Deterministic Lead Time Research Articles

Using Blockchain to Improve Buffer-Stock-Sharing and Combat Cheating Behaviors Under Virtual Pooling

Blockchain is a disruptive technology, which is crucial for business operations. In this article, we analytically explore how two manufacturers can achieve efficient buffer stock sharing using the blockchain technology (BCT). We first build an analytical basic model with a deterministic lead time for material replenishment and quantify the benefit of adopting a buffer stock sharing scheme. In the absence of BCT, we demonstrate the natural occurrence of a cheating problem. We analytically derive the overall value of blockchain technology (OVBCT) for the buffer stock sharing scheme and highlight the conditions under which it is increasing or decreasing in demand uncertainty. We also show how the buffer stock service level can be improved with the use of BCT. To show robustness of the analytical findings, several extended cases are explored. Novel buffer stock division rules are then generated under the proposed buffer stock sharing scheme, which makes the alliance profitable. In addition, an n-manufacturers alliance is further analytically explored. We find that the core findings from the basic model continue to hold in the extended models. Finally, we establish the conditions for achieving Pareto improvement with the use of BCT by considering the logistics services adopted.

Performance evaluation of a two-echelon inventory system with network lost sales

Inventory systems are largely analyzed in the literature under the common assumption of backorders due to the complexity of lost sales. In this paper, we consider a two-echelon inventory system composed of a central warehouse and multiple local warehouses subject to lost sales. The demand faced by each local warehouse is a Poisson process and the stock in the warehouses is controlled according to a continuous review base-stock policy. This system has been analyzed in the literature under deterministic or exponential lead-times at the central warehouse, deterministic lead times at the local warehouses and approximate performance evaluations have been proposed for two cases: (1) the demand is lost if no items are available in the local warehouse, the central warehouse, or in the pipeline in between (i.e., a waiting time threshold for incoming demand equal to the local warehouse lead time), and (2) when there is a waiting time threshold less than the local warehouse lead time. Based on a queuing network representation of the system, we extend the performance analysis of the system in the first case by considering generally distributed lead times both at the central and local warehouses and by providing the exact closed-form expressions for the inventory performance measures. In the second case, we provide new approximate solutions under generally distributed lead times at the central warehouse. We numerically show that our exact and approximate solutions perform equally or better than those presented in the literature under deterministic lead times.

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.

Asymptotically Optimal Inventory Control for Assemble-to-Order Systems

We consider assemble-to-order (ATO) inventory systems with a general bill of materials and general deterministic lead times. Unsatisfied demands are always backlogged. We apply a four-step asymptotic framework to develop inventory policies for minimizing the long-run average expected total inventory cost. Our approach features a multistage stochastic program (SP) to establish a lower bound on the inventory cost and determine parameter values for inventory control. Our replenishment policy deviates from the conventional constant base stock policies to accommodate nonidentical lead times. Our component allocation policy differentiates demands based on backlog costs, bill of materials, and component availabilities. We prove that our policy is asymptotically optimal on the diffusion scale, that is, as the longest lead time grows, the percentage difference between the average cost under our policy and its lower bound converges to zero. In developing these results, we formulate a broad stochastic tracking model and prove general convergence results from which the asymptotic optimality of our policy follows as specialized corollaries. Funding: This study is based on work supported by the National Science Foundation [Grant CMMI-1363314].

Impact of information sharing on bullwhip effect in a non-serial supply chain with deterministic lead time

Impact of information sharing on bullwhip effect in a non-serial supply chain with deterministic lead time

Optimisation of the Automated buffer positioning model under DDMRP logic

Abstract This paper discusses the buffer positioning problem in a hybrid Make-To-Order/Make-To-Stock (MTO/MTS) setting with deterministic lead times. With a more demanding market, delivery times have become more competitive. A dynamic amount of inventory is made immediately available at certain points of the manufacturing process, including the final product, allowing to improve the flow of materials and meet more competitive deadlines. This work is particularly interested in optimizing buffer positioning in the context of Demand Driven Material Requirement Planning (DDMRP), where the decision maker can process the location and the sizing of the inventory buffers in complex Bills of materials (BOMs) in the most efficient strategy all while minimizing inventory costs under service time constraint. To do so, an improvement of the existing model of the two first steps of DDMRP: the strategic inventory positioning and calculating the buffer levels, is proposed. A linearization of the model and better solutions in shorter computational times compared to the literature are given by the enhanced model which is proven through various simulations. A cost objective function was evaluated in this model, and was solved using CPLEX and its CP Optimizer. These simulations would prove a better and more efficient approach for an enhanced DDMRP implementation.

A manufacturer-buyers integrated inventory model with various distributions of lead times of delivering equal- sized batches of a lot

The single manufacturer multi-buyer integrated inventory supply chain problem with deterministic lead time of delivering batches (sub-lot) of a lot has received considerable attention. Because of influences by various factors, usually deviations occur in the times of setup of machines, inspection, loading, transportation, unloading etc., which result deviation in the lead time of delivering batches of a lot. Although the single-manufacturer single-buyer integrated supply chain problem with a particular distribution of lead times has received some attention, a model considering various distributions of lead times is unavailable. Also, the single-manufacturer multi-buyer integrated supply chain problem with stochastic lead time has received no attention from researchers. To fill up these gaps, here we develop a single-manufacturer multi-buyer integrated inventory supply chain model with various distributions of lead times of delivering equal-sized batches of a lot. Then an optimal solution technique to the model is developed, and illustrated with numerical examples. The significant potential benefit is highlighted by comparative study on solutions to numerical problems. Sensitivity analyses on the effects of various parameter values upon the minimal total cost solutions are carried out. The shortcomings of the current solution method are highlighted along with the indication of future research scope.

USE OF DYNAMIC REGRESSION MODEL FOR REDUCTION OF SHORTAGES IN DRUG SUPPLY

The study is given to the use of dynamic regression model for reduction of shortages in drug supply: Purpose – the use of a dynamic regression model to identify the influence of lead-time on the reduction of time delays in drugs supply. To reach the goal, the author focuses on the improvement of drugs availability and the minimisation of time delays in drugs supply. Research methodology – the application of dynamic regression method to minimise shortage. The author suggests a dynamic regression model and accompanies it with autocorrelation and heteroskedasticity tests: Breush-Godfrey Serial Correlation LM Test for autocorrelation and ARCH test for heteroskedasticity. Findings – during analysis author identifies the relationship between lead-time and time delays in drugs supply. The author delivers a specific regression model to estimate the effect of deterministic lead-time on shortage. Probability F and Probability Chi-Square of this testing show that there is no significant autocorrelation and heteroskedasticity. Research limitations – the research is delivered for a one-month time frame. For the future, the study could review other periods. The author has incorporated the lead-time component in shortage reduction study by leaving capacity uncertainty component unresearched. The future studies could incorporate both elements into shortage reduction case analysis. Practical implications – presented framework could be useful for practitioners, which analyse drug shortage reduction cases. The revision of supply time table is recommended for pharmacies aiming to minimise the shortage level. Originality/Value – the analysis of deterministic lead-time and identification that the periodicity of shortage is evident each eight days. The study contributes to lead-time uncertainty studies where most of the authors analyse the stochastic lead-time impact on shortages.

Bullwhip Effect of Weighted Moving Average Forecast under Stochastic Lead Time

The bullwhip effect is well-known as the propagation of fluctuation from downstream to upstream under stochastic demand. Researches in literature assume deterministic lead time, but it may be stochastic because of disruption of production. In this article we analyze the bullwhip effect of weighted moving average forecast under stochastic lead time. Under a general setting we express a performance measure on bullwhip effect theoretically. Numerical results give effects of parameters of forecasting and the lead time distribution on the bullwhip effect.

A stochastic micro-periodic age-based inventory replenishment policy for perishable goods

In this paper, we propose a micro-periodic inventory replenishment policy for quickly perishable goods with fixed and known lifetime of items, deterministic lead time, fixed given order cycle, mixed issuing policies (FIFO and LIFO), age-based stock, imperfect items and target customer service level under random demand. The inventory policy is based on time of day (morning, midday, afternoon or evening). The results of our simulation study show that the proposed micro-periodic inventory policy leads to waste reduction of 66% as well as a partial decrease in cost compared to inventory policy with planning on a daily basis.

Coordinating overseas and local sourcing through a capacitated expediting transportation policy

We consider an assembly system that adopts both overseas sourcing and local sourcing for different components. Local sourcing has a short and deterministic lead-time. Overseas sourcing can be divided into two stages and each stage has uncertain transportation duration. A capacitated expediting service could be adopted after first-stage transportation. In this study, we derive an optimal expediting policy for overseas sourcing and an optimal responsive sourcing policy for local sourcing. In addition, we discuss the impacts of lead-time volatility and the decision of safety lead-time, which are relevant in implementing the expediting service.

A simulation–optimization approach for a service-constrained multi-echelon distribution network

Academic research on (s,S) inventory policies for multi-echelon distribution networks with deterministic lead times, backordering, and fill rate constraints is limited. Inspired by a real-life Dutch food retail case we develop a simulation-optimization approach to optimize (s,S) inventory policies in such a setting. We compare the performance of a Nested Bisection Search (NBS) and a novel Scatter Search (SS) metaheuristic using 1280 instances from literature and we derive managerial implications from a real-life case. Results show that the SS outperforms the NBS on solution quality. Additionally, supply chain costs can be saved by allowing lower fill rates at upstream echelons.

Pengembangan Model Vendor Managed Inventory dengan Banyak Retailer yang Mempertimbangkan Ketidakpastian Lead Times

<p><em>An inventory management system in supply chains called Vendor Managed Inventory (VMI) is very promising due to the cost efficiency resulted from implementing such system. This research aims to develop a vendor managed inventory for multiple retailers. The model also takes into account lead time uncertainties from vendor to its retailers. A mathematical formulation for VMI with multiple retailers is first developed using deterministic lead times. Subsequently, lead times uncertainties are then taken into account where modes lead times are broken into two components: modes and delays, each with their respective probabilities. In turn, an approximation model is used to solve the problem because the complexity aroused from the model is difficult to solve using analytical methods. It is shown that the proposed approximation method is able to solve VMI problem with multiple retailers and uncertain lead times. Furthermore, the total inventory cost is significantly reduced when compared to the usual economic order quantity method because stockouts are less frequent. </em></p>

A Continuous Review Inventory System with Lost Sales and Emergency Orders

We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models.

Reinforcement learning approaches for specifying ordering policies of perishable inventory systems

Developed RL policies perform better than the other algorithms.RL learn better when the age of the products is used in state representation.Age and demand variance are important for perishable inventory management.The value of the age becomes critical when the lifetime of the product decreases. In this study, we deal with the inventory management system of perishable products under the random demand and deterministic lead time in order to minimize the total cost of a retailer. We investigate two different ordering policies to emphasize the importance of the age information in the perishable inventory systems using Reinforcement Learning (RL). Stock-based policy replenishes stocks according to the stock quantities, and Age-based policy considers both inventory level and the age of the items in stock. The problem considered in this article has been modeled using Reinforcement Learning and the policies are optimized using Q-learning and Sarsa algorithms. The performance of the proposed policies compared with similar policies from the literature. The experiments demonstrate that the ordering policy which takes into account the age information appears to be an acceptable policy and learning with RL provides better results when demand has high variance and products has short lifetimes.

Cost and environmental trade-offs in supply chain network design and planning: the merit of a simulation-based approach

We develop a simulation-based optimization methodology for the joint design and planning of globalized supply chains (SCs) under minimization objectives for cost and CO2 emissions. The assumptions required for the analytical optimization of such SCs include deterministic lead times, no-backorder occurrences at central distribution facilities, and powers-of-two replenishments of inventories at the SC nodes. The paper aims to investigate whether and how will the decisions that stem from the analytical optimization process change when these assumptions are relaxed. The proposed methodology is employed in a realistic SC structure. The results reveal that (i) the optimal order cycles of the nodes of the SC are not necessarily powers of two, (ii) the central distribution facilities have the option to operate at lower service levels, (iii) the network’s cost and CO2 emissions under optimality are reduced by approximately 0.9%, and (iv) the strategic network design decisions align with those of the analytical solution.

Economic and social collaborative decision-making on visit interval and service level in a two-echelon pharmaceutical supply chain

In this paper, simultaneous coordination of visit interval and service level in a two-echelon pharmaceutical supply chain (PSC) with stochastic demand is studied. In the investigated model, a single pharmaceutical supplier (pharma-supplier) visits a single pharma-retailer at constant intervals and subsequently delivers the order after a deterministic lead-time. The pharma-retailer employs a periodic review inventory system and decides on the PSC service level, which impacts on the pharma-supplier's profitability. On the other hand, the pharma-supplier has full authority over the visit interval which determines order delivery frequency and consequently impacts on the pharma-retailer's inventory costs. Firstly, both members' decisions under decentralized and centralized decision-making structures are investigated, and afterward collaboration models are proposed in two different scenarios: (1) economic collaborative decision-making and (2) social collaborative decision-making. Finally, a set of numerical examples is carried out to compare the performance of different decision-making structures. The results indicate that collaborative decision-making on visit interval and service level could be of great benefit, both socially and economically.

Impact of lead time variability in supply chain risk management

In this article, we study the impact of lead time variability on the performance of supply chain risk management in the beer industry. The stakeholders considered are the empty aluminum can supplier, the brewery and the distributor. The stochastic lead time model developed is an extension of the previously developed base model (with deterministic lead time) under which commodity price risk and demand uncertainty are managed via an integrated risk management approach using operational methods and financial derivatives. Simulation-based optimization is used to model and analyze such a complex system. We find that lead time variability does not always deteriorate the supply chain performance. Only high levels of lead time variability are found to justify more the need for a coordinated supply chain. The findings also reveal the need for using different hedging strategies to manage products flows across the supply chain under stochastic lead time versus the deterministic case. Managerial insights for the supply chain studied are argued based on experimental design findings.

Approximated closed-form minimum-cost solutions to the (S − 1, S) policy with complete backordering

In this paper, we consider the continuous review (S − 1, S) policy with complete backordering, deterministic and constant lead-time, and with a Poissonian lead-time demand. Moreover, we take into account two different expressions of the total expected cost depending on the customer-service criterion adopted. First, we approximate the Poissonian lead-time demand with a well-suited Gaussian random variable. Although this system can be easily solved with a simple algorithmic approach, it is interesting to be aware of the direct analytical functional relationship between the optimal value of the decision variable and the parameters of the model. Hence, the second step consists in providing some approximated closed-form minimum-cost solutions for both cost models considered under a Gaussian lead-time demand. An extensive numerical study is finally shown to characterise the precision achieved by the approximations developed.

The inventory billboard effect on the lead-time decision

This research brings together two important research streams: lead-time management and the inventory billboard effect. While traditional inventory theory, which assumes that demand is independent of the average on-hand inventory, recommends that lead-time be reduced to the lowest level possible, it is clearly not the case when inventory exhibits the billboard effect, which refers to the demand stimulating effect of inventory. We use analytical models to examine the firm׳s optimal lead-time decision in the presence of the inventory billboard effect in two scenarios: with and without inventory based competition. We begin with the single firm scenario, where a firm employs the base stock policy for the infinite horizon continuous-review inventory problem with a deterministic lead-time and inventory dependent demand. The firm׳s decisions are to choose the optimal lead-time and the corresponding base stock level to maximize its expected profit rate. We find that the inventory billboard effect favors a long lead-time, because a long lead-time results in a higher inventory level, which in turn induces more demand. We then consider the case where two firms compete on inventory for customer demand. We completely characterize the unique Nash equilibrium and provide closed-form solutions, which allow us to conclude that inventory based competition pressures both firms to increase the lead-time. Our numerical studies show that the extent to which demand depends on inventory amplify the impact of competition on the optimal decisions and the associated profit. Our findings suggest that lead-time reduction, although widely advocated by popular production philosophies such as Just-in-Time, has to be carefully evaluated when inventory exhibits billboard effect.