Random Lead Time Research Articles

Integrated quality strategy in production and raw material replenishment in a manufacturing-oriented supply chain

This paper deals with the coordination of production, replenishment and inspection decisions for a manufacturing-oriented supply chain with a failure-prone transformation stage, random lead time and imperfect delivered lots. Upon reception of the lot, the manufacturer executes an acceptance sampling plan with a zero non-conforming criterion. If the sample does not contain non-conforming items, the lot is accepted; otherwise, it is rejected. In this work, two strategies regarding the refused sampled lot are studied. The first one involves a return of the lot to the supplier, who commits to improving the quality of the lot, while the second assumes that the manufacturer performs a 100 % inspection and rectification operation. This work presents two main objectives. The first one is to jointly optimize, in a stochastic and dynamic context, the ordering point of raw material, the lot size of raw material, the final product inventory threshold and the severity of the sampling plan using a simulation-based optimization approach. The second one is to determine the best of the two quality control strategies. The in-depth study has shown that no strategy could be preferred in all the cases. For this reasons, we present an easy decision-making tool (indifference curves) to help the manager select the best quality control strategy when considering the entire supply chain.

Replenishment, production and quality control strategies in three-stage supply chain

In this paper, we propose to jointly integrate and coordinate production, replenishment and quality inspection decisions in a three-stage supply chain control problem. The transformation stage produces one final product type and responds to a stable market demand. After a random lead time, the supplier delivers raw materials in batches which may each contain a certain proportion of defective items. When a lot of raw materials is received, a lot-by-lot acceptance sampling plan is applied, and then a decision is taken with regards to a 100% screening or discarding of the sampled lot. In this article, we focus on the existing interaction between the applicable quality control decisions and the replenishment and production control decisions. The objective is to determine a control policy for production, replenishment and quality activities which minimizes the total cost, including purchasing costs, production and quality inspection costs, as well as the inventory/backlog costs. A simulation model and a Response Surface Methodology are used to find the optimal parameters of the proposed policy. The obtained results show that the integration of 100% screening or discarding decisions in a new “hybrid” one is more beneficial, and guarantees a better coordination at a lower cost.

Supply planning for multi-levels assembly system under random lead times

Production costs and inventory control in supply chain and are very important elements for companies. Finished products have to be produced at lowest costs. For this reason, planners must reduce average stock levels and determine optimal safety lead times. In this paper we deal with a model of a multi-levels assembly system. Several types of component and one type of finished products are considered. The demand in each period is known in advance and procurement lead times are independent random discrete variables with known probability distributions. In this study we try to determine optimal order release dates for components at last level of BOM to minimize the sum of the average inventory holding cost for components and the average backlogging and inventory holding costs for the finished product. A simulation model is proposed and a genetic algorithm is used to analyze and optimize the planned lead times.

A memetic algorithm for a stochastic lot-sizing and sequencing problem

A stochastic multi-product lot-sizing and sequencing problem is considered. Two kinds of uncertainties are integrated into the model: defectives items due to the machines' imperfections and random lead time because of randomly arising breakdowns and uncertain repair time. There are also sequence-dependent set-up times between two items of different types. The optimization problem is to maximize the probability of overall demand satisfying. In the previous work only the lot-sizing part of the problem was considered (a decomposition approach was used). Here we study the entire problem with sequencing and lot-sizing decisions integrated.

A prognostics-based spare part ordering and system replacement policy for a deteriorating system subjected to a random lead time

Prognostics-based spare part ordering and system replacement (PSOSR) policies are at the forefront of the prevalent prognostics and health management discipline. However, almost all of the existing researches in this domain ignore the stochasticity of the lead time. With this in mind, this paper proposes a PSOSR policy based on the real-time health condition of a deteriorating system subjected to a random lead time. In doing so, the degradation path of the interested system is modelled by a Wiener process, and the associated life distributions can be predicted recursively according to the real-time health condition of the system. In turn, the proposed policy can also be updated dynamically based on these real-time obtained life distributions. The policy, which – in addition to incorporating the stochasticity of the lead time – integrates the decision-making issues of both spare part ordering and system replacement – is finally applied to a case study of an inertial navigation system served in a type of aircraft. The experimental results validate the policy’s effectiveness and superiority.

Research on Genetic Optimization for Multinational Food Companies with Random Lead Time

This study aims to investigate the inventory optimization problems for multinational food companies with random lead time. Multinational organizations play an increasingly important role in the world economy. The majority of their activities seem to be driven by market-seeking considerations. In this study we considered a multinational organization in which lead times are stochastic. There is a determined due date that if demands are not prepared for delivery in that day, backlogging cost would happen. In contrast to most of studies in this field that consider sum of these cost, this study attempts to make a tradeoff between these objectives' affects using multi- objective approach based on genetic algorithm. Furthermore, effectiveness of our proposed method is compared against an adapted non-dominated sorting genetic algorithm which has been presented for this problem.

COORDINATED PRICING AND INVENTORY CONTROL WITH BATCH PRODUCTION AND ERLANG LEADTIMES

This paper addresses a joint pricing and inventory control problem for a batch production system with random leadtimes. Assume that demand arrives according to a Poisson process with a price-dependent arrival rate. Each replenishment order contains a single batch of a fixed lot size. The replenishment leadtime follows an Erlang distribution, with the number of completed phases recording the delivery state of outstanding orders. The objective is to determine an optimal inventory-pricing policy that maximizes total expected discounted profit or long-run average profit. We first show that when there is at most one order outstanding at any point in time and that excess demand is lost, the optimal reorder policy can be characterized by a critical stock level and the optimal pricing decision is decreasing in the inventory level and delivery state. We then extend the analysis to mixed-Erlang leadtime distribution which can be used to approximate any random leadtime to any degree of accuracy. We further extend the analysis to allowing three outstanding orders where the optimal reorder point becomes state-dependent: the closer an outstanding order is to its arrival or the more orders are outstanding, the lower selling price is charged and the lower reorder point is chosen. Finally, we address the backlog case and show that the monotone pricing structure may not be true when the optimal reorder point is negative.

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process and seek an optimal policy that specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). We characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base stock and lattice-dependent rationing.

Inventory Management Models in Supply Chains: A Literature Review

In this paper, we review inventory management models for designing inventory policies for final products and raw materials in supply chains, considering random demand and lead times. (1) Random Demand Models, (2) Random Lead Times Models, (3) Inventory Policy Models, and (4) Integrated Inventory Management Model. For each section we present summary tables describing the main characteristcs of models found in the literature. Special emphasis is placed on the lack of methodologies for modeling random issues of the system. Research and development opportunities in the context of the Colombian industry are also identified.

Incorporating Stochastic Lead Times Into the Guaranteed Service Model of Safety Stock Optimization

Effective end-to-end supply chain management and network inventory optimization must account for service levels, demand volatility, lead times, and lead-time variability. Most inventory models incorporate demand variability, but far fewer rigorously account for lead-time variability, particularly in multiechelon supply chain networks. Our research extends the guaranteed service model of safety stock placement to allow random lead times. The main methodological contribution is the creation of closed-form equations for the expected safety stock in the system; this includes a derivation for the early-arrival stock in the system. The main applied contributions are the demonstration of real stochastic lead times in practice and a discussion of how our approach outperforms more traditional heuristics that either ignore lead-time variability or consider the maximum lead time at each stage.

Newsboy Problem: Viability of Optimal Initial Selling Price and Ordering Policies in the Presence of Exogenous Price Decline and Random Lead Time

Analysis of empirical sales data lead us to consider newsboy model for four practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies are conducted to assess the effects of lead time and price decline.

A multi-level inventory system with a make-to-order supplier

We study a supply network comprising a factory, a central warehouse using a discrete-time reorder point–reorder quantity policy and multiple regional distribution centres applying discrete-time base-stock policies under consideration of a fill rate constraint. The warehouse is supplied from the factory, which has a limited capacity and which follows a make-to-order strategy. The complete system is analysed by decomposition into three layers that are linked through layer-specific random replenishment lead times. An overall optimisation model including as decision variables the processing time in the factory and the parameters of the inventory policies applied in the warehouse and the distribution centres is formulated and solved.

Optimization of Reorder Point Strategy of Assembly Manufacturer with Random Variables

For assembly system, randomness and variableness make it impossible to control the inventory accuratelyspecially. Because the negative effect of them have ripple effects. So we investigate reorder point optimizationstrategy of assembly manufacturing system with random demand and random lead time. We seek themanufacturers order strategy for the minimum integration of the supply chain inventory cost. And we use scalebenefits parameters of suppliers in this system to reflect actual influence of the lot’s scale. Numerical example oftwo components assembly system is given to illustrate the effectiveness of the reorder point strategy. From thenumerical simulation, it is can be seen backorder rate and order scale effect will impact the total supply chaincost dramatically.

Two-Commodity Markovian Inventory System with Compliment and Retrial Demand

are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity. ) , ( 1 1 Q s type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size N . These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities and the number of demands in the orbit, is obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated with numerical examples.

Integration of additional purchase cost to reduce the lead time uncertainty for one level assembly system

We consider the supply planning for one level assembly system under uncertainty of lead times. The finished product need several components for the assembly operation. The lead times can be uncertain for different reasons such as machine breakdowns, transport delay, strike, etc. In literature, this type of problem was studied in the case of random lead times that follow continuous distributions as well as in the case of any discrete laws with known distribution. We consider the case of discrete distributions to be closer to the industrial reality because often in real life situations the lead time is expressed as the number of periods. Typically, this is an inventory control problem where the objective is to minimize the component holding and backlog costs for the finished product due to the uncertainty of lead times. Indeed, as the finished product is assembled by using several types of components, the assembly is stopped even if a single type of component is delayed. The other components are stored between their arrival and the arrival of the latest component. To reduce stock and backlog costs, we propose to pay the supplier more, if he/she agrees to decrease his lead time uncertainty. A model describing this choice is suggested.

Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems

AbstractAssemble‐to‐order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order‐based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein–Chen approximation as well as its error‐bound for order‐based fill rate for a multiproduct multicomponent ATO system with random leadtimes to replenish components. This approximation gives an expression for order‐based fill rate in terms of component‐based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement in order‐based fill rates when the base‐stock level for any component changes. Numerical studies demonstrate that the approximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base‐stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Multi-product sequencing and lot-sizing under uncertainties: A memetic algorithm

The paper deals with a stochastic multi-product sequencing and lot-sizing problem for a line that produces items in lots. Two types of uncertainties are considered: random lead time induced by machine breakdowns and random yield to take into account part rejects. In addition, sequence dependent setup times are also included. This study focuses on maximizing the probability of producing a required quantity of items of each type for a given finite planning horizon. A decomposition approach is used to separate sequencing and lot-sizing algorithms. Previous works have shown that the sequencing sub-problem can be solved efficiently, but the lot-sizing sub-problem remains difficult. In this paper, a memetic algorithm is proposed for this second sub-problem. Computational results show that the algorithms developed can be efficiently used for large scale industrial instances.

A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

A mathematical modelling of a continuous review stochastic inventory system with a single server is carried out in this work. We assume that demand time points form a Poisson process. The life time of each item is assumed to have exponential distribution. We assume(s,S)ordering policy to replenish stock with random lead time. The server goes for a vacation of an exponentially distributed duration at the time of stock depletion and may take subsequent vacation depending on the stock position. The customer who arrives during the stock-out period or during the server vacation is offered a choice of joining a pool which is of finite capacity or leaving the system. The demands in the pool are selected one by one by the server only when the inventory level is aboves, with interval time between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The joint probability distribution of the inventory level and the number of customers in the pool is obtained in the steady-state case. Various system performance measures in the steady state are derived, and the long-run total expected cost rate is calculated.

A multi-item inventory system with expected shortage level-dependent backorder rate with working capital and space restrictions

Article history: Received 1 June 2011 Received in revised form July, 29, 2011 Accepted 30 July 2011 Available online 3 August 2011 In this paper, a new multi-item inventory system is considered with random demand and random lead time including working capital and space constraints with three decision variables: order quantity, safety factor and backorder rate. The demand rate during lead time is stochastic with unknown distribution function and known mean and variance. Random constraints are transformed to crisp constraints with using the chance-constrained method. The Minimax distribution free procedure has been used to lead proposed model to the optimal solution. The shortage is allowed and the backlogging rate is dependent on the expected shortage quantity at the end of cycle. Two numerical examples are presented to illustrate the proposed solution method. © 2012 Growing Science Ltd. All rights reserved

Fuzzy Random Continuous Review Inventory Model with Imperfect Quality

This paper examines the continuous review inventory system with imperfect items under fuzzy random lead time demand and fuzzy annual demand. A fuzzy random model under the fuzzy defective rate is developed. The optimal order quantity which minimizes the total expected cost per year is derived by employing the expectation theory and signed distance method. Moreover, the influence of the fuzzy randomness of the lead time demand and the backorder rate on the optimal order quantity and the average annual total cost is analyzed via numerical examples.