Analyzing a stochastic inventory system for deteriorating items with stochastic lead time using simulation modeling

We examine the effect of stochastic lead times on Just-in-Time (JIT) delivery. We find that with stochastic lead times there is a possibility of order crossover, and what order crossover does is to transform the original lead times into effective lead times, which is an AR(1) process that is an autoregressive process of Order 1. The mean of this process is the same as the mean of the original lead time, but its variance could be much smaller. The implication is that when we consider order crossover in the analysis, the cost could be less than otherwise (but never less than that with deterministic lead times). The literature on JIT with stochastic lead times has never considered order crossover, which produces the effective delivery times (EDT). Here, we demonstrate some important properties of the EDT: that it is a Cauchy sequence, and hence it converges; that it is an AR(1) process; and that it stochastically dominates the parent lead time distribution.

Due to rapid increases in the automotive markets in emerging economies, leading car manufacturers rapidly expand their manufacturing capacity in countries such as China. A certain portion of key performance components however continue to be sourced from developed countries. We study such a manufacturer that imports high-value components from a developed country. There are two available transportation modes: a slow mode with low cost and long and stochastic lead time, and a fast mode with high cost and short and deterministic lead time. Moreover, the manufacturer is subject to a credit constraint that bounds both the in-warehouse inventory and the number of outstanding orders (because it needs to pay for the components in advance). Consequently, the cheapest hedge against demand and supply uncertainty—inventory—is only available to a limited extent and the decision maker must turn to using the fast transportation mode for a much larger share of the orders. We model the manufacturer’s ordering policy and study its performance using simulation. Our study shows the adverse effects that the credit limit has on the growth opportunities of such companies in developing countries that import high-value components or other goods from developed countries. We show that especially the reduction in lead time variability can substantially reduce these adverse effects. Realizing that this variability is primarily caused by the import customs procedures, governments in developing economies have a means to assist their local manufacturers.

Inventory Management with Stochastic Lead Times

This study develops a mathematical model for an integrated vendor-buyer inventory with defective items and inspection error. We assume an imperfect production process with a known of defective probability. The buyer conducts a 100% quality check. However, due to an imperfect inspection process, the quality-controller may reject a good item as a defective item (Type I error), or accept a defective item as a non-defective item (Type II error). Different from existing research, we incorporate freight cost (a function of shipping weight and the distance between the vendor and the buyer) and stochastic lead time (a function of production and transportation times). The objective of the study is to minimize the joint total expected cost. This study indicates that Type I error is more significant when it is compared with Type II error. We also illustrate how the joint total expected cost and the lead time are significantly influenced by the distance of the buyer and the vendor. The results of our analysis also show that lead time can be shortened if the vendors speed up their shipment with smaller production lot sizes. Numerical examples and sensitivity analysis are given to illustrate the results.

In this article we analyze a lost sales two-commodity perishable inventory system, under Poisson demands and exponential lifetimes. The maximum inventory level for the i-th commodity is fixed as . If the total net inventory level drops to a prefixed level , an order will be placed for units of -th commodity . The lead time for replenishment is assumed to be exponential. The limiting probability distribution for joint inventory level, mean inventory levels and mean reorder rates and mean shortage rates in the steady state are computed. The total cost function is expressed in terms of system performance measures obtained. The results are illustrated numerically. Key words : Perishable item, Joint replenishment, Stochastic lead time, Markov process.

The simulation models are used as for decision support and learning in enterprises and in schools. Tree cases of successful applications demonstrate usefulness of weak anticipative information. Job shop scheduling production with makespan criterion presents a real case customized flexible furniture production optimization. The genetic algorithm for job shop scheduling optimization is presented. Simulation based inventory control for products with stochastic lead time and demand describes inventory optimization for products with stochastic lead time and demand. Dynamic programming and fuzzy control algorithms reduce the total cost without producing stock‐outs in most cases. Values of decision making information based on simulation were discussed too. All two cases will be discussed from optimization, modeling and learning point of view.

The paper studies an integrated vendor–buyer model with shortages under stochastic lead time which is assumed to be variable but depends on the buyer’s order size and the vendor’s production rate. The replenishment lead time and the market demand uncertainty are assumed to be reduced by changing the regular production rate of the vendor at the risk of paying additional cost. Shortages are partially backlogged and the backlogging rate depends on the length of the buyer’s replenishment lead time. The proposed model is formulated to obtain the net present value (NPV) of the expected total cost of the integrated system through optimization of (i) the buyer’s order quantity, (2) the buyer’s safety factor, and (3) the vendor’s production rate. Theoretical results are derived to demonstrate the existence and uniqueness of the optimal solution. Through extensive numerical study, some valuable managerial insights are obtained.

A new data-driven framework to select the optimal replenishment strategy in complex supply chains

When dealing with uncertainties in the supply chain and ensuring customer satisfaction, efficient management of lead time plays a significant role. Likewise, besides managing inventory and pricing strategies adeptly in multi-retailer supply chains, it has become inevitable for firms to embrace green and sustainable business practices. In this context, this paper considers a two-level supply chain consisting of a single manufacturer and multiple retailers in which the manufacturer produces a single product and delivers it to the retailers in equal-sized batches. Each retailer faces a price and green-sensitive market demand. The lead time is assumed to be a random variable that follows a normal distribution. Shortages for retailer inventory are allowed to occur and are completely backlogged. The centralized model and a decentralized model based on the leader-follower Stackelberg gaming approach are developed. A price discount mechanism between the manufacturer and retailers is proposed. For the acceptance of this contract, the upper and lower limits of the price discount rate are established. Numerical outcomes exhibit that the price discount mechanism effectively coordinates the supply chain and enhances both environmental and economical performances. A sensitivity analysis with respect to some key parameters is performed, and certain managerial insights are emphasized.

Sustainable multi-biofuel production with stochastic lead time and optimum energy utilization under flexible manufacturing

Inventory control management is an essential matter in supply chain, which helps to maintain an optimum level of investment in the inventory. This requires a global optimization of a complex logistics and inventory system. In this paper, we present a simulation model characterizing the complex dynamic behavior of procurement system that takes into account the coupling with production planning, in the context of stochastic demand and delivery lead-time. We have carried out this model in order to fill up the existing researches, as this area of study has not been dealt with sufficiently in the literature. Moreover, this model was developed for multiple-supplier, multiproduct and convergent bill of materials, also we introduced two characteristics to model each type of decision, the anticipation period and the delay in obtaining. The outcomes of our simulator are in the form of several scenarios generated by simulation replications, these results proving the strength of the chosen approach.

A major assumption in the analysis of (s, S) inventory systems with stochastic lead times is that orders are received in the same sequence as they are placed. Even under this assumption, much of the work to date has focused on the unconstrained optimization of the system, in which a penalty cost for unsatisfied demand is assigned. The literature on constrained optimization, wherein a service level requirement needs to be met, is more sparse. In this paper, we consider the constrained optimization problem, where orders are allowed to cross in time. We propose a feasible directions procedure that is simulation based, and present computational results for a large number of test cases. In the vast majority of cases, we come within 5% of estimated optimality.

We develop a queuing model to evaluate production and subcontracting policies commonly used in an assembled-to-order manufacturing system with service level constraints. The manufacturer determines production and inventory levels for the components using a base stock policy, and inventory is replenished from suppliers that have stochastic lead times. Customer demands for the assembled products can be satisfied only when all the required components are available and unsatisfied demands are backordered. The manufacturer offers high level of service to the customer and reserves the option, if necessary, to produce components internally at a faster rate and higher cost. Using queuing models we compare the performance of two policies: on-hand inventory based policy and leadtime based policy and compare these policies to obtain the condition where each policy is better than the other.

Two echelon cold supply chain model is developed in which warehouse and retailer are the two main actors of supply chain. The model is based on energy consumption cost for chiller system and the stochastic lead time. To incorporate the quality degradation, global stability index (GSI) method is used. The objective is to analyze the effect of retailer’s storage temperature and nutritional index weightage on the total cost of supply chain. A breakdown structure of all the associated costs is developed to formulate the total cost of cold chain. A numerical example is used for better understanding. To find the optimal solution, the model is numerically solved by using matlab genetic algorithm. The sensitivity analysis is being performed to study the model behavior against different parameters. Keywords: Cold chain, echelon valuation, quality degradation, global stability index, stochastic lead time

This paper describes a practical method for setting safety lead-times for purchased components in assembly systems with uncertainty in the supply process. The approach is specifically designed to be used in an MRP procurement environment. A two-stage production model in which suppliers were uncapacitated with stochastic lead times was developed. Then, a combinatorial optimization method that took advantage of structural properties was developed to produce an optimal integer solution of safety lead-times. In addition to yielding a practical lead-time setting tool, the model led to some interesting policy insights: (1) the flexibility achieved by bringing parts in early may have value even in situations with ideal suppliers; (2) purchasing components in batches offers some of the same protection as does safety lead time, but is less precise and subsequently more expensive; and (3) ignoring the complicating issues of MRP procurement results in far from optimal results.