Vendor-managed Inventory Systems Research Articles

Optimal green investments and replenishment decisions in vendor-managed inventory systems for non-instantaneous deteriorating products with partial backordering

Optimal green investments and replenishment decisions in vendor-managed inventory systems for non-instantaneous deteriorating products with partial backordering

Optimal operational service levels in vendor managed inventory contracts - an exact approach

Vendor Managed Inventory (VMI) contracts are anchored on a fill rate at which the vendor is expected to meet the end-customer demand. Violations of this contracted fill rate due to excess and insufficient inventory are both penalized, often in a linear, but asymmetric manner. To minimize these costs, the vendor needs to maintain an operational fill rate that is different from the contracted fill rate. We model, analyze and solve an optimization problem that determines this operational fill rate and the associated optimal inventory decision. We establish that, for some special, yet popular, models of demand (e.g. truncated normal, gamma, Weibull and uniform distributions), the optimal solution can be derived in closed form and computed precisely. For other demand distributions, either the optimization problem becomes ill-defined or we may need to use approximate solution methods. An extensive computational study reveals that, for realistic values of problem parameters, the operational fill rate is often larger (by as much as 20%) than the contracted service level, possibly explaining the inventory glut commonly observed in real-world VMI systems.

Pricing and inventory policy for non-instantaneous deteriorating items in vendor-managed inventory systems: a Stackelberg game theory approach

Recent improvements in technologies highlight the importance of life-cycle management in the supply chain. This is more important when dealing with non-instantaneous deteriorating items due to the fact that these goods begin losing their marginal values once they are stored as inventories in the warehouses. In this regard, an accurate inventory policy should be taken into account for this type of deterioration. Considering different aspects of the supply chain, many assumptions have been made in the literature for inventory policies of non-instantaneous deteriorating items. Many of these simplifying assumptions are used in order to avoid the complexity of formulations and mathematical modelling. However, in this paper, a thorough and comprehensive model based on the Stackelberg game is proposed in order to consider a two-echelon supply chain with uncertain demand that is dependent upon price and time. Furthermore, a price-discount strategy is applied within the deterioration period as a persuasion strategy to increase customer demand and reduce deterioration costs. The different relationships between inventory parameters and variables are investigated by a precise sensitivity analysis, and the robustness of the presented results is confirmed. The results suggest the appropriate time for the beginning of a discount strategy and the amount of discount.

Automated vending machine with IoT infrastructure for smart factory application

Vending Machine (VM) is a beverage that can operate in a standalone manner to serve beverage or snack purchase transactions. VM technology, especially in the development of the Internet and smart business, has progressed and easier for users, in this case, the seller, the buyer, and the developers. The Internet of Things (IoT) is a new technology paradigm envisioned as a global network of machines and devices capable of interacting with each other. The IoT is recognized as one of the most important areas of future technology and is gaining vast attention from a wide range of industries. The true value of the IoT for enterprises can be fully realized when connected devices can communicate with each other and integrate with vendor-managed inventory systems, customer support systems, business intelligence applications, and business analytics. This article offers a conceptual VM, the system design using e-money payment and online information management. Major components of the machine are, a scanner to take the input from users, large storage space to store the beverages and snacks, sensors to detect the motion, inventory monitoring system to keep track of the storage, and an inventory monitoring system.

CAR: heuristics for the inventory routing problem

Vendor managed inventory (VMI) is a streamlined approach to inventory and order fulfillment and is a system in which vendors continuously and automatically replenish a trading partner’s inventory. Vendors must ensure appropriate quantities of storages at the point of demand and must ensure optimal distribution plans, including routing of the distribution vehicles. This problem is known as the inventory routing problem (IRP) and seeks to integrate the routing of vehicles used for collection and distribution, with conventional inventory management. This paper addresses an IRP with a manufacturer that supplies a product using a fleet of vehicles to a set of warehouses over a defined time horizon. We develop a mixed integer linear program to determine the optimal allocation and the routing schedule for warehouses over the defined time horizon. To solve this problem, we propose a three-phase heuristic approach, called CAR: clustering of receiver nodes, allocation of quantities to these nodes, and routing of delivery vehicles through clusters of nodes. Computational studies are carried out and experimental trials conducted over a large number of data sets provide encouraging results and show usefulness of the solution approaches. The proposed ILP would provide optimal solution to the problem but it demands huge computational effort. However, CAR2, a proposed heuristic, is able to get solutions 7.41% better than the upper bound solutions obtained from CPLEX. These approaches can easily be implemented into existing VMI systems.

Optimizing vendor-managed inventory systems with limited storage capacity and partial backordering under stochastic demand

A supply chain member’s coordination is a challenging issue and a key factor of success in business markets. In vendor-managed inventory systems, the vendor makes replenishment decisions at the site of buyer by which the supply chain can be coordinated more efficiently. Two integrated vendor managed inventory systems under continuous review and periodic review replenishment policies are developed considering partial backordering and limited storage capacity at the buyer’s side. Furthermore, traditional retailer managed inventory systems under the same settings are developed to compare against the integrated systems. Efficient algorithms are presented to derive the optimal values of decision variables. Finally, numerical experiments and comprehensive sensitivity analysis are used to show the applicability and efficiency of the proposed VMI systems.

A matheuristic solution approach for the production routing problem with visit spacing policy

The production routing problem (PRP) is an integrated operational planning problem that combines the two well-known optimization problems, vehicle routing problem (VRP) and lot-sizing problem (LSP). The PRP especially arises in vendor managed inventory (VMI) systems. The solutions obtained in VMI systems tend to benefit both the vendor and the retailers, however, solving PRPs by aiming only cost minimization may not provide satisfactory results to both parties. To remain competitive, companies also need to consider the service quality level. Visit spacing policy (VSP) is especially important to provide higher quality service to the retailers. In the VSP implementation, visit times of the retailers are regulated by imposing a minimum and a maximum time interval between two consecutive visits to the same retailer to ensure smoother operations. In this study, we extend the basic version of the PRP by taking into consideration the VSP. For its solution, an iterative matheuristic algorithm (MA) is proposed. The proposed MA is tested on a set of randomly generated problem instances with VSP as well as on standard PRP and the inventory routing problem (IRP) with VSP benchmark instances. The results indicate the effectiveness of the algorithm. Although not designed especially for the standard PRP and the IRP with VSP, the developed MA has also managed to improve the best known solutions for 388 out of 1174 standard PRP and the IRP with VSP test instances. Moreover, an extensive computational study is performed to reveal the effect of the VSP on the PRP.

An Inventory Routing Policy Under Replenishment Lead Time

The inventory routing problem (IRP) arises in vendor-managed inventory systems, which is a combination of vehicle routing and inventory management. Differing from the traditional IRPs in which the time consumption in transportation is often ignored, in this paper, we take the time consumption into consideration, which brings the lead-time to replenishment. In this situation, the lead-time for replenishment depends on the routing decisions made by the vendor. Consequently, IRPs become more interesting because decisions on the replenishment quantity and routing depend more tightly on each other. The general case of the IRP with replenishment lead-time (i.e., one vendor and N retailers) is modeled mathematically. To solve the problem, first a simple case (i.e., one vendor and two retailers) is analyzed to obtain the theoretical optimal policy. By proving the K-convexity of the objective function, we confirm that the structure of the optimal replenishment and routing policy is of switching curve type. In this policy, the state space, which is composed of the inventory positions of the two retailers, is divided into several domains; and for inventory positions in each domain, there exists an optimal order-up-to level. This structure reveals, for managerial insight, that when lead-time is considered, the current routing decision is not independent of the previous one. Second, since the optimal policy is difficult to realize in practice, a myopic policy that is easier to implement is proposed and numerical experiments are conducted to examine the near-optimal performance of the myopic policy. Finally, the myopic policy is extended to a realistic-size IRP with replenishment lead-time (i.e., the IRP for the case of one vendor and multiple retailers) and a numerical example is provided to indicate the feasibility of the policy.

Optimization of operational level transportation planning in forestry: a review

ABSTRACTTransportation of forest products accounts as a major contributor to the total operational costs; hence, its optimization has become an important aspect in supply chain planning. Transportation optimization at the operational level includes decisions related to product flow, storage, pre-processing, and routing and scheduling of vehicles. The decisions and constraints in the model depend on the type of product that is transported. Earlier review articles on forest transportation optimization focused only on log transportation, while in this review paper, products such as logs, biomass, pulp and furniture are considered and their similarities and differences are highlighted. Most of the previous studies focused on optimizing the total cost of transportation, while environmental aspects of truck routing and scheduling in forestry were not considered. Uncertainties in parameters such as supply and demand quantities and transportation time were not explored fully in the models. In addition to storage and truck routing and scheduling, considering pre-processing (e.g. sorting, grinding, blending, bucking) decisions at forest sites, satellite yards and the mills in the models could be done in future studies. It is important that aspects related to truck configuration, type and capacity be considered in the models as there is limited accessibility of large trucks such as large chip vans to forest sites. Management practices such as just-in-time production and vendor-managed inventory systems could be considered in forest supply chain planning. Using big data and business analytics techniques are other new trends that could improve decision-making related to logistics and transportation planning in forestry.

Closed-loop Inventory Routing Problem for returnable transport items

Increasing concerns on supply chain sustainability have given birth to the concept of closed-loop supply chain. Closed-loop supply chains include the return processes besides forward flows to recover the value from the customers or end-users. Vendor Managed Inventory (VMI) systems ensure collaborative relationships between a vendor and a set of customers. In such systems, the vendor takes on the responsibility of product deliveries and inventory management at customers. Product deliveries also include reverse flows of returnable transport items. The execution of the VMI policy requires vendor to deal with a Closed-loop Inventory Routing Problem (CIRP) consisting of its own forward and backward routing decisions, and inventory decisions of customers. In CIRP literature, traditional assumptions of disregarding reverse logistic operations, knowing beforehand distribution costs between nodes and customers demand, and managing single product restrict the usage of the proposed models in current food logistics systems. From this point of view, the aim of this research is to enhance the traditional models for the CIRP to make them more useful for the decision makers in closed-loop supply chains. Therefore, we propose a probabilistic mixed-integer linear programming model for the CIRP that accounts for forward and reverse logistics operations, explicit fuel consumption, demand uncertainty and multiple products. A case study on the distribution operations of a soft drink company shows the applicability of the model to a real-life problem. The results suggest that the proposed model can achieve significant savings in total cost and thus offers better support to decision makers.

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

The integration of distribution and routing constitutes the Inventory Routing Problem (IRP), an important aspect of Vendor Managed Inventory (VMI) systems. IRP involves decisions on timing of deliveries, sizes of shipments and routing of vehicles. In the context of supply chain collaboration, the scope of IRP expands to include replenishments at the depot. This paper studies an IRP involving multiple products from different suppliers, a central depot (CD) and a set of warehouses. We develop an integrated Integer Linear Programming (ILP) model to determine the optimal replenishments from suppliers to the CD as well as the routing schedules of vehicles from CD to the multiple warehouses over the defined time horizon. We propose an extended three-phase heuristic called CARE (Clustering, Allocation, Routing -Extended). In the heuristic, the replenishment schedules, from suppliers to the CD (for multiple products in the defined time horizon), is solved using a dynamic programming (DP) model. The routing schedules of vehicles from CD to the multiple warehouses is then modeled and solved as a capacitated IRP (CIRP) problem. With the replenishment schedules as an input from the DP model, the CIRP is solved in three-phases: Cluster the nodes, Allocate to these nodes and Route delivery vehicles through clusters of nodes. Three variants of heuristics are proposed based on the changes to the routing phase – CARE1, CARE2, and CARE3. Computational results for a broad range of test instances yield promising results and show usefulness of the solution approaches. Particularly, the proposed heuristics outperformed CPLEX upper bounds for larger problems with lesser computational effort. The average improvement obtained by the heuristics over CPLEX upper bounds for 15 and 20 warehouse problems, respectively, are: CARE1 – 0.94% and 3.6%, CARE2 – 1.36% and 4.26%, CARE3 – 2.87% and 6.08%. We also show that the results from the proposed heuristic are statistically better than the CPLEX upper bounds. The proposed approaches can easily be implemented into existing VMI systems.

Multiple-vendor, multiple-retailer based vendor-managed inventory

Vendor-managed inventory is a coordinated system where a vendor decides about the retailer’s replenishment quantity and time. This work studies a two-echelon distribution work composed of multiple vendors and retailers in traditional and vendor-managed inventory systems where unsatisfied demands are lost sales. We also consider that the retailers’ demand is stochastic following a uniform distribution. The mathematical models are developed and applied in vendor-managed inventory and traditional systems. Under the traditional supply chain, the vendor incurs the cost of holding and production setup, while a retailer incurs expenses for inventory holding, ordering, transportation and lost sales. In a vendor-managed inventory system, as the vendor is responsible for his retailers, the retailer’s costs are transferred to the vendor. We aim to identify benefits of vendor-managed inventory. The total cost per unit time is used as a comparable measure between vendor-managed inventory and traditional systems. Numerical examples and a sensitivity analysis of key parameters include the vendor’s setup cost and holding cost; the retailer’s transportation and ordering costs are presented in both vendor-managed inventory and traditional systems. The results illustrate that vendor-managed inventory total system inventory cost is lower than a traditional system where shortage is allowed.

Optimal Replenishment in Vendor Managed Inventory Systems Using Point-of-Sales Data

Events such as spoilage, expiration, employee theft, and customer shoplifting reduce available inventories in retail stores without these reductions being reflected in inventory records. As a result, inventory records often include phantom inventories, i.e., units of good not actually available for sale. These phantom inventories can cause replenishment delays which lead to stockouts and ultimately hurt service levels. In this paper, we study how inventory managers can fully utilize point-of-sales (POS) data for the design of replenishment strategies that account for the existence of such phantom inventories. The optimal replenishment policy in the presence of phantom inventories is complex. However, analyzing the structure of the optimal replenishment problem we are able to propose a simple policy which rarely acts sub-optimally and hence performs close to the optimal policy. This simple policy is based on a threshold on the estimated fraction of demand to be met on a given day conditional on the POS data up to that day, a statistic that we refer to as the daily expected service level.

Supply chain coordination in vendor-managed inventory systems with stockout-cost sharing under limited storage capacity

We examine vendor-managed inventory (VMI) systems with stockout-cost sharing between a supplier and a customer using an EOQ model with shortages allowed under limited storage capacity, in which a stockout penalty is charged to the supplier when stockouts occur at the customer. In the VMI systems the customer and the supplier minimize their own costs in designing a VMI contract and making replenishment decisions, respectively. We compare the VMI systems with an integrated supplier–customer system where the supply chain total cost is minimized. We show that VMI with stockout-cost sharing and the integrated supplier–customer system result in the same replenishment decisions and system performance if and only if the supplier's reservation cost is equal to the minimum supply chain total cost of the integrated system. On the other hand, we also show how VMI along with fixed transfer payments as well as stockout-cost sharing can lead to the supply chain coordination regardless of the supplier's reservation cost. We also provide several interesting computational results.

Políticas de distribuição com lote econômico de entrega em problemas de roteirização com estoque gerenciado pelo fornecedor e sistema logístico em três níveis

Em sistemas de gerenciamento de estoque pelo fornecedor (Vendor Managed Inventory - VMI), as decisões logísticas são centralizadas no Centro de Distribuição (CD), possibilitando uma redução simultânea dos custos de armazenagem e transporte. Sua operação requer a resolução de um complexo problema de otimização combinatória, denominado Problema de Roteirização e Estoques (PRE) que consiste no gerenciamento do estoque do cliente, no estabelecimento da frequência e quantidade de produto entregue, além do roteiro percorrido pelo veículo ao longo de um horizonte de planejamento. Este trabalho apresenta três novas políticas de distribuição baseadas no cálculo de lote econômico de entrega para o PRE. Um modelo de Programação Linear Inteira Mista Binária (PLIMB) foi proposto considerando um sistema logístico de três níveis, sendo uma Base de Fornecimento (BF), um CD e um conjunto de clientes. Também foi proposta uma nova abordagem heurística que decompõe o PRE em dois subproblemas: o primeiro é responsável pela programação das entregas e a formação de grupos de atendimento ao longo do horizonte de planejamento. O segundo subproblema constrói os roteiros para os grupos formados no primeiro estágio, empregando heurísticas clássicas de construção de rotas, juntamente com procedimento de melhorias intrarrotas. Ajustes entre rotas são realizados por uma nova estratégia de busca ampla em vizinhança. Cenários de pequeno, médio e grande porte, com variações no custo de estocagem e de transporte, foram gerados a partir de dados da literatura e parametrizados no contexto da pesquisa. Extensivos testes computacionais foram conduzidos a fim de evidenciar a eficiência das políticas de distribuição propostas e a efetividade da estratégia heurística utilizada.

The impact of cooperation mechanism on the chaotic behaviours in nonlinear supply chains

The chaotic behaviours of nonlinear inventory systems are investigated via control theory, nonlinear system theory, and chaos theory. Two well-established production and distribution scheduling algorithms, automatic pipeline, variable inventory and order-based production control system (APVIOBPCS) with demand information sharing (DIS) and vendor managed inventory (VMI) supply chains are adopted and analysed by bifurcation diagram and Lyapunov exponent spectrum. Simulation results show that with the target inventory parameter ([2) changes, behaviours of the DIS and VMI systems are different from that of traditional inventory system. The Lyapunov exponent confirms that behaviours of DIS supply chain members shift between chaotic and periodic movement with [2 increases. The system shows periodic movement when [2 is set between 1 and 1.5. For VMI system, the system is not sensitive to [2 and keeps periodic movement. Therefore, the DIS and VMI supply chain members can effectively reduce inventory, and keep periodic movement simultaneously. [Received 13 July 2013; Revised 13 January 2014; Revised 10 June 2014; Accepted 14 June 2014]

An optimised target-level inventory replenishment policy for vendor-managed inventory systems

In vendor-managed inventory (VMI) systems the supplier is responsible for replenishing customers and for deciding when and how much to deliver. One of two inventory policies is typically employed by the supplier. The first one, called the maximum level (ML) policy, gives full freedom to the supplier to deliver any quantity as long as it respects customer inventory capacities. The alternative, which is more constrained, is called the order-up-to (OU) policy. It states that the supplier has to bring the customer inventory up to its maximum capacity level upon delivery. We propose a new tactical policy in the context of VMI systems, called optimised target-level (OTL), under which when the supplier visits a customer, the quantity delivered is such that the final inventory will always be at the same customer-dependent OTL. We perform a computational evaluation of this new policy against both traditional strategies on benchmark instances. We show that it yields lower costs and inventory levels than the OU policy, and is only marginally more expensive than the ML policy, while being easier to implement.

The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory

Abstract A Vendor Managed Inventory (VMI) partnership places the responsibility on the vendor (rather than on buyers) to schedule purchase orders for inventory replenishment in the supply chain system. In this research, the supply chain network considers the Silver–Meal heuristic with an augmentation quantity replenishment policy between both traditional and VMI systems. We consider time-varying stochastic demand in two-echelon (one vendor, multiple retailers) supply chains. This paper seeks to find the supply chain that minimizes system cost through comparing performance between traditional and VMI systems. A mathematical model is developed, and total supply chain cost is used as the measure of comparison. The models are applied in both traditional and VMI supply chains based on pharmaceutical industry data, and we focus on total cost difference compared through the use of Adjusted Silver–Meal (ASM) and Least Unit Cost heuristics. Finally, a numerical example and a sensitivity analysis are also illustrated to show the applicability of the model.

Heuristics for dynamic and stochastic inventory-routing

The combination of inventory management and vehicle routing decisions yields a difficult combinatorial optimization problem called the Inventory-Routing Problem (IRP). This problem arises when both types of decisions must be made jointly, which is the case in vendor-managed inventory systems. The IRP has received significant attention in recent years, with several heuristic and exact algorithms available for its static and deterministic versions. In the dynamic version of the IRP, customer demands are gradually revealed over time and planning must be made at the beginning of each of several periods. In this context, one can sometimes take advantage of stochastic information on demand through the use of forecasts. We propose different heuristic policies to handle the dynamic and stochastic version of the IRP. We perform an extensive computational analysis on randomly generated instances in order to compare several solution policies. Amongst other conclusions we show that it is possible to take advantage of stochastic information to generate better solutions albeit at the expense of more computing time. We also find that the use of a longer rolling horizon step does not help improve solutions. Finally, we show that ensuring consistent solutions over time increases the cost of the solutions much more under a dynamic environment than in a static setting.

Multi-period channel coordination in vendor-managed inventory for deteriorating goods

This study examines the problem of optimally dynamic joint decisions, including replenishment scheduling/quantity, retail price, wholesale price, and revenue-sharing allocation, in a vertically decentralised single-manufacturer Stackelberg and single-retailer channel over a multi-period planning horizon, subject to deteriorating goods and multivariate demand function. This study uses a calculus-based formulation combined with dynamic programming techniques to solve the channel coordination decision problem. Additionally, three arrangements, namely price-only contract, revenue-sharing contract, and revenue-sharing plus linear rebate and side-payment contract for channel coordination, are developed under retailer-managed inventory (RMI) and vendor-managed inventory (VMI) systems, respectively. The analysis reveals that the proposed policy under the VMI system with the revenue-sharing plus linear rebate and side-payment contract tends to obtain low retail prices and large demand quantity, and results in near-perfect coordination, including greater system efficiency and Pareto improvements, for the vertically decentralised dynamic channel.