An operational policy for a single vendor multi buyer integrated inventory supply chain system considering shipping time

Since its introduction, the concept of integrated inventory supply chain has received a considerable amount of attention. The majority of studies in the last three decades revealed an increase in holding cost as product moves further down the chain or up the chain. A recent study Hoque (2008) considered vendor’s setup cost and inventory holding cost. Some research also considered fixed transportation cost, which is unrealistic. This study focuses on a single-vendor, multi-buyer scenario and presents three models. First, two models illustrate the transferring of equally-sized batches. Then, a third model considers the transferring of unequally-sized batches in a lot. This study relaxes the assumption that vendor’s holding cost must be greater than or less than all buyer’s holding costs in the system. Also, this research facilitates unequal transportation time and cost for different buyers for greater flexibility. The total system cost is calculated by summing the annual operational cost for all the parties in the system. Optimum values of the decision variables are determined using a direct search method. As presented by the third model, a numerical example demonstrates that the total system cost is less when compared with other two models presented. This study also presents the following: solution procedures to solve each model, many numerical examples to support mathematical findings, and performance comparisons among three findings. In order to justify the lot-splitting approach for solving the integrated inventory problem, alternative models with no lot splitting are devised and tested under the same circumstances. Alternative models with no lot splitting produce similar or better results. Under the same circumstances, the alternate third model is observed to be offering the least total cost for the system. This study also presents a sensitivity analysis to check the robustness of the three models. The future extension of this research may involve considering storage capacity constraint and random demand

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

Multi-Item Single-Vendor-Single-Buyer Problem with Consideration of Transportation Quantity Discount

This paper deals with the problem of shipping multiple commodities from a single vendor to a single buyer. Each commodity is assumed to be constantly consumed at the buyer, and periodically replenished from the vendor. Furthermore, these replenishments are restricted to happen at discrete time instants, e.g., a certain time of the day or a certain day of the week. At any such time instant, transportation cost depends on the shipment quantity according to certain discount scheme. Specifically, we consider two transportation quantity discount schemes: LTL (less-than-truckload) incremental discount and TL (truckload) discount. For each case, we develop MIP (mixed integer programming) mathematical model whose objective is to make an integrated replenishment and transportation decision such that the total system cost is minimized. We also derive optimal solution properties and give numerical studies to investigate the problem.Singapore-MIT Alliance (SMA

A Cooperative Inventory Model for Vendor-Buyer System with Raw Material Decisions, Deterministic Lead Time and Stochastic Demand

This study investigates integrated inventory problem for a two-stage supply chain consisting of a single vendor and single buyer. We develop a model for coordinating the replenishment decisions for raw material procurement, production, and shipment under stochastic environment. For attaining the model objective, we develop an algorithm to determine the optimal shipment-sized, safety factor, number of shipment and number of raw material replenishment based on minimum expected total cost. Furthermore, numerical examples are given to illustrate the effect of primary parameters on the lot size, safety factor, number of batches and expected total cost. The results from numerical examples shows that making production-inventory decisions jointly can reduces expected total cost comparing with making decisions individually. Keywords: Supply chain, replenishment decision, raw material procurement, production, shipment, stochastic

A Multiple-Buyer Single-Vendor in a Continuous Review Inventory Model with Ordering Cost Reduction Dependent on Lead Time

In this competitive environment, integration between two or more business entities is an important way to gain competitive advantages as it lowers supply chain cost. This paper presents a multiple-buyer single-vendor integrated inventory system with ordering cost reduction on lead time. The options of ordering cost reduction included lead time of every buyer can be reduced at an added crash cost. Lead time plays a vital role in supply chain management and inventory management system. A lead time means that time gap between the placing of an order and its actual arrival in the inventory. In this paper, we study a continuous review model. The model is formulated to integrated total cost of the vendor-buyers system to determine the optimal solutions of order quantity, ordering cost, lead time and the number of deliveries between the vendor and buyers in a production cycle. Finally, a numerical example and effects of key parameter are included to illustrate the results of the proposed model

Optimal production-shipment decisions for the finite production rate model with scrap

This paper is concerned with the decision-making on the optimal production batch size and optimal number of shipments for a finite production rate model with random scrap rate. The classic finite production rate (FPR) model assumes a continuous inventory issuing policy for satisfying product demand and perfect quality for all items produced. However, in a real life vendor-buyer integrated production-inventory system, a multiple shipment policy is practically used in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. All nonconforming items produced are assumed to be scrap, and the finished (perfect quality) products can only be delivered to customers if the whole lot is quality assured at the end of the production run. The fixed-quantity multiple instalments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modelling is employed and the renewal reward theorem is used to cope with the variable production cycle length. The long-run average cost for the proposed model is derived, and its convexity is proved by the use of the Hessian matrix equations. A closed-form optimal production-shipment policy for such an imperfect FPR model is obtained and a special case is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage

Replenishment policies for a tree-type three echelon supply chain system

One of the common goals which most companies have is to maximize profits. There are two way to increase profit: increasing revenue or reducing cost. Lacking of ability to keep the cost down could potentially drive the companies out of the business. In recent years, many researchers have been paying more attention on improving supply chain system due to high potential of creating cost savings. The supply chain network considered in this research is a tree-type, three-echelon single producer, multiple distributors, and multiple retailers system. The goal of this research is to develop a replenishment policy which satisfies customers’ demand and minimizes the total production-inventory system cost. Three inventory models are developed here. First, tree-type, three-echelon distribution (producer, distributor and retailers) model with end customers’ backorders (TDB) at retailer’s level is developed. Second, the variation of downstream holding cost (DHV) is studied and a model is developed to investigate the effect downstream holding cost structure. Third, a model is developed to improve the retailer’s service rate (ISR). This model combines the features of TDB and DHV models together (allowable backorder and reduced delivery interval at retailer’s level). Operational schedules of TDB are constructed and the limitations of DHV model are established. The improvement in the ISR model is confirmed and demonstrated through numerical examples. Significance and conclusions of this research are highlighted along with an indication of future research