Inventory decision in a periodic review inventory model with two complementary products

Interaction effect across complementary products plays an important role in characterizing the optimal inventory policy. The inventory levels of complementary products are interrelated due to interaction between demand streams. In this paper, we consider a periodic review base-stock policy in the presence of two complementary products with interrelated demands and joint replenishment. Demands are modeled by a Poisson process and any unmet demand is lost. Demands can be in sets of one unit of each or jointly. If an arrival demand requests two products jointly and one of the products is not in stock, then the whole demand is lost. We aim to investigate how this interrelated demand phenomenon influences the optimal base-stock levels and the period length of a periodic review policy. We utilize the renewal reward theorem to derive the explicit expression of the expected profit rate in the system. The goal is to determine the optimal period length and the base-stock levels such that the expected profit rate is maximized. Enumeration and approximation algorithms are employed to find the optimal and near-optimal solutions, respectively. The approximation algorithm is based on a scenario with independent demand processes which results in an explicit expression for the long-run profit per time unit and leads to analytical solutions for optimal policies. Our numerical results reveal that the solutions obtained by the approximation algorithm are close to optimal solutions. Numerical experiences show that the maximum profit in the system is achieved if the proportion of customers with jointly demand increases. Moreover, the interaction effect between demand processes has a significant impact on the control policy performance when the units lost sales and unit holding costs are high, and the demand rare is low.

Simulating Marginal and Dependence Behaviour of Water Demand Processes at Any Fine Time Scale

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf’s joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h.

Measure and Analysis of the Bullwhip Effect in Supply Chain When Demand Correlation Exists between Two Market Groups Under the First-Order Moving-Average Demand Processes

With supply chains becoming increasingly global, the issue of bullwhip effect, a phenomenon attributable to demand fluctuation in the upstream section of the supply chains, has received greater attention from many researchers. The phenomenon in which the variation of upstream members' orders is amplified than the variation of downstream members' demands in the supply chain is called the bullwhip effect (BWEF). Most of existing research studies did not realize the demand dependency of market demands. Thus, this research focused on the study of the influence of the demand correlation coefficient between two market groups on the BWEF. The incoming demand processes are assumed the separate first-order moving-average, [MA(1)] demand patterns. The scope of the supply chain structure used in this research is composed of one manufacturer and two distribution centers. The general result reveals that the coefficient of correlation is one of several factors affecting the BWEF.

Study of the Bullwhip Effect in a Multistage Supply Chain with Callback Structure considering Two Retailers

With the purpose of researching the bullwhip effect when there is a callback center in the supply chain system, this paper establishes a new supply chain model with callback structure, which has a material supplier, a manufacture, and two retailers. The manufacture and retailers all employ AR(1) demand processes and use order-up-to inventory policy when they make order decisions. Moving average forecasting method is used to measure the bullwhip effect of each retailer and manufacture. We investigate the impact of lead-times of retailers and manufacture, forecasting precision, callback index, and marketing share on the bullwhip effect of both retailers and manufacture. Then we use the method of numerical simulation to indicate the different parameters in this supply chain. Furthermore, this paper puts forward some suggestions to help the enterprises to control the bullwhip effect in the supply chain with callback structure.