Setting procurement safety lead-times for assembly systems

We consider an inventory system for continuous decaying items with stochastic lead time and Poisson demand. Shortage is allowed and all the unsatisfied demands are backlogged. Moreover, replenishment is one for one. Our objective is to minimize the long-run total expected cost of the system. Firstly, we have developed the mathematical model with deterministic lead time. Since the stochastic lead time makes the model complex especially when lead time has complicated probability distribution and it is difficult to prove convexity of the objective function, we have applied simulation modeling approach. The simulation model has no limitation on lead time or any other parameters. The simulation model is validated by comparing its outputs and analytical model's results for the deterministic lead time case. Furthermore, we use optimizer module of the applied software to find near optimal solutions for a number of examples with stochastic lead time.

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.

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.

Inventory Management with Stochastic Lead Times

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.

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

This study presents a reinforcement learning–based approach to optimize replenishment policies in the presence of uncertainty, with the objective of minimizing total costs, including inventory holding, shortage, and ordering costs. The focus is on single-level assembly systems, where both component delivery lead times and finished product demand are subject to randomness. The problem is formulated as a Markov decision process (MDP), in which an agent determines optimal order quantities for each component by accounting for stochastic lead times and demand variability. The Deep Q-Network (DQN) algorithm is adapted and employed to learn optimal replenishment policies over a fixed planning horizon. To enhance learning performance, we develop a tailored simulation environment that captures multi-component interactions, random lead times, and variable demand, along with a modular and realistic cost structure. The environment enables dynamic state transitions, lead time sampling, and flexible order reception modeling, providing a high-fidelity training ground for the agent. To further improve convergence and policy quality, we incorporate local search mechanisms and multiple action space discretizations per component. Simulation results show that the proposed method converges to stable ordering policies after approximately 100 episodes. The agent achieves an average service level of 96.93%, and stockout events are reduced by over 100% relative to early training phases. The system maintains component inventories within operationally feasible ranges, and cost components—holding, shortage, and ordering—are consistently minimized across 500 training episodes. These findings highlight the potential of deep reinforcement learning as a data-driven and adaptive approach to inventory management in complex and uncertain supply chains.

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.

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

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.

In this paper, we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst-case performance guarantees. In particular, we introduce dual-balancing policies for lost-sales models that are conceptually similar to dual-balancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost. That is, in each period, we balance two opposing costs: the expected marginal holding costs against the expected marginal lost-sales cost. Specifically, we show that the dual-balancing policies for the lost-sales models provide a worst-case performance guarantee of two under relatively general demand structures. In particular, the guarantee holds for independent (not necessarily identically distributed) demands and for models with correlated demands such as the AR(1) model and the multiplicative autoregressive demand model. The policies and the worst-case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times. Our analysis has several novel elements beyond the balancing ideas for backorder models.

We developed this inventory model under price dependent demand in stochastic environment. Here probabilistic lead time is considered and shortages are allowed (if occur) over a finite time horizon. Generalising the work of Maiti et al. (2009) more precisely, we consider this model with just-in-time set up cost where deterioration is taken into account and backlogging rate has been considered as a negative exponential function of the waiting time. Taking all these into account, mathematical expression for expected average profit is derived. A closed form of analytic solution for maximising the expected average profit function is obtained when demand is constant. Numerical examples are carried out to identify the most sensitive parameter.