A supply chain model with vendor-managed inventory,consignment, and quality inspection errors

This paper considers the integration between quality control and production inventory control in supply chain management. Specifically, we study the effect of inspection errors on the costs incurred in a supply chain system with a single vendor and multiple buyers. In this system, the vendor enters into a vendor-managed inventory (VMI) and a consignment stock (CS) partnership with several buyers. We assume that the items made by the vendor are not in perfect quality, but they contain a given proportion of defective units. We also assume that quality inspection of these items by the buyers is subject to sampling errors. Three cases indicating to different levels of supply integration are considered: VMI–CS system, traditional system and integrated system. For each case, a mathematical model is formulated, an optimum solution is developed, and a numerical example is solved.     

Comments on ‘vendor-managed inventory with consignment stock agreement for single vendor–single buyer under the emission-trading scheme’

Zanoni, Mazzoldi, and Jaber [Zanoni, S., L. Mazzoldi, and M. Y., Jaber. 2014. Vendor-managed inventory with consignment stock agreement for single vendor–single buyer under the emission-trading scheme. International Journal of Production Research 52 (1): 20–31] consider a joint economic lot size problem under the vendor-managed inventory with consignment stock agreement and an emission-trading scheme. They show that the total cost of the system is a jointly convex function by simply showing that every element of the Hessian is positive. Noticing this mistake, we analyse the same problem in this technical note. We first provide a closed-form solution when the production rate is given. In order to avoid a complete search over all possible production rates, we then develop an efficient continuous approximation algorithm. Computational experiment shows that the approximation algorithm is effective and efficient.     

Vendor-managed inventory with consignment stock agreement for single vendor–single buyer under the emission-trading scheme

This paper presents a joint economic lot size (JELS) model for coordinated inventory replenishment decisions under the vendor-managed inventory (VMI) with consignment stock (CS) agreement and an emission-trading scheme. The paper assumes a single product that flows along a two-level supply chain system, with a single vendor and a single buyer. The total cost of the system is the performance measure, which is the sum of the vendor’s and the buyer’s total costs. The total cost includes the set-up and order costs, inventory holding costs, greenhouse gases (GHG) emissions tax and penalty costs. A mathematical model is proposed to determine: (1) the vendor’s production lot size quantity; (2) the number of shipments sent by the vendor to the buyer in a cycle; and (3) the production rate that minimises the total cost of the supply chain. Some numerical examples are carried out, as well as comparisons with the traditional JELS model for a classic two-level supply chain. Results show that the performance of the system is better when it is operated under a VMI with CS agreement, which is capable of reducing the traditional inventory holding costs and, for some values of given parameters, the GHG emissions tax and penalty costs.     

Vendor managed inventory with consignment stock for supply chain with stock- and price-dependent demand

This paper presents a single vendor–single buyer coordinated model. The vendor produces a single deteriorating item and transfers it to the buyer in equal shipments. The model is based on vendor managed inventory with consignment stock (VMI-CS) agreement in which the vendor uses the buyer’s warehouse. The buyer stocks items both on his shelf and in his warehouse. The demand is assumed to be linearly sensitive to inventory level and selling price. The objective is to determine variables that maximise the total profit. An exact solution procedure is proposed to find the optimal solution. Numerical results show that supply chain members will benefit from the advantages of economies of scale in coordinated model with VMI-CS policy.     

An analysis of the general benefits of a centralised VMI system based on the EOQ model

Within a vendor-managed inventory (VMI) agreement, the upstream supply chain member (the vendor) takes responsibility for managing the inventory of the downstream member (the customer) within specific levels previously agreed upon without the need of orders from the customer side to be placed. Therefore, the vendor can focus on optimising production efficiency and capacity planning, while the customer has to improve forecast accuracy. This paper analyses the benefits a VMI agreement could bring for a one-supplier, multiple-customer case through analysing two cases: a supply chain managed in a traditional manner and VMI when both the vendor and the customers belong to the same organisation. The analysis is based on the economic ordering quantity (EOQ) formula and its related total cost, and the novelty is captured by evaluating one vendor, multiple buyers, and multiple product situations. The modelling is done so as to capture the needs and factors which occur within the pharmaceutical industry and a numerical application will be executed with data from one of the main leaders within the pharmaceutical field.     

Improving a supplier's quantity discount gain from many different buyers

We consider the pricing and inventory decisions of a vendor who supplies a single product to multiple heterogeneous buyers. The problem is analyzed as a Stackelberg game in which the vendor acts as the leader by announcing its pricing policy to all the buyers in advance and the buyers act as followers by choosing their order quantity and the sassociated purchasing price independently under the vendors' pricing scheme. We propose in this paper a pricing policy for the vendor that offers price discounts based on the percentage increase from a buyers' order quantity before discount. The proposed policy is defined as a discrete all-unit quantity discount schedule with many break points. We show that: (i) the proposed policy offers a higher price discount to a buyer ordering a larger quantity and hence complies with general fair trade laws; (ii) an explicit solution is obtained for the vendors' optimal decision; and (iii) although suppliers in reality normally offer price discounts based on a buyers' unit increase in order quantity, the proposed policy is superior for the vendor when there are many different buyers. Other benefits of the proposed pricing policy are demonstrated by numerical examples.     

Modelling on vendor-managed inventory policies with equal and unequal shipments under GHG emission-trading scheme

This paper studies five different stock control policies in the supply chain management. The lead time can be shortened by extra investment between two entities. The vendor produces a single product and delivers the order quantity in a number of unequal shipments to the buyer. The unit holding cost is divided into financial and storage components. The vendor takes care of financial component until the products are sold to the end customers to encourage them to buy more products. In order to reduce emissions from production and to protect the environment, some legislative actions have been taken such as implementing taxes and penalties. The cost function also includes these taxes and penalties. The optimal solutions of this constrained mixed integer non-linear programming problem are obtained by using the Genetic Algorithm (GA). Numerical examples are employed and comparison works are carried out with other existing literatures. Results show that the performance of the system is better when it is operated under unequal shipment policies and vendor-managed inventory (VMI) agreement.     

The consignment stock of inventories under buyer's warehouse space limitation

In this paper, coordination between a single vendor (or manufacturer) and a buyer (or retailer) via the delivery schedule in a production and distribution system is presented. A continuous deterministic model with centralised decision process is developed. To satisfy the buyer's demands, the product is delivered in discrete batches from the vendor's stock to the buyer's stock subject to consignee's warehouse space capacity constraint. A more general type of consignment stock (CS) policies is analysed. The inventory patterns and the cost structure of production distribution cycles (PDC) are described under the constraint – when the ratio α of the sizes of delayed to just in time (JIT) for the vendor deliveries is given. Also, an analysis how an upper buyer's warehouse space limit can act as a key factor for implementing the generalised CS-policies successfully. Numerical examples are presented to illustrate the performance of model and the results. A comparative study of the results shows that the generalised CS-policies performs better.     

VMI versus information sharing: an analysis under static uncertainty strategy with fill rate constraints

A vendor-managed inventory (VMI) relationship between a downstream retailer and an upstream vendor consists of two distinct components: (i) information sharing (IS) and (ii) a shift in decision-making responsibility. This study compares these two components of VMI in a two-stage serial supply chain based on the ‘static uncertainty’ strategy under dynamic and random demand with fill rate constraints. Numerical experiments are conducted using analytical models to identify the conditions where the incremental value of VMI over IS is significant. The results provide guidelines relevant to academia and supply chain practitioners in taking VMI adoption decision above and beyond IS according to their specific business environment.     

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.     

A vendor-managed inventory scheme as a supply chain coordination mechanism

In this paper, we have considered a vendor-managed inventory (VMI) arrangement in a supply chain (SC), where the buyer imposes a penalty for shipments exceeding an upper limit. We have shown as how the industry practice of VMI under penalty can be used as a SC coordination mechanism. The vendor can influence the buyer to increase the batch size without making the buyer worse off. We also discuss how such a penalty scheme may be derived. Further, we have established the equivalence of VMI under deterministic demand with that of quantity discount models, thus highlighting the need to incorporate both cooperation and coordination perspectives while analysing SC collaboration mechanisms.     

Operational and environmental decisions for a two-stage supply chain under vendor managed consignment inventory partnership

Supply-chain-based organisations are nowadays facing intense pressure to abide to environmental regulatory requirements while they are striving to be responsive to customers’ needs at the least cost possible. As supply chain activities are among the top contributors to carbon emissions, several recent research works have investigated the impact of carbon regulation policies on economic and environmental supply chain performance. This paper presents integrated economic and environmental models for the one-vendor one-buyer supply chain problem under a vendor managed consignment inventory (VMCI) arrangement. Through the developed models, we study the impacts of two carbon reduction policies, namely carbon cap and carbon tax policies, on supply chain wide costs and carbon emissions. We first provide a much simpler and more compact formulation for the basic single-vendor single-buyer supply chain under VMCI agreement. We also present an environmental-based VMCI model where reduction of carbon footprint is considered as the only objective function. We then extend these two basic models to include each of the two carbon emissions reduction policies. We identify structural properties for the optimal solutions of the two hybrid economic and environmental models and propose algorithms to generate optimal solutions. The results of the computational experiments reveal that the implementation of carbon reduction policies, through carbon cap and carbon tax, may call for the adjustment of the vendor’s production and buyer’s delivery quantities to reduce carbon footprint without significantly increasing the operational costs.     

A systematic literature review of remanufacturing scheduling

This paper studies a vendor–buyer integrated inventory system with buyers’ variable demand and warehouse space limitation where the consignment stock (CS) replenishment operates under a controllable lead time. Within any cycle, the production rate, the number of shipments and the shipping size are all fixed. Based upon the CS policy, the vendor agrees to maintain the buyer’s inventory to be above a safety level and less than the buyer’s space limitation. Due to the uncertainty in the demand, shortages/over stocks are sometimes inevitable. In such cases, penalties are incurred to discourage such occurrence. The holding cost consists of a storage component and a financial component, and the lead time is controlled with an extra investment which is a function of both the shipment size and the reduced time. Two-constraint, five-variable mix-integer optimisation models are established to describe the CS system. Two doubly-hybrid meta-heuristic algorithms are employed to solve the models that are complex and difficult to solve with available techniques. Two numerical examples are used to illustrate the solution procedure and the analysis of the computational results reveals the effects of some important parameters used for the annual joint total expected cost of the integrated system. The computational efficiency and quality of the solutions are evaluated by comparing them with other existing and popular methods. The results founds in all comparative evaluation are very encouraging and competitive.     

Comparing different coordination scenarios in a three-level supply chain system

The consignment stock (CS) policy, independently or coupled with vendor managed inventory (VMI), has been practised by businesses and shown to be profitable. It helps to reduce or eliminate out-of-stock instances caused by fluctuations in demand. CS brings several benefits to collaborating parties. Unlike the two-level supply chain models in the literature, this paper considers a three-level supply chain that consists of a supplier, a vendor and a buyer with CS policy agreements. The paper also examines four coordination scenarios (a combination of traditional and CS) in conjunction with a payment scheme between adjacent parties. Nine coordination cases (models) are provided. A sensitivity analysis is performed to study the effects of some parameters on the performance of the developed models. Most of the results showed that a combination of traditional and CS policies returned a higher total system profit.     

Consignment stock theory with a fixed batch manufacturing process

This paper deals with stock control in a supply chain. The focus is on consignment stock (CS), an innovative collaborative relationship, which can create a win–win situation between the vendor and the buyer. Recently some analytical formulations have been proposed to optimise CS, and the present paper extends these models by considering a new critical factor: a fixed batch production process at the vendor's plant. This kind of production is typical if there are batch processing machines that can hold and simultaneously process a finite number of items, such as kilns for long heat treatment. Specifically, we consider a deterministic single-vendor single-buyer system. The buyer consumes a single product at a constant rate and is replenished by the vendor who produces in batches and incurs set-up costs. Each batch is dispatched to the buyer in a number of shipments, some of which may take place while production is still running. To minimise total operating costs (that is, manufacturing, replenishment and holding), two alternative production and shipment policies are proposed and analytically formulated as integer optimisation models. A step by step heuristic procedure to obtain the optimal solution is finally presented and demonstrated through numerical examples.     

The implication of vendor inventory liability period in a decentralised assembly system

This paper investigates a decentralised assembly system that consists of one manufacturer and multiple suppliers who produce the complementary components. In a single selling season, the manufacturer initially sets a vendor inventory liability period (VILP) to control the suppliers’ delivery times, and the suppliers simultaneously determine when to deliver their components. Given the firms’ equilibrium strategies, we find that it is not wise for the manufacturer to set an overly long VILP, since having no inventory is not always beneficial to the manufacturer. A supplier may choose to postpone his delivery when the length of the VILP increases or the other suppliers’ deliveries are delayed, and either of these conditions is detrimental to the supplier’s profitability. We also examine the impact of VILP under different situations and find that having VILPs customised for different suppliers can reduce the manufacturer’s cost as well as improve the supply chain’s overall efficiency.     

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.     

Joint pricing and inventory strategies in a supply chain subject to inventory inaccuracy

This paper focuses on pricing strategies, inventory policies for a supply chain when Radio Frequency Identification (RFID) technology is adopted to cope with inventory inaccuracy. The supply chain consists of one supplier and one retailer, in which the RFID tag price is shared between the supplier and the retailer. We present and compare the performance differences between a wholesale price contract and a consignment contract when the retailer is the Stackelberg leader and the supplier is the follower. Based on the optimal pricing and inventory decisions, an interesting observation of contract selection is that there are two critical values of inventory available rate such that when the inventory availability is less than the lower value, both the supplier and the retailer prefer a consignment contract; when the inventory availability is greater than the upper value, a wholesale price contract is their best choice; when the inventory availability is between the two values, the supplier prefers a wholesale price contract and the retailer prefers a consignment contract. Additionally, there exist threshold values of RFID tag price and sharing rate to determine the contract preference for the retailer. Furthermore, the profits of both the supplier and the retailer are independent of the RFID tag price sharing rate in a wholesale price contract, and the supplier has the incentive to invest in RFID tag cost in a consignment contract.     

Vendor-managed inventory and the effect of channel power

We analyze decentralized supply chains that follow general continuous review (Q, R) inventory policies subject to vendor-managed inventory agreements where the supplier chooses the order quantity Q, and the retailer chooses the reorder point R. Within the VMI scenario, we explore the effect of divisions of channel power on supply chain and individual agent performance by examining different game theoretic models. Optimal policies and analytical results, including existence and uniqueness proofs for equilibrium solutions under VMI, are derived. Numerical results are provided to compare the effectiveness of VMI and to analyze different channel power relationships under a variety of environmental conditions. We find that VMI can result in considerable supply chain savings over traditional relationships and that the relative division of channel power can significantly effect the performance of VMI. Interestingly, we find that the greatest system benefits from VMI arise in asymmetric channel power relationships, but that individual agents lack the incentive to assume a leadership role.     

Consignment stock policy with unequal shipments and process unreliability for a two-level supply chain

This paper considers a vendor managed inventory model with consignment stock policy in which a single vendor delivers a single product to a single buyer in unequal-sized shipments. The vendor’s production process may produce some defective items during a production run. The buyer performs a screening process immediately after receiving each delivery from the vendor and the vendor bears the warranty cost of defective item, if any. The buyer either scraps or repairs the defective items by sending them to a repair factory. The average expected profit of the integrated system is derived using renewal reward theorem and a solution procedure is suggested to determine the optimal shipment policy of the vendor. Numerical examples are taken to determine both the equal and unequal shipment policies and compare their relative performances.