Single-vendor Single-buyer Research Articles

Efficient Formulation for Vendor–Buyer System Considering Optimal Allocation Fraction of Green Production

The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production system. The proposed model simultaneously focuses on green and regular production methods with an optimal allocation fraction of green and regular productions. Unlike the classical mathematical formulation, cycles do not depend on each other, and consequently, each model parameter can be adjusted to be responsive to the dynamic nature of demand rate and/or price fluctuation. A rigorous heuristic approach is used to derive a global optimal solution for a joint hybrid production system. This paper accounts for carbon emissions from production and storage activities related to green and regular produced items along with transportation activity under a multi-level emission-taxing scheme. The results emphasize the significant impact of green production on emissions. That is, the higher the allocation fraction of green production, the lower the total amount of emissions generated by the system, i.e., the system becomes more sustainable. Adopting a hybrid production method not only decreases the greenhouse gas (GHG) emissions dramatically, but also reduces the minimum total cost per unit time when compared with regular production. One of the main findings is that the total system cost generated by the base closed-form formula of the proposed model is considerably lower in the first cycle (subsequent cycles) than that of the existing literature, i.e., 33.59% (16.13%) when the regular production method is assumed. Moreover, the optimal production rate generated by the proposed model is the one that minimizes the emissions production function. In addition, the system earns further revenue by utilizing a mixed transportation policy that combines the Truck Load (TL) and Less than Truck Load (LTL) services. Illustrative examples and special cases that reflect different realistic situations are compared to outline managerial insights.

Optimizing production-inventory replenishment and lead time decisions under a fill rate constraint in a two-echelon sustainable supply chain with quality issues

This paper considers a single vendor-single buyer coordinated supply chain under stochastic demand. GHG emissions arise from the vendor's production process. A carbon tax and penalties for exceeding multiple emissions limits are considered. A random number of defectives characterises the batch received by the buyer, who performs an inspection activity. Setup and transportation times are controllable through a capital investment, whose outcome is uncertain. An optimisation problem is formulated under the minimax distribution-free approach. The objective is to find the production-inventory replenishment policy and the length of setup and transportation times that minimise the long-run expected total system cost rate considering a fill rate constraint. Several properties of the cost function are demonstrated, and an optimisation method is developed. Finally, numerical experiments are carried out to draw insights on the effect of the model parameters, including different legislation schemes concerning GHG emissions, on the optimal system performance. The novelty of the paper consists into investigating the effect of a controllable lead time on coordinated supply chain decisions in presence of GHG emissions and quality issues, in a stochastic environment. A major finding is that controlling lead time enhances both the overall cost efficiency and the environmental sustainability of the system.

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.

Production/Inventory Policies for a Two-Echelon System with Credit Period Incentives

Trade credit is a crucial source of capital particularly for small businesses with limited financing opportunities. Inventory models considering trade credit financing have been widely studied. However, while there is extensive research on the single-vendor single-buyer inventory model allowing delays in payments, the systems where the vendor supplies to more than one buyer have received less attention. In this paper, we analyze a two-echelon inventory system where a single vendor supplies an item to two buyers who face a constant deterministic demand. The vendor produces the items at a finite rate and offers the buyers a delay payment period. That is, the buyers can delay the payment for the purchased items until the end of the credit period. Therefore, during such a period, the buyers sell the items and use the sales revenue to earn interest. At the end of the credit period, the buyers should pay the purchasing cost to the vendor for which external funding may be necessary. It is widely accepted that, in general, centralized policies reduce the total cost of the supply chain. Therefore, we first deal with an integrated model assuming that the vendor and the buyers make decisions jointly. However, in some cases, the buyers are not willing to collaborate, and the management of the supply chain has to be carried out in a decentralized manner. Hence, we also address the problem under a non-cooperative setting. Numerical examples are presented to illustrate both models. Additionally, we perform a computational experiment to compare both strategies, and a sensitivity analysis of the parameters is also carried out. From the results, we derived that, in general, it was more profitable to follow the integrated policy excepting when the replenishment costs for the buyers were high. Finally, in order to validate the computational results, a statistical analysis is performed.

Inventory Model for Imperfect Quality Deteriorating Items with Carbon Tax Regulation

Emissions of carbon are one of the primary causes of global warming. Several countries are currently working on reducing carbon emissions. For many countries, carbon taxes and cap policies are the key mechanisms used to accomplish this goal. To deal with this issue, a sustainable economic production quantity (SEPQ) carbon tax and cap model is considered in order to control carbon emissions. Based on carbon emissions and defective rate, we present an integrated single-vendor single-buyer inventory model for deteriorating items with imperfect quality. Screening has been done on the produced units to find the imperfect units, but the screening rate is below or equal to the production rate and greater than demand. A secondary market buys the defective products at a discount price. In order to reduce work-in-process inventory and carbon emissions, the study aims to increase throughput times. We also examine the effect of carbon tax regulation on the potential emission reduction from the developed deteriorating item model. Results from the application of a numerical example and sensitivity analysis confirm the impact of carbon tax regulation on reducing carbon emissions.

Consignment stock policy in an integrated vendor-buyer model for deteriorating item with stock dependent demand under buyer’s space limitation

In this paper, a single-vendor single-buyer integrated inventory model for a deteriorating item with consignment stock policy is developed, assuming that the market demand is stock dependent and there is space limitation on the buyer’s storage capacity. Both equal and unequal shipments from the vendor to the buyer are considered. The effects of the buyer’s space capacity on the average cost, shipment size, and production batch are studied through numerical example. It is deduced that production rate is the key factor to determine whether to use equal or unequal shipment strategy. Sensitivity analysis is carried out to establish the robustness of the solutions of the models developed.

Closed-form solution for lot-sizing problem in manufacturing systems with imperfect matching

Integrated single-vendor single-buyer problem has received a lot of attention as it is the building block for wider supply chains. This paper considers a manufacturing system in which a single manufacturer procures raw materials from a single supplier, processes them to produce finished products, and delivers to a just-in-time (JIT) customer. The manufacturer's production cycle is imperfect where the production uptime and cycle time are not exact integer multiples of the shipment interval to the customer. The closed-form solution for the optimal batch size is developed to minimize the total cost of procurement and production. It is found that the total cost under imperfect matching is always lower than or equal to that under perfect matching. Different from previous works under perfect matching, it is found that the optimal total cost is a piecewise concave function of the ordering and setup costs, and also a piecewise convex function of the shipment size to the customer.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of delivering equal and unequal-sized batches

In this paper a single-manufacturer multi-retailer integrated model is developed by extending the ideas of two single-vendor single-buyer integrated models, where Normal distribution of lead times of delivering equal- and/or unequal- sized batches of a lot was considered. In the original models, the mean lead time of delivering batches was assumed to be equal to sum of the times of setting up the used machine, processing of the first batch and inspection, loading, transfer and unloading of that batch. However, delivery time of each of the batches from the second to the last of the same lot is only concerned with the time of inspection, loading, transfer and unloading of that batch, not on the additional time of setting up the machine and processing of the first batch. As a result, extra inventories are accumulated during delivering those batches. In our model the mean lead time is assumed to be the mean of the times of inspection, loading, transfer and unloading of a batch. The supply chain flow is synchronized by transferring the lot either only with equal-sized batches or only with unequal-sized batches, and generating a notification point to the manufacturer to start processing of a next lot in time so that the mean lead times of batches is maintained. Then an optimal solution policy to that model is presented along with an algorithm and it is illustrated with numerical example problems. The benefit of this policy is highlighted by comparative studies on numerical example problems and significant reduction in the minimal total cost for a single-manufacturer 5-retailer numerical problem is found.

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

A vendor managed inventory on consignment with penalty as a supply chain coordination arrangement

This paper presents a mathematical two echelon vendor-managed inventory (VMI) model on consignment scheme in supply chain, in which the vendor pays a penalty for every extra unit which exceeds a specific upper limit to the buyer. In this arrangement the vendor can decide about the batch size he wants to transship to the buyer. Two cases are discussed in this paper; single vendor-single buyer and single vendor-two buyers. In this study after a review of coordination in supply chain and VMI on consignment, we discuss vendor-managed inventory scheme in comparison with traditional inventory control system. The optimal batch size is calculated and the paper investigates how a VMI on consignment arrangement with penalty can coordinate the supply chain. Numerical examples and sensitivity analysis is presented to illustrate the performance of model and the results.

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.

An optimal decision policy for a single-vendor single-buyer production-inventory system with leaning effect, fuzzy demand and imperfect quality

This papers studies the optimization of an integrated SVSB (single-vendor single-buyer) production-inventory system consisted of a manufacturer and a retailer. Productivity learning effect, imperfect quality, fuzzy demand and backlogging are incorporated in the model to minimize the total cost of the retailer and the manufacturer. An algorithm is developed to solve the model to obtain the optimal order quantity of the retailer, optimal shipment number for one production cycle of the manufacturer and the optimal maximum backlogging of the retailer. Numerical examples show that the optimal shipment decreases with the increase of the learning coefficient. When the learning coefficient is small, the fluctuation of demand will have an important impact on the optimal cost. In the early phase of production, the learning effect is significant in reducing cost, but its role is limited in the latter phase.

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 vendor–buyer integrated inventory system with variable lead time and uncertain market demand

In this paper, we consider a single-vendor single-buyer integrated inventory model in which the replenishment lead time is assumed to be a linear function of batch size, setup time, and transportation time. Both the vendor and the buyer are interested to invest in reducing the ordering cost. Shortages, if occur in buyer’s inventory, are partially backlogged with a certain limit of backorder price discount. The objective of the study is to derive the optimal decisions and the best investment policy by minimizing the expected annual total cost of the integrated system. The existence and uniqueness of the optimal solution are investigated and an efficient algorithm is designed to find the optimal solution of the proposed model numerically. We demonstrate the aids of reducing order-processing cost through numerical examples and show that it has significant effect on lot sizing decisions. It is also observed that transportation delay forces the buyer to stock more in order to defend the stock-out situation.

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