A Closed-Form Approximation Solution for an Inventory Model with Supply Disruptions and Non-ZIO Reorder Policy (original) (raw)
Related papers
Cost-effective ordering policies for inventory systems with emergency order
Computers & Industrial Engineering, 2009
Most of the studies on inventory control reported in earlier contributions deal with the optimization problems minimizing an expected cost criterion such as the long-run average cost. However, when the plant engineers design the inventory systems in practical situations, they must take account of reliability into the inventory system as well as economical aspect, where reliability can be defined as the probability that the stock is not depleted until a pre-specified time. In this paper, we discuss the inventory control policies that provide a balance between economical and reliability requirements. By applying the cost effectiveness criterion, which simultaneously includes the effects of system availability and expected cost, as optimality one, we derive the optimal inventory replenishment policies of two kinds of inventory models. Finally, with a set of numerical examples, we show that the optimal inventory policies of the models under consideration make the stationary availability increase.
Inventory management under random supply disruptions and partial backorders
Naval Research Logistics, 1998
We explore the management of inventory for stochastic-demand systems, where the product's supply is randomly disrupted for periods of random duration, and demands that arrive when the inventory system is temporarily out of stock become a mix of backorders and lost sales. The stock is managed according to the following modified (s, S) policy: If the inventory level is at or below s and the supply is available, place an order to bring the inventory level up to S. Our analysis yields the optimal values of the policy parameters, and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands.
A vendor managed inventory policy with emergency orders
Journal of Industrial and Production Engineering, 2020
Due to the large amount of money engaged with inventory along supply chains, especially with inventory holding costs, it is extremely important to employ a good inventory policy in order to meet the customer demand without delays. This paper presents a vendor-managed inventory policy with emergency orders, for a supply chain which consists of a single vendor and a single retailer where the retailer faces Poisson customer demand. Two mathematical models were developed using two approaches. Approach 1 used the concept of demand rate while approach 2 is based on total demand received during the cycle. The formulated models are used to determine the optimal base stock level, delivery quantity to the retailer and cycle length such that the total expected inventory cost is minimized. Numerical experiments and sensitivity analysis were conducted to examine the behavior of the optimal solution and provide general guidelines and implications.
Industrial Engineering and Management, 2017
This study considers a reliable location – inventory problem for a supply chain system comprising one supplier, multiple distribution centers (DCs), and multiple retailers in which we determine DCs location, inventory replenishment decisions and assignment retailers to DCs, simultaneously. Each DC is managed through a continuous review (S, Q) inventory policy. For tackling real world conditions, we consider the risk of probabilistic distribution center disruptions, and also uncertain demand and lead times, which follow Poisson and Exponential distributions, respectively. A new mathematical formulation is proposed and we model the proposed problem in two steps, in the first step, a queuing system is applied to calculate mean inventory and mean reorder rate of steady-state condition for each DC. Next, regarding the results obtained from the first step, we formulate a mixed integer nonlinear programming model which minimizes the total expected cost of inventory, location and transporta...
Optimal inventory policies with non-stationary supply disruptions and advance supply information
Decision Support Systems, 2012
We consider the production/inventory problem of a manufacturer (or a retailer) under non-stationary and stochastic supply availability. Although supply availability is uncertain, the supplier would be able to predict her near future shortages -and hence supply disruption to (some of) her customers-based on factors such as her pipeline stock information, production schedule, seasonality, contractual obligations, and non-contractual preferences regarding other manufacturers. We consider the case where the information on the availability of supply for the near future, which we refer to as advance supply information (ASI), is provided by the supplier. The customer demand is deterministic but non-stationary over time, and the system costs consist of fixed ordering, holding and backorder costs. We consider an all-or-nothing type of supply availability structure and we show the optimality of a state-dependent (s, S) policy. For the case with no fixed ordering cost we prove various properties of the optimal order-up-to levels and provide a simple characterization of optimal order-up-to levels. For the model with fixed ordering cost, we propose a heuristic algorithm for finding a good ordering strategy. Finally, we numerically elaborate on the value of ASI and provide managerial insights.
International Journal of Management Science and Engineering Management, 2018
Effective response and recovery from disruptions are vital to achieving the supply chain objectives. This study aims to formulate a quantitative model for mitigating disruptions in a supply chain. An inventory model has been developed for a manufacturer with one supplier and one retailer by considering random capacity of the supplier and random availability of both the supplier and the retailer assuming zero delivery lead time. Backorders are allowed and it has two parts-unit dependent and both unit and time-dependent. This study suggests an optimal order quantity and a reordering point so that the average cost per cycle gets minimized. A genetic algorithm is used to solve the proposed inventory model. The applicability of the proposed model has been tested using a numerical example. Finally, sensitivity analysis is performed to examine the robustness of the model.
Annals of Operations Research
This study develops an inventory model to solve the problems of supply uncertainty in response to demand which follows a Poisson distribution. A positive aspect of this model is the consideration of random inventory, delivery capacities and supplier's reliability. Additionally, we assume supplier capacity follows an exponential distribution. This inventory model addresses the problem of a manufacturer having an imperfect production system with single supplier and single retailer and considers the quantity of product (Q), reorder points (r) and reliability factors (n) as the decision variables. The main contribution of our study is that we consider supplier may not be able to deliver the exact amount all the time a manufacturer needed. We also consider that the demand and the time interval between successive availability and unavailability of supplier and retailer follows a probability distribution. We use a genetic algorithm to find the optimal solution and compare the results with those obtained from simulated annealing algorithm. Findings reveal the optimal value of the decision variables to maximize the average profit in each cycle. Moreover, a sensitivity analysis was carried out to increase the understanding of the developed model. The methodology used in this study will help manufacturers to have a better understanding of the situation through the joint consideration of disruption of both the supplier and retailer integrated with random capacity and reliability.
A newsvendor inventory model with an emergency order to supply a non-increasing fraction of shortage
Applied Mathematics and Computation, 2014
This paper generalizes the newsvendor inventory model when the possibility of an emergency order to satisfy the excess of demand exists. In this situation, we assume that there are impatient customers who do not wait for the emergency order and other customers who are willing to wait to satisfy their demand. We consider that the fraction of shortage that is satisfied with delay through the emergency order is described by a function, which is non-increasing with respect to the amount of shortage. Our objective is to determine the optimal order quantity, which maximizes the relevant expected total profit for the period, when the demand follows a uniform probability distribution. As is well known, this distribution is usually used to denote the results of a demand whose values are unknown, except for the fact that such results belong to an interval. The uniqueness and existence of optimal decisions are proved, and a procedure to determine the optimal policy and the maximum expected profit is developed. Illustrative examples, which help us to understand the theoretical results, are also given.
IFAC-PapersOnLine, 2015
The study of a real-time procurement and production mechanism for a multi-stage supply chain system with multiple suppliers subject to an unexpected disruption is presented in this paper. Specifically, a mathematical model is developed for the problem of optimizing replenishment and production decisions for each node after a supply disruption occurrence. The system considered in this research is a three stage supply chain system that consists of three suppliers, one manufacturer and one retailer. The problem that will be considered is an instance of the class of inventory management problems under disruptions with a finite horizon. The solution approach will utilize a heuristic that we have developed in previous works. In addition, an experiment was conducted to study the effects of disruption on the system using predefined scenarios, where supplier prioritization of disruption mitigation strategies was explored. Various disruption scenarios were predefined by combining different disruption locations, as well as different combinations of suppliers. It can be shown that supply disruption at the suppliers with higher inventory holding costs causes higher recovery costs for the overall system. Therefore, it is important for the manufacturer to focus on the suppliers with higher holding cost when planning appropriate strategies for risk management. This optimization study has enabled an increased understanding of the impacts of random disruption events on the total system behaviour, as well as determining priorities in risk mitigation efforts.
Effect of supply disruption on inventory policy
European J. of Industrial Engineering, 2019
This research examines a two-stage supply chain that comprises a supplier who is subject to stochastic disruption and a retailer who has to deal with supply disruption by holding inventory. Under a periodic-review base-stock inventory policy, the main objectives of this study are to determine the optimal inventory policy in the presence of stochastic supply disruption so as to minimise the total inventory cost as well as to analyse the impact of supply disruption on the optimal inventory policy. In this research, the length of a supply disruption is modelled as a continuous random variable, distinguishing it from previous research which modelled the length of a supply disruption as a discrete random variable that receives values only as multiples of the length of a review period. Numerical experiments have been conducted to illustrate the applicability of the proposed inventory model and to examine the effects of various input parameters on the optimal inventory policy. Furthermore, compared with the optimal inventory policy derived when the length of a supply disruption is considered as a multiple of the length of a review period, the proposed inventory model in this research can help derive a more precise optimal inventory policy.