An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

Coordinating Pricing and Ordering Decisions in a Multi-Echelon Pharmacological Supply Chain under Different Market Power using Game Theory

Abstract The importance of supply chains in pharmacological industry is remarkable so that nowadays many pharmacological supply chains have an effective and critical role for supplying and distributing drugs in health area. So, this article studies a three-echelon pharmacological supply chain containing multi-distributor of raw materials, a pharmaceutical factory, and multi-drug distributors companies. The distributors of raw material order raw materials of some drugs to own suppliers and sell them to the pharmaceutical factory. The factory transmutes raw materials to the several finished products and sells them to some drug distributors companies. There are several types of raw materials and finished products. Here, it is supposed that the market powers of partners are different. So, the Stackelberg game among the members of the chain is deemed to analyze the coordination behavior of the members of the proposed chain. The aim of the research is to maximize the total profit of supply chain by employing the optimal pricing and ordering decision policies where the order quantities of the distributors and the selling prices of pharmaceutical factory (manufacturer) and the distributors are the decision variables. Besides, the closed form solutions of the decision variables are presented. At the end, numerical example and some sensitivity analysis are presented

Optimising replenishment policy in an integrated supply chain with controllable lead time and backorders-lost sales mixture

This paper aims to optimize the inventory replenishment policy in an integrated supply chain consisting of a single supplier and a single buyer. The system under consideration has the features such as backorders-lost sales mixture, controllable lead time, stochastic demand, and stockout costs. The underlying problem has not been studied in the literature. We present a novel approach to formulate the optimization problem, which is able to satisfy the constraint on the number of admissible stockouts per time unit. To solve the optimization problem, we propose two algorithms: an exact algorithm and a heuristic algorithm. These two algorithms are developed based on some analytical properties that we established by analysing the cost function in relation to the decision variables. The heuristic algorithm employs an approximation technique based on an ad-hoc Taylor series expansion. Extensive numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms

Modelling of Coordinating Production and Inventory Cycles in A Manufacturing Supply Chain Involving Reverse Logistics

In today’s global and competitive markets selling products at competitive prices, coordination of supply chain configuration, and environmental and ecological consciousness and responsibility become important issues for all companies around the world. The price of products is affected by costs, one of which is inventory cost. Inventory does not give any added value to products but must be kept in order to fulfill the customer demand in time. Therefore, this cost must be kept at the minimum level. In order to reduce the amount of inventory across a supply chain, coordination of decisions among all players in the chain is necessary. Coordination is needed not only for a two-level supply chain involving a manufacturer and its customers, but also for a complex supply chain of multiple tiers involving many players. With increasing attention being placed to environmental and ecological consciousness and responsibility, companies are keen to have a reverse supply chain where used products are collected and usable components remanufactured and reused in production to minimize negative impacts on the environment, adding further complexity to decision making across a supply chain. To deal with the above issues, this thesis proposes and develops the mathematical models and solution methods for coordinating the production inventory system in a complex manufacturing supply chain involving reverse logistics and multiple products. The supply chain consists of tier-2 suppliers for raw materials, tier-1 suppliers for parts, a manufacturer who manufactures and assembles parts into finished products, distributors, retailers and a third party who collects the used products and returns usable parts to the system. The models consider a limited contract period among all players, capacity constraints in transportation units and stochastic demand. The solution methods for solving the models are proposed based on decentralized, semi-centralized and centralized decision making processes. Numerical examples are used by adopting data from the literature to demonstrate, test, analyse and discuss the models. The results show that centralised decision making process is the best way to coordinate all players in the supply chain which minimise total cost of the supply chain as a whole. The results also show that the selection of the length of limited horizon/ contract period will be one of the main factors which will determine the type of coordination (decentralised, centralised or semi-centralised) among all players in the supply chain. We also found that the models developed can be viewed as generalised models for multi-level supply chain by examining the models using systems of different tiers from the literature. We conclude that the models are insensitive to changes of input parameters since percentage changes of the supply chain’s total cost are less than percentage changes of input parameters for the scenarios studied

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

Decentralized and centralized supply chains with trade credit option

The notion of a trade credit period is a common business practice, where a supplier allows a buyer a specified period to make a payment in full for a purchase made. The objective of this thesis is to explore the role of such a credit payment option in supply chain management. Towards this end, a two-echelon supply chain, consisting of a single supplier (e.g. manufacturer) and the cases of both a single and multiple buyers (e.g. retailers) is examined under decentralized (independent) and centralized (coordinated) decision making scenarios. The major emphasis of this research is limited to the case of a single product with price-sensitive deterministic, as well as stochastic market demand.The conditions under which a trade credit period should be offered and its appropriate length are determined from the supplier’s perspective under the decentralized case. Under the centralized decision scenario, the efficacy of a trade credit policy as a supply chain coordination mechanism is thoroughly analyzed and guidelines for pricing, production and delivery decisions are developed. The concepts developed in this study are illustrated via a number of numerical examples, in conjunction with thorough sensitivity analyses involving some selected problem parameters.The major contribution of this thesis is that we incorporate the pricing and inventory issues in supply chains with an endogenous credit payment period. This is the first study that examines the efficacy of trade credit option as a coordination mechanism. We propose a coordination mechanism that coordinates the supply chain, when a trade credit by itself is not sufficient to serve such a purpose, while preserving the benefits of a trade credit option. Also, this study is the first to examine the issues concerning trade credit under price sensitive stochastic demand. Another first for this work is the exploration of the implications of a trade credit policy in supply chains consisting of multiple competing retailers. The effects of the extent of competition and the market size on trade credit policy are evaluated. Our analyses lead to some important practical implications, to serve as managerial guidelines.Ph.D., Decision Sciences -- Drexel University, 201