Supply Lead Time Research Articles

Tradeoffs between base stock levels, numbers of kanbans, and planned supply lead times in production/inventory systems with advance demand information

We numerically investigate tradeoffs between near-optimal base stock levels, numbers of kanbans, and planned supply lead times in base stock policies and hybrid base stock/kanban policies with advance demand information used for the control of multi-stage production/inventory systems. We report simulation-based computational experience regarding such tradeoffs and the managerial insights behind them for single-stage and two-stage production/inventory systems.

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.

Value of information in remanufacturing complex products

Remanufacturing facilities usually face a trade-off between limited information about remanufacturing yields and potentially long supplier lead times. To improve production performance, these firms may attempt to acquire more timely and accurate information about remanufacturing yields or alternatively, to reduce the lead times of purchased parts. We develop four decision-making models to evaluate the impact of yield information and supplier lead time on manufacturing costs. We identify the operating conditions under which these capabilities are valuable, along with their relative impact on facility performance. Each model is formulated as an infinite horizon, stochastic dynamic program (Markov decision process). Our results indicate that the yield information is generally quite valuable, while investments in supplier responsiveness provide trivial returns to products with few parts. However, as product complexity increases with large number of target parts, the value of short lead times increases.

ライフサイクルシミュレーションに基づく循環プロセス管理方式の検討 : 部品リユースを考慮した部品発注方式(生産システムの設計・管理・評価)

When part reuse strategy is adopted in the closed loop manufacturing, parts are supplied from disassembly plants as well as new part manufacturing plants. This paper deals with ordering policies of new parts so as to make the most use of reused parts in the production process. We propose to consult the information in the disassembly plant in determining the order quantity of new parts in order to avoid excess and shortage of part stock, when supply lead time of new parts and reused parts are different. Effectiveness of the proposed method is evaluated by the life cycle simulation.

Yield information and supplier responsiveness in remanufacturing operations

When making used product disassembly and procurement decisions, managers of remanufacturing facilities usually face limited information on remanufacturing yields or a potentially long supplier lead time. To help making the decision, managers may attempt to identify the reparable parts early in the recovery process, to develop a responsive supplier with reactive capacity, or to implement an information system that helps to identify the wear state of the used machines that are available for remanufacturing. This paper provides optimal lot-size policies for each of these scenarios, which are then used to compare the relative value of the alternatives under a broad range of parameters. We find that: (1) as the yield variance increases, the benefits of developing early detection capability of the process yield at the disassembly stage outweigh the advantage of having suppliers with short lead times; (2) as the shortage cost increases, it is preferable to have a responsive supplier that can deliver with short lead times; and (3) as the purchase, repair or holding cost increase, it is preferable to have the capability to detect process yield early.

Modeling the flexibility of order quantities and lead-times in supply chains

The underlying assumption of a good supply chain is that buyers and suppliers are willing to accommodate the uncertainties and variations in each other's businesses. We define supply chain flexibility as the robustness of the buyer–supplier relationship under changing supply conditions. This flexibility provides an effective parameter for characterizing the behavior of asynchronous supply chains. A highly flexible relationship is one in which there is little deterioration in the procurement price under different supply conditions. In this paper we introduce a measure for estimating supply chain flexibility as a function of varying order quantities and varying supply lead-times. Our survey indicates that order quantities and supply lead-times are the two most common changes which occur in supply chains, and are most often the cause of buyer–supplier grievance. Since buyers are not always able to predict downstream conditions, they will often issue procurement orders that are for a smaller quantity than normal, and/or shorter supply lead-time than normal. In an inflexible relationship a supplier will only accept these orders at a much higher unit price. Using the proposed model a buyer is able to estimate the flexibility of potential supply chain partners, and hence make a quantifiable choice. The measure itself can be specified in the supply chain contract. Further, in conjunction with a parametric representation of the buyer's procurement behavior, the model is able to estimate the annual procurement cost of a given relationship.

Impact of supplier's lead time and forecast demand updating on retailer's order quantity variability in a two-level supply chain

Motivated by the dramatic boom-and-bust cycles in semiconductor industry, we use an analytical model to analyze two important factors that can contribute to the high degree of order quantity variability experienced by semiconductor manufacturers: supplier's lead time and forecast demand updating. Specifically, we use a two-level supply chain model to study how the supplier's variable delivery lead times and the correlation of the external demands can amplify the variability of the order quantities of the downstream member in the supply chain. Based on our analytical and numerical results, some useful insights are used for managing supplier's lead time performance in order to reduce order quantity variability in a supply chain. For instance, our results suggest that in allocating scarce capacity by the supplier, higher priority should be given to those products whose demands are highly variable and correlated for maintaining consistent delivery lead times for these products.

A two-echelon inventory system with supply lead time flexibility

The impact of manufacturing flexibility on inventory investments in a distribution network consisting of a central depot and a number of local stockpoints is investigated. The lead time of outstanding orders in the pipeline of the central depot can be shortened by the use of flexibility. Stock levels are controlled by a periodic review echelon-order-up-to-policy under service level constraints.

On the Complementary Value of Accurate Demand Information and Production and Supplier Flexibility

We study the value of information, production flexibility, and supplier flexibility for a good for which an initial and a subsequent order may be placed. We consider a Bayesian model of demand in which the unknown mean demand rate is assumed to have a prior, which is a mixture of two normal distributions corresponding to the demand forecast for an innovative (fashion) good. We develop three models of production flexibility: a static model requiring initial placement of both orders, a partially dynamic model requiring a fixing of the time that the second order will be made, and a fully dynamic model with no restrictions on ordering. Supplier flexibility is modeled through supply lead times. We observe that the magnitude of the savings from the static to the fully flexible model, corresponding to the sum of the values of information and production flexibility, reflects all sources of variability: differences between demand means of the prior mixture, variability within each prior, and variability about the observed mean. We observe that as the difference between high and low demand cases increases, the value of information increases, though for long lead times, production flexibility is required to take advantage of the updated information. Further, we observe that the greater the uncertainty within each prior distribution, the greater the value of information relative to the value of production flexibility, particularly for long lead times. However, the greater the uncertainty around the mean demand, which is the uncertainty that cannot be resolved through observation, the lower the value of information. Finally, we observe that the value of supply flexibility grows initially in a concave then convex manner as a function of the supply lead times.

The Value of Production Schedule Integration in Supply Chains

AbstractThis study explores the value of integrated production schedules for reducing the negative effects of schedule revisions in supply chains involving buyer and supplier firms. A stochastic cost model is developed to evaluate the total supply chain cost with integrated purchasing and scheduling policies. The model minimizes the costs associated with assembly rate adjustment, safety stock, and schedule changes for all supply chain members. Through experimentation, the paper examines the impact of several environmental factors on the value of schedule integration. This study finds that schedule integration can lead to overall cost savings in a supply chain, but some firms may have to absorb costs in excess of those they would incur with independent scheduling. Environments with high inventory holding costs and long supplier lead times may not find it beneficial to adopt an integrated schedule. Forecast effectiveness plays a critical role in realizing the benefits of schedule integration. The paper concludes with suggestions for future research.

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.

Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty

We consider a problem faced by a contract assembler that both assembles finished goods and procures the associated component parts for one of its major customers. Because of rapid changes in technology and ongoing engineering changes, all parts subject to obsolescence are purchased only for the current customer order. The procurement lead times of the components are random. Moreover, although the order for the finished product has a defined due date, the contract allows the customer to change the order quantity. Consequently, the assembler also faces a random demand. The assembler must determine how much to order and when to order each component part. The objective is to minimize the total expected cost, including the cost of holding components prior to their assembly, penalties for tardiness visa-vis the assembly due date, and overage and underage costs in satisfying the demand quantity. We present some structural results and discuss insights regarding optimal policies. We also present several simple heuristic policies and compare them to optimal policies. Computational results indicate that ignoring lead time variability can be costly, but relatively simple heuristics that consider lead time variability perform quite well.

Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times

We consider an inventory model where two suppliers are used concurrently to replenish one stock item. The unit demand is assumed to be normally distributed and the supplier lead times are mixtures of Erlang distributions. The lead time distributions need not be identical. This paper presents closed form expressions to evaluate the means and variances of the effective lead times, the probability of no stockout at a fixed reorder level and the potential lost sales. When the lead times are not identical, at a comparable service level, it is possible to achieve a lower average stock level by using unequal order splits. Several data sets are used in the paper to illustrate the method.

94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand

A two-stage inventory system is considered where Poisson demand occurs at Stage 1, and Stage 1 replenishes its inventory from Stage 2, which in turn orders from an outside supplier with unlimited stock. Each shipment, either to Stage 2 or to Stage 1, incurs a fixed setup cost. Under the assumption that the supply leadtime at Stage 2 is zero, we characterize a simple heuristic policy whose long-run average cost is guaranteed to be within 6% of optimality, i.e., a 94%-effective policy. The paper also provides heuristic policies for more general inventory systems and reports computational results.

The impact of inventory information distortion due to customer order cancellations

In this paper we study the impact of cancellations of customer orders on an inventory system. We develop a periodic review (s, S) inventory model with Poisson demands, deterministic demand leadtimes and supply leadtimes. When no set up cost is present for replenishment, the behavior of the system cost can be studied analytically. For the case with a fixed set up cost, we derive the operating characteristics of the model via an embedded Markov chain analysis. Based on this, we formulate the total cost function and suggest a two-phase approach to optimization. Our model can be used to compute cancellation fees and to evaluate the impacts of various conditions of cancellation. We find that cancellations, as major sources of inventory information distortion, increase total system costs, and the magnitude of the cost impact depends on the probability of cancellation and the expected cancellation time. Other relevant lessons and insights are also discussed. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 213–231, 1999

Optimal control policies for a periodic review inventory system with emergency orders

We describe a periodic review inventory system where emergency orders, which have a shorter supply lead time but are subject to higher ordering cost compared to regular orders, can be placed on a continuous basis. We consider the periodic review system in which the order cycles are relatively long so that they are possibly larger than the supply lead times. Study of such systems is important since they are often found in practice. We assume that the difference between the regular and emergency supply lead times is less than the order-cycle length. We develop a dynamic programming model and derive a stopping rule to end the computation and obtain optimal operation parameters. Computational results are included that support the contention that easily implemented policies can be computed with reasonable effort. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 187–204, 1998

An Optimising Model for Supply Chain Management

Abstract A linear programming model is developed for the centralised co-ordination of supply chains over many plants and inventory points. Production and supply lead-times are included in the model so that the upstream impact of downstream demand variation can be evaluated and appropriate action taken in time. A simple computational example illustrates well the potential of the model.

A periodic review inventory system with two supply modes

We describe a periodic review inventory system in which there are two modes of resupply, namely a regular mode and an emergency mode. Orders placed through the emergency channel have a shorter supply lead time but are subject to higher ordering costs compared to orders placed through the regular channel. We analyze this problem within the framework of an order-up-to- R inventory control policy. At each epoch, the inventory manager must decide which of the two supply modes to use and then order enough units to raise the inventory position to a level R. We show that given any non-negative order-up-to level, either only the regular supply mode is used, or there exists an indifference inventory level such that if the inventory position at the review epoch is below the indifference inventory level, the emergency supply mode is used. We also develop procedures for solving for the two policy parameters, i.e., the order-up-to level and the indifference inventory level.

Systems design of a two-echelon steel industry supply chain

Supply chains are a complex combination of “man” and “machine” and usually difficult to design. In this paper we argue that systems engineering can be used as an effective tool for this purpose as it comprehensively takes into account intricacies associated with modelling the attitudinal, organisational and technological issues. We describe the analysis and modelling of a two-echelon steel industry supply chain that services the construction industry using an integrated system dynamics framework as an example to good total system design. Key features of the framework are outlined and implementation details are provided. One objective of the design is to move more rapidly towards a minimum reasonable inventory (MRI) scenario in the presence of capacity constraints, breakdowns and material supply lead-time bottlenecks. Simulation results are presented showing how the developed model may be viewed as a “Management Information System” to investigate various business strategies.

Investment in the reduction of uncertainties in just-in-time purchasing systems

When the uncertainties of supply caused by lead-time variability, natural disasters, or other reasons are not considered as given, but as manageable, a company invests to reduce these uncertainties to save a company's operating cost. This article examines economic trade-offs of investments directed toward the reduction of uncertainties. Two models are presented. The first introduces the ability of a purchaser to reduce the variance of the lead time of its supplier. The second model adds the ability of the purchaser to not only influence the variance of its supplier's lead time, but to influence the proportion of defective units produced by the supplier. This article develops explicit solutions for jointly choosing optimal variances for both lead time and proportion of defective units within a reorder-point model. Two cases are considered; defective rate is independent of lead time, or defective rate depends on lead time. © 1994 John Wiley & Sons, Inc.