Joint Economic Lot Size Model Research Articles

A sustainable joint economic lot size model for supplier selection under carbon emissions: A case study

Selecting suppliers strategically is a critical challenge in supply chain design, particularly in a dynamic global marketplace where maintaining competitiveness and sustainability is essential. Supplier location is a key factor that significantly impacts supply chain sustainability. Hence, this study proposes a new Sustainable Joint Economic Lot Size (S-JELS) model that integrates average annual cost and total amount of emissions associated with annual activities related to both buyer and supplier. The developed model accounts for costs and emissions from the buyer’s purchasing, inventory management, and transportation activities, as well as from the supplier’s production, packaging, and delivery processes. Additionally, the model incorporates various transportation modes, including shipping, trucking, and rail, to more accurately assess the environmental impact of different supply chain strategies. The proposed JELS model can support managers performing sustainable purchasing decisions and assess a sustainable supplier selection. The developed model is applied in a leather case study characterized by high resource intensity, significant environmental impacts, and complex global logistics to accomplish supplier selection between one domestic and one international supplier, aiming to determine the most sustainable strategy in terms of cost and emission

Coordinating a supplier–retailer JELS model considering product quality assessment and green retailing

Environmental awareness among the people is constantly increasing, which has resulted in massive pressure on companies from various stakeholders including the government and consumers to mitigate the detrimental effects on the environment. This work deals with a joint economic lot size (JELS) model to enhance the greening efforts of a product that flows along a two-level supply chain (supplier–retailer). Both selling price and greening effort level of the product influence the market demand. Here we assume that every individual lot shipped to the retailer carries some random defective items. Each lot received by the retailer goes through an error-free sub-lot sampled inspection process to remove the defective items. A fraction of faulty items are classified as usable and are sold at a salvage value and the rest items are disposed of. The retailer has to bear per item penalty cost for selling the uninspected defective items. We develop the profit function under three decision-making scenarios: centralized, decentralized, and coordinated. Coordination is made based on a trade-credit scheme under which the retailer changes his/her optimal decisions according to a centralized policy. We obtain a minimum and maximum credit period duration which encourages both the retailer and the supplier to follow the coordinated decision-making policy. The coordinated model suggests that more emphasis should be given to the greening effort level for higher profit. It is observed that, in many cases, a sub-lot inspection gives better results compared to a full lot inspection.

A joint economic lot-size model with collaboration of supply chain members

PurposeThe purpose of this study is to investigate a joint economic lot-size model with the possibility of cofinancing between members of a three-echelon supply chain (SC) including one supplier, one manufacture and one retailer. Given the differences in credit as well as differences in access to capital markets, SC members will be able to create a financial alliance to maximize the profits of each member. This study proposed a model to maximize the annuity stream of the SC by considering the financial interaction between SC members.Design/methodology/approachThis joint economic lot-sizing problem was described and modeled mathematically. To evaluate the mathematical model, different scenarios were considered with (and without) the possibility of financial interaction.FindingsIt is suggested that, in addition to the goods and information flow among SC members, proper financial flow can also have an impact on the improvement of SC performance.Originality/valueWhile previous studies consider cofinancing between members of a two-echelon SC, this paper considers a three-echelon SC including one supplier, one manufacturer and one retailer where financial cooperation between different levels of the SC in both upstream and reverse directions will be possible.

A Single Supplier Multi Buyer Supply Chain Coordination under Vendor- managed Inventory: Ensuring Buyers’ Interests in a Decentralized Setting

Our work delves into supply chain coordination involving a single supplier selling a single product to multiple downstream buyers. We consider the case when the supplier proposes implementing vendor-managed inventory (VMI) for each buyer. The VMI contract involves the buyers charging a penalty to the supplier on the excess inventory whenever the supplier exceeds some pre-decided inventory threshold. Unlike the works covered predominantly in the VMI literature involving penalty, where both the penalty and the threshold are exogenous, we develop a model to determine both endogenously. In our study, the supplier deciding on the penalty and the inventory threshold needs to ensure that each of the buyers’ interests is protected, that is, none of the buyers becomes worse off from the optimal position, thereby ensuring the willing participation of all the buyers. We further compared our model with the centralized Joint Economic Lot Size (JELS) model and other existing models. We show that our model has a cost equivalence with the JELS model with unequal order intervals. We also show the superiority of our proposed model over the existing VMI models in terms of the overall costs. Finally, we examine the impact of size and ordering cost on each buyers’ costs through numerical analysis.

Optimization of Joint Economic Lot Size Model for Vendor‐Buyer with Exponential Quality Degradation and Transportation by Chimp Optimization Algorithm

Freight transportation plays a critical role in improving company performance in the modern manufacturing industry. To reduce costs, companies must take advantage of the use of large vehicles. It caused fewer deliveries, but inventory costs and degradation quality are high. One of the joint economic lot size (JELS) problems in supply chain is Integrated Single‐Vendor Single‐Buyer Inventory Problem (I‐SVSB‐IP). This study developed the I‐SVSB‐IP model that considers raw materials’ exponential quality degradation and transportation costs. The objective function of this research was to maximize the Joint Total Profit (JTP). Three decision variables used were inventory cycle time (T), raw material ordering frequency (m), and frequency of delivery of finished products to buyers (n). This study proposed a sophisticated Chimp Optimization Algorithm (ChOA) procedure to solve the I‐SVSB‐IP problem. A case study on the food industry in Indonesia was presented to optimize the I‐SVSB‐IP. The results showed that the ChOA procedure had produced an optimal solution compared to the state‐of‐the‐art algorithm. This study also demonstrated a sensitivity analysis of decision and transportation variables to cost, revenue, and JTP. The results show that increasing transport frequency of ordering raw materials (m) and finished products to buyers (n) enhances the total cost and reduces joint total profit. In addition, increasing the rate of quality degradation of raw materials reduces JTP.

Heuristic analyses of separate and bundling sales for complimentary products under consignment stock policy

In the real world, various products are displayed simultaneously on the shelf; therefore, their demands/prices affect each other. This paper aims at studying a joint economic lot-sizing model with two complementary products in a supply chain consisting of a vendor and a buyer. The vendor sends items to the buyer's warehouse in equal-size batches applying vendor-managed inventory with consignment stock policy. The buyer stocks items at the warehouse and on the shelf. Two mixed-integer nonlinear models that consider bundling and separate sales have been proposed and solved through different solution algorithms such that the profit is maximized. The concavity of both models' objective functions is investigated and the effect of considering complementation between products and bundling strategy is studied. Numerical experiments indicate that the bundle's marginal profit is greater than a single product's marginal profit. Moreover, the supply chain members can also take advantage of economies of scale in bundling sales.

Inventory and sales decisions in a vendor–buyer system with imperfect items and learning in inspection

ABSTRACT In this study, we propose a joint economic lot-sizing model to include learning process along with errors in inspection and full backordering system. We aim to study pricing and inventory decisions in a two-level supply chain involving a single vendor and a single buyer in which the demand is sensitive to price and company’s advertisement efforts. The mathematical inventory model is developed analytically and solved using a proposed algorithm. The objective of the model is to maximise joint total profit by simultaneously determining optimal shipment size, number of deliveries, backorder quantity and product selling price. A numerical example is provided to show the application of the model and to investigate the impact of key parameter’s changes on model behaviour. By comparing the integrated/centralised model to the independent/decentralised model, we note that the integrated/centralised model provides better profit to the system, along with lower selling price and smaller amount of backorder.

An optimal inventory policy for a multi-echelon closed-loop supply chain of postconsumer recycled content products

This research studies a production-recycling inventory model for postconsumer recycled content products made from a mix of virgin and recycled materials with specific proportions. The proportion is known as the postconsumer recycled content level. We study a closed-loop supply chain (CLSC) where a recycling facility and a supplier respectively ship the recycled and virgin raw materials to a manufacturer. The manufacturer mixes them based on the proportion to produce these products for a retailer. The recycling facility recycles the used products collected by a material recovery facility. The paper develops a joint economic lot-size model (JELS) to maximize the chain-wide total profit. A branch-and-bound algorithm is developed, along with the convex analysis to find the exact solution. To coordinate the CLSC, we present models called disproportionate profit-sharing (DPS) and proportional profit-sharing (PPS) operating under quantity discount. The DPS would give more powerful members, a higher proportion of the extra profits resulting from the JELS. However, the PPS guarantees equitable increases in the individual profits accruing to all members from the JELS. Whereas the DPS works properly in vertically integrated CLSCs and decentralized ones with dominant player(s), the PPS is appropriate for decentralized ones with no dominant players. Additionally, we prove the optimal level of postconsumer recycled content is often either at its maximum or minimum allowable. However, the zero-derivative points within the range can be optimum in a particular case. Consequently, we present decision trees for managers to determine the right profit-sharing method and the optimal postconsumer recycled content level.

A joint economic lot-size model for sustainable industries of recycled content products

Coupling forward and reverse operations in closed-loop supply chains (CLSCs) can lead to a higher degree of sustainability. Previous studies on CLSCs have focused on the products that are either purely remanufactured or purely new. The emphasis on recycling necessitates research that considers recycled content products, which are made from a mix of virgin and recycled material. We study a CLSC consisting of a manufacturer, a retailer, a supplier, a material recovery facility (MRF) and a recycling facility. The supplier and the recycling facility provide the virgin and recycled raw materials, respectively, to the manufacturer who mixes them based on a predefined proportion known as the recycled content level to produce the finished products for the retailer. The recycling facility recovers the manufacturer’s production waste as well as the used products collected by the MRF. We aim at maximising the chain-wide profit by optimising the shipments among the supply chain parties. We propose a Branch-and-Bound algorithm to obtain the optimal solution, and a heuristic procedure, which provides the optimal solution in 96% of all tested instances. In addition, we prove the optimality of a bang-bang policy for the recycled content level in most cases.

Improving Supply Chain Profit through Reverse Factoring: A New Multi-Suppliers Single-Vendor Joint Economic Lot Size Model

Supply chain finance has been gaining attention in theory and practice. A company’s financial position affects its performance and survivability in dynamic and volatile markets. Those that have weak financial performance are vulnerable when operating in environments that are uncertain and financially unstable. Companies adopt various solutions and techniques to manage, effectively and efficiently, the flow of money to and from its suppliers and buyers. Reverse factoring is an innovative technique in supply chain financing. This paper develops a joint economic lot size model where a vendor coordinates operational and financial decisions with its multiple suppliers through the establishment of a reverse factoring arrangement. The creditworthy vendor systematically informs a financial institution (e.g., bank) of payment obligations to selected suppliers, enabling the latter to borrow against the value of the relevant accounts receivable at low interest (borrowing) rates. The paper also presents a numerical example and a sensitivity analysis to illustrate the behavior of the model and to compare the economic and operational performance of a supply chain with and without a reverse factoring agreement. The results show that the establishment of a reverse factoring agreement within the supply chain improves the economic performance and impacts on the operational decisions.

Joint economic lot size models with warehouse financing and financial contracts for hedging stocks under different coordination policies

The rapid expansion of emerging markets, combined with the influence of hedge funds and market speculators, highly increased commodity prices. At the same time, the global economic recession and an adverse credit environment, caused the price of commodities to drop with alarming speed. This huge volatility in prices generates a significant commodity risk, which creates issues of concern for companies while determining production, procurement, and risk-mitigation strategies. The context described is particularly challenging for those companies that have limited market power, since they may hardly transfer price increases to the end customers. In this regard, we extend the inventory theory by combining the operation management with two specific financial techniques, that may allow the commodity risk mitigation. Specifically, the warehouse financing practice and the use of futures contracts are included and investigated in the traditional joint economic lot size model, under two different coordination policies, as means for hedging stocks. The decision variables are the order quantity, the number of shipments between the vendor and the buyer, and the production rate. A numerical study is also presented in order to provide managerial insights on the economic performance of the different scenarios. The paper compares also the numerical results of the two financing practices with a base model, i.e. without any kind of supply chain finance. The results highlight that both the financing practices allow to reduce the total cost of the supply chain, and that the convenience of one practice, over the other, strictly depends on the relevant parameters distinguishing the case study.

Managing unreliability in automotive supply networks - an extension of the joint economic lot size model

Within assembly network supply chains, supply disruptions can occur on every supplier-buyer link. Managing this network unreliability can help to reduce schedule instability and increases the overall efficiency of the supply chain accordingly. In this line, a stylised assembly network supply chain model is proposed with two suppliers and a single buyer using the joint economic lot sizing approach. This supply network can be disrupted by a shortage occurring at one of the two suppliers due to random machine breakdowns, which consequently creates dependent requirements variations affecting both the buyer and the entire network. First, the basic joint economic lot sizing model is extended by the said schedule instability. Second, a solution approach is presented concerning the determination of optimal lot sizes, the investment into the reliability of the supply network as well as the determination of safety stocks. Furthermore, the sensitivity of relevant model parameters is investigated by means of a numerical example. Managerial implications are accordingly derived focusing on the reliability of the supply network members and internal incentive structures.

Managing unreliability in automotive supply networks – an extension of the joint economic lot size model

Managing unreliability in automotive supply networks – an extension of the joint economic lot size model

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.

Optimization of a Joint Economic Lot Size Model for a First-tier Supplier with Sequential Processes Using a Genetic Algorithm

As corporate competition intensifies in the 21st century, optimal in the integrated supply chain is more important than optimization of individual company. Our research examines a series of integrated supply chain systems comprising a single raw material supplier, a first-tier supplier with multiple processes, and a single original equipment manufacturer in the Korean automotive industry. Unlike other papers, we have studied the situation in which the first-tier supplier has an assembly process. We have also analyzed the situation in which the demand for semi-finished products occurs in the first-tier supplier process or in which semi-finished products are purchased from subcontractors and put into production. The objective function is to minimize the sum of production costs, inventory holding costs, ordering costs, and setup costs in the integrated supply chain. To solve this problem, we formulated nonlinear programming, and developed a genetic algorithm. The results showed that using a dynamic lot size is cheaper than using a fixed lot size. In addition, the lower the setup cost, the smaller the lot size, and when a certain level is reached, the lot size will be the same even if the cost changes.

A SINGLE-VENDOR SINGLE-BUYER INTEGRATED PRODUCTION-INVENTORY MODEL WITH QUALITY IMPROVEMENT AND CONTROLLABLE PRODUCTION RATE

In the classical vendor-buyer inventory models, the common unrealistic assumption is that all the items manufactured are in good quality. However, in reality, it can be observed that there may be some defective items produced and then delivered to the buyer. Thus, the existence of defective items would consequently give significant influence to system behavior. In addition, a manufacturing flexibility such as the capability to adjust production capacity becomes a key success factor for increasing system flexibility as well as reducing total cost. Here, we investigate how a quality improvement program and adjustable production rate can help the supply chain to reduce the total cost. This paper studies the effect of quality improvement and controllable production rate in joint economic lot size model consisting of single-vendor and single-buyer under stochastic demand. The model gives allowance to the vendor to adjust production rate and also to invest an amount of capital investment to reduce the defect rate. The lead time is comprised of production time and setup and transportation time. The model also considers a situation in which the shortages in buyer side are assumed to be partially backordered. To solve the model, an iterative algorithm is proposed to determine simultaneously safety factor, delivery lot size, delivery frequency, production rate and process quality for minimizing total cost is proposed. The result from this study shows that allowing the vendor to both adjust the production rate and reduce the defective product by adopting quality improvement policy can reduce the individual and total cost. In the example given, the proposed model gives significant total cost saving of 45.9% compared to the model without controllable production rate and quality improvement.

Coordination of a production network with a single buyer and multiple vendors with geometrically increasing batch shipments

This paper considers the joint economic lot size model for the special case where multiple vendors supply a single product to a single buyer. The production lots of each vendor are transferred to the buyer in batches increasing in size according to a fixed factor, where the size of the batches may differ from vendor to vendor. To coordinate the production cycles of the vendors and the consumption cycle of the buyer, we use two different shipment policies, namely one policy where batches are shipped to the buyer directly after their completion, and one policy where shipments are made whenever the inventory at the buyer reaches zero. Mathematical models are proposed for each policy, and solution procedures are suggested. Subsequently, the performance of the policies is evaluated in a numerical experiment, and both policies are compared to the situation where batches of equal sizes are shipped from the vendors to the buyer. The paper concludes with suggestions for further research.

Additive manufacturing impacts on a two-level supply chain

ABSTRACTAdditive Manufacturing (AM) is a recent and rapidly developing technology, which has brought about significant disruptions in the manufacturing arena. To capture the full spectrum of changes resulting from AM's introduction into the industry, it is not sufficient to look at it just as a disruptive set of technologies but, rather, take a system's approach. It must be noted that the investigation of AM's impacts cannot be limited to an individual actor, but should encompass the whole supply chain to fully consider the relevant changes in strategic as well as tactical decision-making and operations. This paper presents an analytic approach based on Joint Economic Lot Sizing model, and aims at capturing the most significant impacts resulting from the implementation of the AM concept on a two-level supply chain. This assessment of AM from inventory and logistics standpoints is targeted at providing insights into how manufacturers could adapt their supply chains’ planning to accommodate new paradigms introduced by AM. A numerical example followed by sensitivity analysis of a real industrial case study is presented to provide evidence for the main findings and further generalise them.

Joint economic lot sizing model with stochastic demand and controllable lead-time by reducing ordering cost and setup cost

This paper derives a mathematical integrated production inventory model of single vendor and buyer to investigate the effects of capital investment in setup cost of the vendor and order processing cost of the buyer on the decision variables of the model. Main purpose of this study is to minimize the integrated total cost of the vendor and buyer by optimizing the delivery lot size, lead-time, setup and order processing cost and number of deliveries per order simultaneously while lead-time demand follows normal distribution and unknown distribution, i.e., distribution free case. This model is analyzed by calculus method and justified with appropriate numerical illustrations. Numerical results show that significant savings can be achieved at optimal investments in reducing lead time, ordering cost and setup cost. Finally, sensitivity analysis of the key parameters is carried out and some managerial implications are also included.

A joint economic lot size model for a supplier-manufacturer-retailers supply chain of an agricultural product

Smooth supply of processed agricultural products to the market is necessary for survival of human beings. Minimization of the management cost of these products plays an important role in delivering them to customers with reasonable prices. Although single-manufacturer single-retailer two-tier supply chain (SC) models are available in the literature, there is a lack of a three-tier SC model concerning agricultural products. This study presents a three-tier joint economic lot size SC model of delivering agricultural products, consisting of a single seasonal supplier, a single manufacturer and multiple retailers. The demand of a product is assumed to be a deterministic constant. The objective is to find the number of shipments and shipments sizes in a cycle from the supplier to the recipient to minimize the total cost of ordering, setup, shipment and holding. The model is solved following both the algebraic and the differentiation methods. They are found to provide the same solution theoretically. Also, we develop an algorithm to find integer number of shipments to manufacturer and retailers in obtaining the minimal total cost solution to the problem. A sensitivity analysis on a solution of a numerical problem shows that a manager can control the frequency of shipments with an extra cost.