceed level M are transferred to the SW at a negligible amount of time for those used in related products. Our cost structure includes a fixed order cost, a variable cost for each item supplied by the distributor, a cost for the additional maintenance, a salvage payment for each transferred item from the PW to the SW, and a loss cost for each unsatisfied item due to demands. We seek to determine the optimal thresholds that minimize the expected overall cost under the discounted criterion. Applying first-passage time results, we present a simple set of equations that provide managers with a useful and an efficient tool to derive the optimal thresholds. Sensitivity analysis and fruitful conclusions along with future scope of research directions are provided.

Research on Inventory Simulation of Pulse Supply Chain Based on Controllable Lead Time

In the e-commerce environment, how supply chain enterprises respond to surge demands has become an urgent issue to address. This article takes into consideration the overall interests of the supply chain system, aiming to maximize the supply chain profit. By applying system dynamics theory, an in-depth analysis is conducted on a two-tier supply chain consisting of a single manufacturer and a single retailer with controllable lead times. A system dynamics model is constructed using Vensim simulation software as the modeling platform, and simulation analyses are performed for both single and multiple surge demands. The findings reveal that in both single and multiple surge demand scenarios, implementing a controllable retailer lead time strategy leads to higher profits compared to normal lead time and random lead time strategies. Moreover, as the lead time is compressed, the profit exhibits an increasing-to-decreasing trend. Additionally, when both the manufacturer and retailer lead times are controllable, the profit of the entire supply chain surpasses that of the normal lead time and random lead time strategies.

Replenishment strategies for lost sales inventory systems of perishables under demand and lead time uncertainty

We develop an inventory control policy for perishable products considering both random demand and random lead time. We consider a B2C retail environment where excess demand is lost. The policy dynamically determines the optimal replenishment quantity under a service level constraint in every period, allowing for order-crossing, a widely disregarded characteristic in the literature. Regarding perishability, we compare the two most extreme issuing policies, first-expired-first-out (FEFO) and last-expired-first-out (LEFO), and evaluate our policy to existing inventory policies for perishables that typically ignore lead time uncertainty.We obtain several interesting findings. First, we show that ignoring lead time uncertainty and planning based on the expected lead time significantly undershoots the target service level. Even planning with the maximum lead time, under LEFO, the achieved service level would still fall considerably below the target, which the lost-sales structure can explain. On the other hand, under FEFO, the achieved service level would overshoot the target service level, which leads to unnecessary waste. Second, a more reliable lead time can significantly reduce waste, especially under LEFO. Third, our model allows us to distinguish between past, present, and future lead time uncertainty and thus to consider partial lead time information. We show the value of lead time information on outstanding orders. Fourth, we evaluate the impact of a fast but unreliable delivery option and a slow but reliable delivery option on the retailer’s average waste and ordering process. We find that the optimal choice depends on the demand characteristics.

Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility

The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and the other as a complimentary item (Commodity-II). Demand arrives according to a Poisson process, and service time is exponential at a queue-dependent rate. We investigate a strategy of (s,Q) type control for commodity-I with a random lead time but instantaneous replenishment for commodity-II. If the waiting hall reaches its maximum capacity of N, any arriving primary client may enter an infinite capacity orbit with a specified ratio. For orbiting consumers, the classical retrial policy is used. In a steady-state setting, the joint probability distributions for commodities and the number of demands in the queue and the orbit, are derived. From this, we derive a waiting time analysis and a variety of system performance metrics in the steady-state. Additionally, the physical properties of various performance measures are evaluated using various numerical assumptions associated with diverse stochastic behaviours.

Queuing Models for Analyzing the Steady-State Distribution of Stochastic Inventory Systems with Random Lead Time and Impatient Customers

In material management, the inventory systems may have good management aspects in terms of materials; however, this negatively affects the relationship between the facility and customers. In classical inventory models, arriving demands are satisfied immediately if there is enough on-hand inventory. Traditional inventory models consider optimization problems and find the optimal policy of decision variables without computing the stationary distribution of the inventory states for random demand. Hence, a detailed analysis of inventory management systems requires a joint distribution of system stock levels and the number of requests to be investigated thoroughly. This research provides a new stochastic mathematical model for inventory systems with lead times and impatient customers under deterministic and uniform order sizes. The proposed model identifies the performance measures in a stochastic environment, analyzing the properties of the inventory system with stochastic and probabilistic parameters, and finally, validating the model’s accuracy. To analyze the system, balance equations were derived from a mathematical characterization of the underlying queuing model dependent on the Markov chain formalism. The precise performance was achieved by examining the graphical representation of the service process in a steady-state as a function of both arrival distribution and the customer patience coefficient, while it was challenging to derive an optimal curve fit in a three-dimensional space that features two input variables and a single output variable.

Impact of Barrett oesophagus diagnoses and endoscopies on oesophageal cancer survival in the UK: A cohort study

BackgroundCurrent guidelines recommend endoscopic surveillance for Barrett oesophagus (BE), but the value of surveillance is still debated. Using a combination of primary care, secondary care and cancer registry datasets, we examined the impact of a prior BE diagnosis, clinical and risk factors on survival from oesophageal cancer and adenocarcinoma.MethodsRetrospective cohort study of patients aged 50 and above diagnosed with malignant oesophageal cancer between 1993 and 2014 using Clinical Practice Research Datalink (CPRD). All prior BE diagnoses and endoscopies were identified from CPRD and Hospital Episode Statistics. Histology information was obtained from linked cancer registry data. We used flexible parametric models to estimate excess hazard ratios (EHRs) for relative survival. We simulated the potential impact of lead‐time by adding random lead‐times from a variety of distributions to all those with prior BE.ResultsAmong our oesophageal cancer (n = 7503) and adenocarcinoma (n = 1476) cohorts only small percentages, 3.4% and 5.3%, respectively, had a prior BE diagnosis. Two‐year relative survival was better among patients with BE: 48.0% (95% CI 41.9–54.9) compared to 25.2% (24.3–26.2) without. Patients with BE had a better prognosis (EHR = 0.53, 0.41–0.68). Survival was higher even if patients with BE had fewer than two endoscopies (50.0%; 43.6–57.3). A survival benefit was still observed after lead‐time adjustment, with a 20% absolute difference in 2‐year survival using a 5 year mean sojourn time.ConclusionsPatients with a prior BE diagnosis had a survival advantage. This was not fully explained by surveillance endoscopies.

Exploiting Random Lead Times for Significant Inventory Cost Savings

Taking Advantage of the Lead Time Randomness in Supply Chains Randomness in lead times is a major—and increasingly important—issue of inventory management, as a variety of risk factors motivate companies to diversify their supply sources and rely on distributed networks of suppliers. In “Exploiting Random Lead Times for Significant Inventory Cost Savings,” A. Stolyar and Q. Wang show that, surprisingly, instead of being a damaging factor to supply chain performance, randomness may be harnessed for potentially very substantial reductions of inventory costs. Specifically, the theoretical analysis and simulation results in the paper demonstrate that, under certain conditions, appropriately designed novel policies can significantly outperform the conventional base stock policies.

Research on Distribution and Inventory Cooperation of Agricultural Means Supply Chain

This paper constructed a biobjective model based on the total cost and time satisfaction to provide a desirable solution to the distribution and inventory cooperation of agricultural means supply chain. The model simulated how the distribution center and retailers collaborate to meet the needs of the order customer in the random lead time and out-of-stock loss costs. By the features of the model, the biobjective genetic algorithm was improved based on elitism selection, aiming to improve the quality of noninferior solution in biobjective model. Finally, the influence degree of the lead time of delivery, unit inventory cost, and unit transport cost on the total cost of the system was quantified through the analysis of examples and sensitivity of model parameters. This research has provided valuable new insights into the distribution and inventory coordination of supply chain.

Genetic algorithm and Monte Carlo simulation for a stochastic capacitated disassembly lot-sizing problem under random lead times

The purpose of this research is to propose several optimization methods for the stochastic multi-period disassembly lot-sizing problem. The case of one type of end-of-life product and a two-level disassembly system is studied. The disassembly lead times are discrete random variables with a known and bounded probability distribution. The objective is to optimize the expected value of the total cost, which is the sum of setup cost, overload cost, inventory holding cost and backlogging cost. Three approaches were developed to solve the studied problem: (i) a two-stage mixed-integer linear programming model based on all possible scenarios for small instances, (ii) a sample average approximation approach based on Monte Carlo simulation for medium-scale instances and, (iii) an optimization approach based on the Monte Carlo simulation and a genetic algorithm for large-scale instances. Experimental results show the effectiveness of the proposed models which can be used to support decision-making on replenishment and disassembly plans.

A triple [formula omitted]-thresholds base-stock policy subject to uncertainty environment, returns and order cancellations

This paper studies a continuous-review (S,s,ℓ) inventory model that extends the familiar (S,s)-policy by including returns and order cancellations. The demand and return processes follow independent compound Poisson processes. We assume a random shelf life, a random lead time and early losses. Our objective is to find a replenishment level S, a reorder level s, and a threshold cancellation level ℓ that minimizes the total expected cost per time unit under lost sales. The cost structure includes variable and fixed costs for an order, a holding cost, a penalty cost, a handling cost for returns, a relocation cost, and costs for end of life and early loss. Via Markovian framework, we derive the steady-state probabilities for the inventory level, and construct closed-form expressions for the average cost functions. Using a numerical study, we investigate how the best S,s and ℓ, are impacted by the system’s parameters, such as returns, demands (rate, mean and variability), and order cancellations. We illustrate the impact of the return flow on the best policy and the cost, and show that ignoring returns may yield a substantial loss. Consequently, we compare our model to a relatively simple one with no returns but with less demand, and specify when the latter model can be used as a good approximation. Finally, we identify situations where an earlier-cancellation policy is more cost effective. Our framework is completed by providing two efficient search algorithms for numerically finding the optimal parameters. We show that both algorithms significantly reduce the computational effort compared to the basic algorithm.

Optimal preventive replacement last policy for a successive random works system with random lead time

Most systems deteriorate with age and use, and eventually, fail from either or both causes in random environment. It is reasonable in commercial industries that only one spare item is available for replacement. Selecting a cost efficient and effective replacement strategy to improve system reliability and inventory of spare parts is crucial work. In this paper, we consider an operating system which works at successive random times and models an imperfect maintenance action under two types of age-dependent failures, repairable minor failures (R) and unrepairable catastrophic failures (U). R failures are followed by a minimal repair and U failures are removed by a corrective replacement. A notation of preventive replacement last policy is considered in which the system is replaced before any U failures at age T or at number N of working times, whichever occurs last. A spare unit for replacement can be delivered upon order and is available only when the random lead time is finished. The main objective is to determine an optimal schedule (T, N) of that minimizes the mean cost rate function in a finite time horizon. The existence and uniqueness of optimal PRL policy are derived analytically and computed numerically.

A Joint Optimization Model of (s, S) Inventory and Supply Strategy Using an Improved PSO‐Based Algorithm

This paper mainly discussed the problem of a multiechelon and multiperiod joint policy of inventory and supply network. According to the random lead time and customers’ inventory demand, the (s, S) policy was improved. Based on the multiechelon supply network and the improved, the dynasty joint model was built. The supply scheme in every period with the objective of minimum total costs is obtained. Considering the complexity of the model, the improved particle swarm optimization algorithm combining the adaptive inertia weight and grading penalty function is adopted to calculate this model and optimize the spare part problems in various environments.

Supply Chain Model for Expiring Items Following Ramp-Type Demand With Stochastic Lead Time Under Crisp and Fuzzy Environment

Supply chain models with deteriorating items, season pattern demand, expiration and uncertain lead time, though common in practice; had received little attention from researchers. In this article, the authors proposed a collaborative system with ramp type seasonal pattern demand rate for expiring items with supplier's random lead time under crisp and fuzzy environment considering the effect of inflation and time value of money. For the seasonal kind of items, demand rate follows the combination of increasing-steady-decreasing demand patterns. A supplier's lead time is a stochastic function of his managing cost; thus, the extra costs incurred on the retailer due to the uncertainty in lead time in terms of shortages costs and lost sales costs are owed by the supplier. Numerical examples are cited to illustrate the results and its significant features. Finally, to study the effect of change of parameters sensitivity analysis is presented and necessary observations are made.

A state-dependent perishability (s, S) inventory model with random batch demands

We consider continuous-review perishable inventory models with random lead times and state-dependent Poisson demand. The paper revises an earlier work of Barron and Baron (IISE Trans 1–52, 2019). While the former studies unit Poisson demands, this paper deals with demand uncertainty and allows for random batch demands. We conduct a comprehensive analysis of two main models that have different lead times and perish times under backorders or lost sales. Thus, our models can be applied to many industries, in situations where the system is subject to random perishability, random lead time, and demand uncertainty. With a probabilistic approach, we derive a long-run average cost function under the (S, s) replenishment policy. Numerical examples are used to demonstrate the impact of changing batch size and other system parameters on the optimal policy. Our numerical study indicates that, although the Markovian policy can be used as a good approximation of the average total cost, it performs better for a general perish time. We further show that the optimal cost may differ for a different average batch size, while the batch variability seems to provide some robustness.

QMCD approach for perishability models: The (S, s) control policy with lead time

We consider cost minimization for an (S, s) continuous-review perishable inventory system with random lead times and times to perishability, and a state-dependent Poisson demand. We derive the stationary distributions for the inventory level using the Queueing and Markov Chain Decomposition (QMCD) methodology. Applying QMCD, we develop an intuitive approach to characterizing the distribution of the residual time for the next event in different states of the system. We provide comprehensive analysis of two main models. The first model assumes a general random lifetime and an exponential distributed lead time. The second model assumes an exponential distributed lifetime and a general lead time. Each model is analyzed under both backordering and lost sales assumptions. We consider a fixed cost for each order, a purchase cost, a holding cost, a cost for perished items, and a penalty cost in the case of shortage. Numerical examples are provided and show that variability of lead time is more costly than that of perishability time. Therefore, after reducing lead time and increasing perishability time, managers should focus on reducing variability of lead time.

The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

We quantify the bullwhip effect (which measures how the variance of replenishment orders is amplified as the orders move up the supply chain) when both random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and the correlated demands are described by a first-order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the bullwhip behaviour with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. We find maxima and minima in the bullwhip measure as a function of the demand auto-correlation.

Scenario-based stochastic linear programming model for multi-period disassembly lot-sizing problems under random lead time

Abstract In the last few years, there has been a growing interest in the disassembly scheduling problem to fulfil the demands of individual disassembled parts over a given planning horizon. An analysis of the literature shows that the disassembly lead time is often considered deterministic. Indeed, in real-life systems, this parameter is rarely known and often has uncertain values that can be caused by the complexity of disassembly operation. In this study, a new scenario-based stochastic linear programming model is proposed to deal with a multi-period, single product type and two-level disassembly lot-sizing problem under lead time uncertainty. The demand for each component is known for each time period and the real disassembly lead time of end-of-life product is an independent random discrete variable with a known probability distribution. The proposed model is used to determine the optimal quantity for disassembled end-of-life products in order to minimize the setup cost for end-of-life product and the sum of average inventory holding and backlogging costs for each component, over the planning horizon and all scenarios.