Integrated inventory model for single vendor–single buyer with probabilistic demand

In this paper, we consider single vendor–single buyer integrated inventory model with probabilistic demand and equal delivery lot size. The model contributes to the current literature by relaxing the deterministic demand assumption which has been used for almost all integrated inventory models. The objective is to minimise expected total costs incurred by the vendor and the buyer. We develop effective iterative procedures for finding the optimal solution. Numerical examples are used to illustrate the benefit of integration. A sensitivity analysis is performed to explore the effect of key parameters on delivery lot size, safety factor, production lot size factor and the expected total cost. The results of the numerical examples indicate our integrated model gives a significant cost savings over independent model

Optimal consignment stocking policies for a supply chain under different system constraints

The research aims are to enable the decision maker of an integrated vendor-buyer system under Consignment Stock (CS) policy to make the optimal/sub-optimal production/replenishment decisions when some general and realistic critical factors are considered. In the system, the vendor produces one product at a finite rate and ships the outputs by a number of equal-sized lots within a production cycle. Under a long-term CS agreement, the vendor maintains a certain inventory level at the buyer’s warehouse, and the buyer compensates the vendor only for the consumed products. The holding cost consists of a storage component and a financial component. Moreover, both of the cases that the unit holding costs may be higher at the buyer or at the vendor are considered. Based upon such a system, four sets of inventory models are developed each of which considers one more factor than the former. The first set of models allows a controllable lead-time with an additional investment and jointly determines the shipping size, the number of shipments, and the lead time, that minimize the yearly joint total expected cost (JTEC) of the system. The second set of models considers a buyer’s capacity limitation which causes some shipments to be delayed so that the arrival of these shipments does not cause the buyer’s inventory to go beyond its limitation. As a result, the number of delayed shipments is added as the fourth decision variable. A variable demand rate is allowed in the third set of models. Uncertainty caused by the varying demand are controlled by a safety factor, which becomes the fifth decision variable. Finally, the risk of obsolescence of the product is considered in the fourth model. The first model is solved analytically, whereas the rest are not, mainly because of the complexity of the problem and the number of variables being considered. Three doubly-hybrid meta-heuristic algorithms that combine two different hybrid meta-heuristic algorithms are developed to provide a solution procedure for the rest of models. Numerical experiments illustrate the solution procedures and reveal the effects of the buyer’s capacity limitation, the effects of the variable demand rate, and the effects of the risk of obsolescence, on the system. Furthermore, sensitivity analysis shows that some of the system parameters (such as the backorder penalty, the extra space penalty, the ratio of the unit holding cost of the vendor over that of the buyer) are very influential to the joint system total cost and the optimal solutions of the decision variables

A fuzzy periodic review integrated inventory model involving stochastic demand, imperfect production process and inspection errors

In this study, we investigate an integrated production-inventory system consisting of a single-vendor and single-buyer. The buyer manages its inventory level periodically at a certain period of time. We consider a fuzzy annual demand, imperfect production, inspection errors, partial backordering, and adjustable production rate in the proposed model. Additionally, it is assumed that the protection interval demand follows a normal distribution. The model contributes to the current literature by allowing the inclusion of fuzzy annual demand, adjustable production rate and imperfect production and inspection processes. Our objective is to optimize the number of deliveries from vendor to buyer, the buyer’s review period, and the vendor’s production rate, so that the joint expected total annual cost incurred has the minimum value. Furthermore, an iterative procedure is proposed to find the optimal solutions of the model. We also provide a numerical example and conduct a simple sensitivity analysis to illustrate the model’s behaviour and feasibility. The results from the sensitivity analysis show that the defective rate, type I inspection error, fuzzy annual demand, fixed production cost, variable production cost and setup cost give impacts to both the review period and production rate. Finally, it is concluded that the proposed model can be applied by managers or practitiones for managing inventories across the supply chain involving a vendor and a buyer

Integrated supply chain inventory model with quality improvement involving controllable lead time and backorder price discount

For the past four decades the integrated vendor and buyer supply chain inventory model has been an interesting topic, but quality improvement of defective items in the integrated inventory model with backorder price discount involving controllable lead time has been rarely discussed. The aim of this paper is to minimize the total related cost in the continuous review model by considering the order quantity, reorder point, lead time, process quality, backorder price discount and number of shipment as decision variables. Moreover, we assume that an investment function is used to improve the process quality. The lead time demand follows a normal distribution. In addition, the buyer offers backorder price discount to motivate the customers for possible backorders. There are some defective items in the arrival lot, so its treatment is also taken in account in this paper. We develop an iterative procedure for finding the optimal values of decision variables and numerical example is presented to illustrate the solution procedure. Additionally, sensitivity analysis with respect to major parameters is also carried out

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment

Supply chain single vendor – Single buyer inventory model with price-dependent demand

Purpose: The aim of this article is developing an integrated production-inventory-marketing model for a two-stage supply chain. The demand rate is considered as the Iso-elastic decreasing function of the selling price. The main research goal of the article is to obtain the optimal values of the selling price, order quantity and number of shipments for the proposed model under independent and also joint optimization. In addition, the effects of the model’s parameters on the optimal solution are investigated. Design/methodology/approach: Mathematical modeling is used to obtain the joint total profit function of the supply chain. Then, the iterative solution algorithm is presented to solve the model and determine the optimal solution. Findings and Originality/value: It is observed that under joint optimization, the demand rate and the supply chain’s profit are higher than their values under independent optimization, especially for the more price sensitive demand. Therefore, coordination between the buyer and the vendor is advantageous for the supply chain. On the other hand, joint optimization will be less beneficial when there isn’t a significant difference between the buyer’s and the vendor’s holding costs. Originality/value: The contribution of the article is determining the ordering and pricing policy jointly in the supply chain, which contains one vendor and one buyer while the demand rate is the Iso-elastic function of the selling pricePeer Reviewe

Efficient near-optimal procedures for some inventory models with backorders-lost sales mixture and controllable lead time, under continuous or periodic review

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimize these novel inventory models. The optimization is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimization procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models

Reducing lead time risk through multiple sourcing: the case of stochastic demand and variable lead time

This paper studies a buyer sourcing a product from multiple suppliers under stochastic demand. The buyer uses a (Q, s) continuous review, reorder point, order quantity inventory control system to determine the size and timing of orders. Lead time is assumed to be deterministic and to vary linearly with the lot size, wherefore lead time and the associated stockout risk may be influenced by varying the lot size and the number of contracted suppliers. This paper presents mathematical models for a multiple supplier single buyer integrated inventory problem with stochastic demand and variable lead time and studies the impact of the delivery structure on the risk of incurring a stockout during lead time