Single-vendor Single-buyer Supply Chain Research Articles

Optimisation of the Single-Vendor Single-Buyer Supply Chain System under Fuzzy Demand Using Optimisation–Simulation Closed Loop Technique

This research aims to model and optimise the most applicable supply chain system, which is a single-vendor single-buyer system with fuzzy buyer demand. An optimisation model of the supply chain system under consideration is built by formulating the objective function, which is minimising the joint total cost between a buyer and a vendor. The model is developed on the basis of a simulation system, and optimisation is carried out by utilising a Genetic Algorithm that has been embedded in the simulation system. This technique is called optimisation–simulation closed loop. The vendor actual condition, which deals with uncertain demands from the main buyer and other small buyers, is considered. To analyse timely supply chain events, a simulation system is developed. A new optimisation model for the single-vendor single-buyer supply chain system with fuzzy demand is developed on the basis of the simulation system. The use of optimisation–simulation closed loop is also a new finding. In this study, the optimisation model of the supply chain under consideration is developed by taking into account a specific condition in which the vendor receives demands from the main buyer and other small buyers. Naturally, buyer demand is uncertain and has been modelled using a fuzzy set. The use of optimisation–simulation closed loop enables the supply chain to make the optimum decision when at the steady state condition.

Technical note on “Inventory management in supply chains with consideration of Logistics, green investment and different carbon emissions policies”

This study presents an extension of the model proposed by Huang et al. (2020), which investigated the effects of carbon policies and green technologies on the integrated inventory management of a two-echelon supply chain with consideration of carbon emissions during the processes of production, transportation, and storage. Specifically, since the inventory policy impacts on the economic and environmental performances of the supply chain, this study proposes a mathematical model for the integrated inventory management of the single-vendor single-buyer supply chain under a consignment stock policy. The aim is, thus, to highlight advantages and disadvantages of the consignment stock agreement with respect to the traditional policy based on the model proposed by Hill (1999). To compare the results, the same three carbon emissions policies are considered: i.e., limited total carbon emissions, carbon taxation, and cap-and-trade. The proposed model can assist firms in determining their optimal inventory policy (i.e., agreement, production quantity, delivery quantity, and green investment amount) with an aim of minimizing the supply chain costs under different carbon emissions policies.

An integrated vendor–buyer supply chain model for backorder price discount and price-dependent demand using service level constraints and carbon emission cost

This paper derives a single-vendor single-buyer supply chain model with setup cost reduction, controllable lead time and backorder price discounts using service level constraints. The customer's demand is assumed to be selling-price dependent and the lead time demand follows a normal distribution. This integrated model is used to optimise the total number of shipments, order quantity, safety factor, setup cost and backorder price discount. An algorithm is developed to obtain the numerical results and to demonstrate the applications and performance of the proposed methodology.

A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder

This paper considers a two-level supply chain which consists of a single-vendor and a single-buyer. The vendor produces a single product in lot and transfers the whole lot to the buyer in a combination of equal and unequal sized batches. All unequal sized batches are in a geometric progression with a fixed common ratio. Consumer's demand is sensitive to the retail price and greening improvement level of the product. At the buyer, planned shortages are allowed and are completely backlogged. Assuming that the buyer has higher decision power than the vendor, we develop non-coordinated decentralised model and coordinated model with cost sharing contract, and the integrated centralised model. The numerical results show that the cost sharing contract gives an impressive improvement in the profits of both the vendor and the buyer over their profits in the non-coordinated system. A sensitivity analysis is performed to explore how the changes in the key model-parameters effect the optimal profits of the vendor and the buyer and the whole supply chain.

A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder

A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder

Energy considerations for the economic production quantity and the joint economic lot sizing

The increased awareness on sustainability, along with several governments’ actions for setting greenhouse gas restrictions, has recently generated a relevant pressure on industries towards the improvement of environmental performances. Among the several aspects, companies’ focus is mainly on energy use, firstly for its relevant and direct impact on the total cost, and secondly for its environmental linkage. The aim of this contribution is the integration of the energy-related objectives in lot sizing, extending the economic production quantity from the manufacturer point of view and extending the joint economic lot size model from the single-vendor single-buyer supply chain perspective, so as to show how this approach can lead to a more sustainable production process. The present work proposes a novel framework for dimensioning production lot sizes, based on both economic and energy implications in processes characterized by a variable production rate. Furthermore, an increased attention for the sustainability of the production–inventory system is introduced by considering energy as a key factor in the lot sizing problem, due to the close link between energy and environmental concerns. A traditional agreement and a vendor managed inventory with consignment stock for the joint economic lot sizing have been investigated explicitly formulating energy in production aspects. A numerical example is also presented to compare the behaviour of the models.

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 single-vendor single-buyer supply chain coordination model with price discount and benefit sharing in fuzzy environment

A single-vendor single-buyer supply chain coordination model with price discount and benefit sharing in fuzzy environment

An optimal policy for an integrated vendor-buyer model with two warehouses under vendor's capacity constraint

The paper considers an integrated single-vendor single-buyer supply chain model in which the vendor is assumed to be capacity constrained. The vendor can keep the excess units beyond the capacity of its own warehouse (OW) in a rented warehouse (RW) whose holding cost is higher than that of the own warehouse. The vendor delivers the buyer's order quantity in a number of equal shipments. The proposed integrated model is formulated and some of its characteristics are studied analytically. Considering the vendor's capacity as a control variable, the optimal decisions of the model are obtained for a numerical example. Sensitivity analysis is also carried out to measure the impact of key model-parameters on the outcome of the model.

Stochastic modeling of a single-vendor single-buyer supply chain with (s, S)-inventory policy

Given the relevance of stochastic modelling in supply chain analysis and the advances in queuing theory in different subject fields (such as in-plant manufacturing systems), the present paper deals with the application of a Bernoulli model to the simple but representative (and frequently cited) case of a single-vendor single-buyer supply chain with (s, S)-inventory policy, where the maximum capacity S has to be restored in the intermediate warehouse whenever the inventory position reaches or drops below the reorder point s.An analytical stochastic model is presented which considers two two sources of uncertainty, supply uncertainty and demand uncertainty. The model is analytically formulated and solved in closed-form in order to compute some significant performance measures and, consequently, support tactical decisions (such as the definition of the design parameters s and S).Then, the model setting up is discussed. Specifically, the problem of relating demand and supply probabilities to the behaviour exhibited by the buyer and (particularly) the vendor is addressed. Finally, some numerical results are provided for illustration.

A closed-form solution for the distribution free continuous review integrated inventory model

In this paper, we develop an integrated inventory model in a single-vendor single-buyer supply chain under an unknown demand distribution at the buyer. It is assumed that each lot delivered to the buyer contains a random fraction of defective items, and lead time can be reduced at an extra crashing cost. We also consider that the unmet demand at the buyer during the stockout period is partially backordered. A model is formulated to minimize the total expected relevant costs of the system considering an exact expression of the service level constraint to ensure that a certain percentage of customer orders are filled by the buyer. Closed-form expressions are derived for the optimal order quantity and safety factor for given lead time and shipment frequency, and then an algorithm is proposed to find the global optimal solution. Finally, a numerical example is presented to illustrate the solution procedure and sensitivity analysis is carried out to analyze the proposed model.

A joint economic lot size model with financial collaboration and uncertain investment opportunity

Establishing long-term relationships among the members of a supply chain has become necessary to enhance the supply chain's competitiveness in a globalized environment. Besides coordinating operational decisions, such as how much and when to produce or to order, the members of a supply chain may also share financial resources or act jointly on the capital market. This is important especially when companies have unequal access to capital, for example because they are located in countries with different economic conditions and banking policies and/or they have different credit ratings. The joint financing of investments across the supply chain may thus ensure the stability of production and of the flow of products to the customers. In addition, it strengthens the established relationships among the supply chain members. The paper at hand takes up these issues and presents a joint economic lot size model that allows investments financed cooperatively by the members of the supply chain. In particular, it considers a two-stage single-vendor single-buyer supply chain and assumes that the vendor has the option to invest in increasing its production rate. The outcome of these attempts to improve production capabilities, however, is uncertain and subject to an investment success probability. Due to different access to capital, the vendor and the buyer may also share the investment and the outcome uncertainty, which can be beneficial to both parties.

Vendor managed inventory with consignment stock agreement for a supply chain with defective items

The pursuit of better coordination schemes is crucial for contemporary supply chains to survive in a highly competitive environment. A supply chain may employ revenue sharing, information sharing and quantity discounts etc. to gain that viable edge. Another recent trend is to store vendor's inventory at the buyer's warehouse, known as vendor-managed-inventory (VMI) with consignment stock (CS) agreement. This paper brings the present literature in VMI with consignment stock closer to real life by introducing the notion of screening defective items. A single-vendor single-buyer supply chain is considered where the vendor ships every production batch in a number of lots to the buyer's warehouse. The buyer withdraws and screens these products while fulfilling the market demand. An analytical model is developed to depict this scenario. The impact of different fractions of defective items, storage costs as well as disposal schemes is also studied. The results indicate that the prominence of the proposed storage scheme over the conventional one remains proportional to the size and number of shipments in a cycle. Besides, the non-financial component of storage costs has a critical impact on the cost of the supply chain.

Coordinating a vendor–buyer supply chain with stochastic demand and uncertain yield

The paper develops a single-vendor single-buyer supply chain model with stochastic demand and uncertain yield where the vendor delivers the buyer’s order quantity in a number of shipments. We formulate the model considering instantaneous/non-instantaneous supplies from the vendor to the buyer and that the buyer’s replenishment time interval does/doesn’t depend upon the input. The optimal shipment policy is determined by maximizing the average expected profit of the whole supply chain. The model is further extended to consider a revenue sharing contract to align incentives of decentralized partners within the supply chain. Numerical examples are provided to illustrate the developed models. It is observed from the numerical study that the coordinated (integrated) policy is beneficial in comparison to the individual policies made by the supply chain partners.

Modified single-vendor single-buyer supply chain model with quality loss for product

In 2009, Darwish developed a single-vendor single-buyer supply chain model with process mean integration for determining the optimal process mean, production lot size, and number of shipment of product to buyer. Taguchi proposed the quadratic quality loss function for measuring the product quality and redefines the product quality as the loss of society when the product is shipped and sold to the customer. The quality cost of conforming products is excluded in Darwish’s model, which is inconsistent with Taguchi’s quality concept. In this paper, the author presents a modified Darwish’s model with quality loss for obtaining the optimal process mean, number of shipment, and production lot size. The numerical results show that the modified model has larger process mean and expected total relevant cost of product, smaller production lot size, and same number of shipment than those of original one. The original Darwish’s model will underestimate the expected total relevant cost of product because he doesn’t consider the quality loss of conforming products.

Integrated product and container inventory model for a single-vendor single-buyer supply chain with owned and rented returnable transport items

This study considers a single vendor supplying a single retailer with a finished product packed in returnable transport items (RTIs), such as containers, pallets or crates, to facilitate its safe shipment. Once received at the retailer’s site, the RTIs are emptied, cleaned, repaired if needed and returned to the vendor to be used for the next shipment. Because of unexpected events, such as damage of RTIs and/or shortage of labour to empty RTIs, the RTI return time is considered stochastic in this study. In case the return of empty RTIs is delayed, the vendor has the option to rent RTIs from a nearby service provider to avoid disruptions in the delivery schedule and finished product shortages at the buyer’s premise. We formulate the problem of coordinating the flow of both the finished product and RTIs and minimising the supply chain wide costs as a mixed-integer non-linear programme. For a convex objective function, we develop an efficient solution procedure that generates the optimal replenishment cycle, the optimal number of RTIs and the optimal number of trucks. The general optimisation model and the solution procedure are illustrated for the case where the RTI return time is exponentially distributed. In addition, we conduct an experimental study to assess the impact of the problem parameters on the decision variables. It is found that renting RTIs is especially beneficial in case both shortage cost and the risk of late RTI returns are high. In addition, the average RTI return time is found to be critical for the performance of the supply chain.

A vendor–buyer JELS model with stock-dependent demand and consigned inventory under buyer’s space constraint

In this article, we consider a single-vendor single-buyer supply chain model in which the vendor produces a single product at a constant rate and delivers to the buyer following a consignment stock policy. The customers’ demand is assumed to be dependent on the on-hand stock displayed at the buyer. An integrated vendor–buyer model is developed and solved for optimal delivery batch size and number of shipments, aiming at minimizing the average cost of the system. The model is further generalized considering the space limitation at the buyer’s end. As coordination mechanism, a contract which distributes the total cost between the vendor and the buyer in an arbitrary ratio is suggested. The proposed model is numerically illustrated and the effects of the buyer’s space constraint on the optimal number of shipments, delivery batch size and overall cost are studied. The outcome of the proposed model is also compared with that of the model under lot-for-lot policy to conclude which of the policies should be preferred to the other and under what conditions.

Optimal policies for integrated inventory system under fuzzy random framework

This study considers a single-vendor single-buyer supply chain system with service level constraint where weekly demand is fuzzy random in nature and lead time is controllable. Furthermore, the interaction between the lead time and ordering cost reduction is allowed. With these considerations, the supply chain problem from decentralized and centralized perspective is examined. Based on signed distance technique for defuzzification and the Kuhn-Tucker condition, the optimal solutions are obtained for each model. For the proposed models, numerical examples are presented and the sensitivity with respect to key parameters is carried out.

Trade credit financing in the vendor–buyer inventory system with ordering cost reduction, transportation cost and backorder price discount when the received quantity is uncertain

Previous ordering cost reduction vendor–buyer inventory models with backorder price discount usually assumed that the buyer must pay to the vendor for the ordered items as soon as the items are received, the received quantity is same as the ordered quantity and the transportation cost is independent of the shipment lot-size. In practice, however, the vendor is willing to offer the buyer a certain credit period without interest to promote market competition as well as the buyer's quantity received may not match with the ordered quantity due to unavailability of the raw material, worker's strike, human errors in counting, transcribing, etc. Furthermore, the discounts are offered for the transportation cost of large ordered quantities. This paper derives a single-vendor single-buyer supply chain model for the ordering cost reduction inventory system with backorder price discount, taking into consideration the effect of transportation cost discount and the condition of permissible delay in payments include the case where the buyer's received quantity does not necessarily match the quantity requisitioned. We take the transportation cost as a function of the shipment lot-size and it is taken to be in an all-unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the proposed inventory problem. Numerical example and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.

Mathematical Modeling and Computational Algorithm to Solve Multi-Echelon Multi-Constraint Inventory Problem with Errors in Quality Inspection

In this research an integrated production-distribution inventory model is developed for a single-vendor single-buyer supply chain system with the consideration of quality inspection errors at the buyer’s end, the buyer’s warehouse has limited capacity and there is an upper bound on the purchase of products. Mathematical modeling is employed in this study for optimizing the replenishment lot-size and total number of deliveries from the vendor to the buyer in one production run with the objective of minimizing integrated expected total cost of the system while satisfying the constraints. We show that the model of this problem is a constrained non-linear programme and propose a simple Lagrangian multiplier algorithmic technique to solve it. The computational effort and time are small for the proposed algorithm and it is simple to implement. A numerical example is given to demonstrate the application and the performance of the proposed methodology. In addition, sensitivity analysis has been carried out to illustrate the behaviors of the proposed model and some managerial insights are also included.