Echelon Inventory System Research Articles

A Heuristic Hybrid Optimization Approach for Spare Parts and Maintenance Workers Under Partial Pooling

The joint planning of spare parts and maintenance workers in a multiple echelon inventory system with lateral and cross-echelon transshipment can reduce the total cost of the system. However, partial pooling is not extensively considered in the joint optimization problem of maintenance resources. In this paper, the objective is to determine the optimal inventory of spare parts and the number of maintenance workers to minimize the total cost of the system considering partial pooling. First, a greedy heuristic is used to obtain the initial inventory. Then, the cat swarm optimization algorithm is formulated to produce nearly optimal results, which can solve larger instances with a faster computation time. Furthermore, a maintenance system with 4 local warehouses, 3 central warehouses and 1 plant serving 5 machine groups is analyzed, in which each machine consists of 5 key components that can breakdown independently. The results verify the effectiveness of the proposed optimization approach. Finally, the total cost for different resource provision scenarios, failure rates and system parameters are discussed.

Coordinated Two-Echelon Inventory Model for Optimal Inventory and Shipment Decisions under Exponential Price Dependent Demand

In this paper, a two echelon inventory system with a single-warehouse and single-retailer is considered. Mathematical model is developed for the retailer, warehouse and for the entire chain by incorporating the ordering/setup costs, carrying costs and transportation costs. Replenishment quantity at the retailer and the number of shipments from the warehouse to the retailer are considered as the decision variables. The objective of the proposed work is to demonstrate the optimality of centralised inventory & shipment decisions and total relevant costs at the respective entities and the chain. Numerical example is considered and the model is solved using the computer program written in MATLAB. From the research findings, it is concluded that the percentage variation in optimality of total transportation cost of the supply chain is in decreasing order with respect to the increased ordering cost of the retailer and set-up cost of the manufacturer. Finally, few managerial implications are derived based on the sensitivity analysis.

Optimality of Cycle Time and Inventory Decisions in a Two Echelon Inventory System with Non linear Price Dependent Demand under Credit Period

In the current day phenomena of globalization, to face the win-win situation between two parties, there should be an understanding with some coordination mechanisms. In most of the recent literature, the widely used approach in supply chain collaboration is credit period. This paper describes about the nonlinear price dependent demand under credit period in a two-echelon inventory system. Single product is shipped from single manufacturer (producer) to the single retailer (vendor), where the manufacturer provides credit period to the retailer. In these criteria, the total supply chain is evaluated in terms of cycle time, retailers’ replenishment quantity, number of deliveries and the total relevant cost. To solve optimality conditions, MATLAB program is written in computer. To see variations in optimality of decision variables, sensitivity analysis is carried out with a numerical illustration. Finally, we present results, some of them are validations, which prove, that our new approach is reliable with nonlinear phenomena. This study aims to applying credit period scenario to the retailer with nonlinear price dependent demand. With this model, some of the managerial decision like cycle time, retailers’ replenishment quantity, number of deliveries and the yearly overall supply chain cost are obtained.

Modeling of a two echelon inventory system under trade credit with finite production rate

The present competitive business situation, it has become typical of providing trade credit by the supplier (may be a manufacturer) to the vendor (may be a retailer) as part of improving the sales revenues. In this particular paper, development of a two echelon inventory model is proposed by considering a one supplier supplying a one kind of product to a one vendor under trade credit with finite production rate. The important aim of the proposed model is to exemplify the optimality of cycle time, inventory levels and total supply chain variable costs of the coordinated model. Ordering costs, carrying costs and transportation costs are considered for the proposed development of the model. The mathematical model is formulated in two fold: the expressions for total variable cost of the vendor and supplier are developed first and then for the entire supply chain. A solution procedure is developed and a MATLAB computer program is written to solve the model along with the sensitivity analysis is carried out.

Continuous Review Two-Echelon (s,S) Inventory System with Partial Backlogging

Inventories exist throughout the supply chain in various forms for various reasons. This paper presents a continuous review two echelon inventory system. The operating policy at the lower echelon is (s, S) that is whenever the inventory level traps to s on order for Q = (S-s) items is placed, the ordered items are received after a random time which is distributed as exponential. We assume that the demands accruing during the stock-out period are partially backlogged. The retailer replenishes their stock from the regular supplier which adopts (0,M) policy, M = n1Q. When the regular supplier stock is empty the replacement of retailer stock made by the outside supplier who adopts (0,N) policy N = n2Q. The joint probability disruption of the inventory levels of retailer, regular supplier and the outside supplier are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system are presented.

Optimality of cycle time and inventory decisions in a two echelon inventory system with exponential price dependent demand under credit period

This work describes and proposes an two echelon inventory system under supply chain, where the manufacturer offers credit period to the retailer with exponential price dependent demand. The model is framed as demand is expressed as exponential function of retailer’s unit selling price. Mathematical model is framed to demonstrate the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. The major objective of the paper is to provide trade credit concept from the manufacturer to the retailer with exponential price dependent demand. The retailer would like to delay the payments of the manufacturer. At the first stage retailer and manufacturer expressions are expressed with the functions of ordering cost, carrying cost, transportation cost. In second stage combining of the manufacturer and retailer expressions are expressed. A MATLAB program is written to derive the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. From the optimality criteria derived managerial insights can be made. From the research findings, it is evident that the total cost of the supply chain is decreased with the increase in credit period under exponential price dependent demand. To analyse the influence of the model parameters, parametric analysis is also done by taking with help of numerical example.

Optimality of Cycle Time and Inventory Decisions in a Two Echelon Inventory System with Price Dependent Demand under Credit Period

Background/Objectives: This paper describes about the optimal values of the variables decision and function of objective of the entire supply chain under credit period with price dependent demand. Methods/Statistical Analysis: Initially the problem is framed with the expressions of the overall variable cost of the retailer and manufacturer is developed separately. Later the problem can be organised with the expressions of the overall variable cost of the retailer and manufacturer is developed for the entire supply chain as a function of retailers ordering costs and manufacturer set up costs along with carrying costs, and transportation cost. Findings: Numerical example is illustrated along with computer programme is solved in MATLAB. The model is solved for optimal values of cycle time, inventory level, number of shipments and the total annual cost of the individual entities and the entire supply chain. Also, the sensitivity analysis is carried out. From the research findings, it is evident that with credit period interpretation, the total annual cost is decreased with increase in trade credit. Applications/Improvements: Based on the research findings, it is concluded that total annual relevant cost of the supply chain becomes less, if the manufacturer permits to delay the retailer payments in more number of days.

Centralised and decentralised three echelon inventory model for optimal inventory decisions under price dependent demand

In this paper, a three echelon inventory system with a single manufacturer supplying a single kind of a product to a single distributor and then to a single retailer, is considered. Mathematical model is developed for annual total relevant costs of the coordinated and non-coordinated supply chain. The novel idea of the proposed model is that the demand is a function of retailer's unit selling price, which in turn is a function of retailer's replenishment quantity with dependence factor. The objective of the model is to demonstrate the optimality of inventory decisions, shipment frequencies and total relevant costs with respect to dependence factor. Numerical illustration is carried out to demonstrate the optimality of replenishment decisions. Finally, managerial insights are inferred in selecting the optimal replenishment quantity and shipment frequency that minimises the total relevant cost of the supply chain.

Optimal lot sizing and inventory decisions in a centralised and decentralised two echelon inventory system with price dependent demand

In the present-day scenario of global competitive environment, the consideration of the elasticity of demand has become one of the significant factors for designing effective supply chain coordination. In this paper, an integrated inventory model for optimal lot sizing and inventory decisions for centralised and decentralised supply chain with a single customer and single supplier considering ordering/setup costs, carrying costs and transportation costs of respective entities has been developed. The main contribution of this work is to demonstrate the implications of a dependence factor over the optimality of inventory levels, number of shipments and the total variable costs under price dependent demand which in turn is a function of replenishment quantity with dependence factor. A computer program is written in MATLAB as per the solution procedure developed to solve the model. Numerical example is devised to illustrate the optimality of decision variables, and objective function and also the sensitivity analysis is carried out.

An Innovative Heuristic in Multi-Item Replenishment Problem for One Warehouse and N Retailers

Joint replenishment problem (JRP) is a type of inventory model which aims to minimize the total inventory cost consisting of major ordering cost, minor ordering cost and inventory holding cost. Different from previous papers, this study considers one warehouse, multi items and N retailers. An innovative heuristic approach is developed to solve the problem. In this paper, we consider a multi echelon inventory system and seek to find a balance between the order cost and the inventory holding costs at each installation. The computational results show that the innovative heuristic provides a near exact optimal solution, but is more efficient in terms of the computational time and the iteration number.

Optimality of Cycle Time and Inventory Decisions in a Two Echelon Inventory System under Credit Period

In the present day scenario of business competition, it has become customary of providing trade credit by the manufacturer to the retailer as part of enhancing the sales turnover. When a manufacturer offers credit period to the retailer, the retailer need not to pay the manufacturer immediately. Under this particular phenomenon, it is essential to analyze the overall performance of the supply chain in terms of cycle time, inventory levels, shipment frequency and the annual total relevant cost of the entire supply chain. In this paper, a mathematical model is developed for a two-echelon inventory system comprising of a single manufacturer supplying a single kind of product to a single retailer. The main objective of the proposed work is to demonstrate the optimality of cycle time, inventory levels, shipment frequency and the total relevant cost of the coordinated supply chain under the novel idea of trade credit. A numerical illustration is carried out with the help of a numerical example and also the sensitivity analysis is carried out.

On the performance of the base-stock inventory system under a compound Erlang demand distribution

In this paper, we propose a new method for determining the optimal base-stock level in a single echelon inventory system where the demand is a compound Erlang process and the lead-time is constant. The demand inter-arrival follows an Erlang distribution and the demand size follows a Gamma distribution. The stock is controlled according to a continuous review base-stock policy where unfilled demands are backordered. The optimal base-stock level is derived based on a minimization of the total expected inventory cost. A numerical investigation is conducted to analyze the performance of the inventory system with respect to the different system parameters and also to show the outperformance of the approach that is based on the compound Erlang demand assumption as compared to the classical Newsboy approach. This work allows insights to be gained on stock control related issues for both slow and fast moving stock keeping units.

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.

Modeling the influence of multiple expiration dates on revenue generation in the supply chain

PurposeInventory control models for perishable products have primarily used a FIFO issuing policy with the objective of minimizing the number of outdated units. This paper aims to develop a model to evaluate an issuing policy for a single product with a fixed shelf life in single echelon inventory system. The issuing policy considers the remaining shelf life of the in‐stock inventory and the expected time that the product will spend in inventory as the decision driver.Design/methodology/approachThe model developed has an objective of maximizing expected revenue over time with a budget constraint. A heuristic algorithm is proposed to iteratively arrive at the best solution to the formulation. The heuristic is tested by employing a simulation model of the system.FindingsThe proposed heuristic is tested against both the FIFO and the random allocation approaches and found to be superior for all the in‐stock with remaining shelf life distribution means of above 40 percent. No significant performance differences were found for the three approaches for remaining shelf life distribution.Research limitations/implicationsThe research is focused on a single product with multiple expiration dates and further research is necessary to determine the best policies for the multi‐product multi‐expiration date environment where the items are substitutable..Practical implicationsRetailers stock items with multiple expiration dates. The customer, for obvious reasons, is more likely to choose the item with the longer remaining shelf life. Therefore, the supply to the retailer's shelves and issuing policies for making available the particular items to the customers affect product outdating and related costs. Revenues will be affected by the extent to which more can be charged for items with a longer remaining shelf life or by the impact of the remaining shelf life on demand. This paper provides for a practical approach to that end.Originality/valueThe proposed issuing policy has not been tested before and thus makes a contribution to the body of knowledge. The flexibility of using different values for acquisition costs, selling prices, salvage value and penalty functions is a particular strength of the proposed model. Moreover, its potential application to inventory control problems for a wide range of perishable products is substantial.

A New Decision Rule for Lateral Transshipments in Inventory Systems

This paper deals with a single–echelon inventory system consisting of a number of parallel local warehouses facing compound Poisson demand. There are standard holding and backorder costs as well as ordering costs at all warehouses. Normally, the warehouses replenish from an outside supplier. However, lateral transshipments between the warehouses are also possible. Such transshipments take no time but incur additional costs. When a demand occurs at a warehouse, the question is whether the whole demand or part of it should be covered by a lateral transshipment from another warehouse. Given a set of alternative decisions, our decision rule minimizes the expected costs under the assumption that no further transshipments will take place. This rule is then used repeatedly as a heuristic. A simulation study illustrates how the suggested technique performs under different conditions.

Rationing safety stock in the USAF's multi echelon inventory system

The United States Air Force (USAF) operates one of the largest multi-echelon inventory systems in the world. Individual bases hold inventory to meet the demands of their customers at the base. These bases are re-supplied by central depots that are, in turn, re-supplied by vendors. The Air Force Logistics Command (AFLC) has proposed the adoption of a method of rationing assets at the depot as a means of improving weapon system availabilities. A large scale simulation model of the USAF's multi-echelon inventory system was used to study the effects of such a rationing procedure. The simulation results demonstrate that the consequences of the proposed rationing scheme are contrary to what had been intuitively expected. In fact, the proposed policy change would have decreased rather than increased performance.