Joint Economic Lot Size Research Articles

A multi-stage joint economic lot size model with lead time penalty costs

This paper studies the case of a multi-stage supply chain where equal- and unequal-sized batches are transported between the stages and where penalty costs are imposed for long lead times. Unlike earlier works, this paper does not restrict the number of stages to a given value, but rather analyses a general case of the model. First, an analytical model of the supply chain is developed and the properties of the model are discussed. Secondly, a simulation study is conducted to analyse the behaviour of the model. The results of our analysis indicate that the performance of upstream stages of the supply chain is more critical to the performance of the supply chain than the performance of downstream stages. Furthermore, our findings show that a supply chain stage may improve its position significantly by coordinating its behaviour with its direct neighbours in the supply chain.

Design of contract parameters in a closed-loop supply chain

We study an extended joint economic lot size problem which incorporates the return flow of remanufacturable used products. The supply chain under consideration consists of a single supplier and a single buyer. The buyer orders a single product from the supplier, uses it for her own needs, and collects the remanufacturable items after use. The ordered items are shipped from the supplier to the buyer in the lot-for-lot fashion by a vehicle which also returns the collected used items from the buyer to the supplier for remanufacturing and subsequent service of the buyer’s demand in the next order cycle. For satisfying the total demand, the supplier manufactures new items or remanufactures used ones received from the buyer. For given demand, productivity, collection rate, disposal cost, setup cost, order cost, holding cost for serviceable and nonserviceable products at the supplier as well as the buyer the lot size (order size) for the supplier (buyer) has to be found which minimizes the total cost. Furthermore, we address a decentralised decision making of the parties under a two-part tariff and determine their equilibrium strategies within the Nash framework.

A joint economic lot-sizing model for the hospital’s supplier with capacitated warehouse constraint

In a vertically integrated supply chain of healthcare groups such as Chang Gung memorial hospitals in Taiwan, the vendor of special medical items and the hospitals are owned by the same business conglomerate; besides, warehouse capacity is one of the scarcest resources that greatly affect the inventory control policies. Taking the vendor’s limited warehouse capacity into account, this article first proposes a generic joint economic lot sizing (JELS) model in determining the optimal production and shipment policy for a two-layer supply chain. The vendor manufactures the requested products in lots and delivers them in batches to the buyer with partial shipment policy. A threshold value which defines those existing JELS problems as a special case of our proposed model, while the manufacturer’s warehouse capacity exceeds it, is attained. Finally, a numerical example is used to characterize the optimal production and replenishment lot-size decisions for the supply chain.

A seller-buyer supply chain model with exponential distribution lead time

Supply chain is an accepted way of remaining in the competition in today's rapidly changing market. This paper presents a coordinated seller-buyer supply chain model in two stages, which is called Joint Economic Lot Sizing (JELS) in literature. The delivery activities in the supply chain consist of a single raw material. We assume that the delivery lead time is stochastic and follows an exponential distribution. Also, the shortage during the lead time is permitted and completely back-ordered for the buyer. With these assumptions, the annual cost function of JELS is minimized. At the end, a numerical example is presented to show that the integrated approach considerably improves the costs in comparison with the independent decisions by seller and buyer.

The joint economic lot size problem: A review

Abstract This article reviews lot-size models which focus on coordinated inventory replenishment decisions between buyer and vendor and their impact on the performance of the supply chain. These so-called joint economic lot size (JELS) models determine order, production and shipment quantities from the perspective of the supply chain with the objective of minimizing total system costs. This paper first describes the problem studied, introduces the methodology of the review and presents a descriptive analysis of the selected papers. Subsequently, papers are categorized and analyzed with respect to their contribution to the coordination of different echelons in the supply chain. Finally, the review highlights gaps in the existing literature and suggests interesting areas for future research.

A VENDOR MANAGED TWO-ECHELON INVENTORY SYSTEM FOR AN INTEGRATED PRODUCTION PROCUREMENT CASE

Joint economic lot size models for purchasers and vendors are more economical than when considering their inventory problems independently. It requires vendors to have a complete knowledge of their purchaser's demands. In such a situation, the vendor shall manage the supply with comparatively more inventory at its end. The operational cost can further decrease provided supply is in sub-batches and logistics cost does not increase substantially. However, determining the right size for these sub-batches becomes an issue. Sub-batches of varying size may cause planning and control problems, but supply in sub-batches of uniform size will not. In this paper, joint economic lot size models are presented for the two supply situations, namely staggered supply and uniform supply. Cases are employed that describe the inventory situation of a single vendor supplying an item to a manufacturer that is further processed before it is supplied to the end-user. Using illustrative examples, the comparative advantages of the uniform sub-batch supply over the staggered alternative are investigated. From the analysis, uniform supply models are found to be comparatively more beneficial and robust than the staggered sub-batch supply.

Collaborative supply chain planning under dynamic lot sizing costs with capacity decision

Studies show that supply chain cooperation improves supply chain performance. However, it remains a challenge to develop and implement the realistic supply chain cooperation scheme. We investigate a two-echelon supply chain planning problem with capacity acquisition decision under asymmetric cost and demand information. A simple negotiation-based coordination mechanism is developed to synchronize production/order strategies of a supplier and a buyer. The coordination scheme shows how the supplier and the buyer modify their production and order policy in order to find a joint economic lot sizing plan, which saves the overall supply chain cost. The allocation of the cooperation benefit is determined by negotiation. Due to the complexity of the multiple periods, multiple level supply chain lot sizing with capacity decision, a heuristic algorithm is developed to find coordination solutions. Finally, the results of the numerical study indicate the performance of supply chain coordination scheme.

Secure collaborative supply chain planning and inverse optimization – The JELS model

It is a well-acknowledged fact that collaboration between different members of a supply chain yields a significant potential to increase overall supply chain performance. Sharing private information has been identified as prerequisite for collaboration and, at the same time, as one of its major obstacles. One potential avenue for overcoming this obstacle is Secure Multi-Party Computation (SMC). SMC is a cryptographic technique that enables the computation of any (well-defined) mathematical function by a number of parties without any party having to disclose its input to another party. In this paper, we show how SMC can be successfully employed to enable joint decision-making and benefit sharing in a simple supply chain setting. We develop secure protocols for implementing the well-known “Joint Economic Lot Size (JELS) Model” with benefit sharing in such a way that none of the parties involved has to disclose any private (cost and capacity) data. Thereupon, we show that although computation of the model’s outputs can be performed securely, the approach still faces practical limitations. These limitations are caused by the potential of “inverse optimization”, i.e., a party can infer another party’s private data from the output of a collaborative planning scheme even if the computation is performed in a secure fashion. We provide a detailed analysis of “inverse optimization” potentials and introduce the notion of “stochastic security”, a novel approach to assess the additional information a party may learn from joint computation and benefit sharing. Based on our definition of “stochastic security” we propose a stochastic benefit sharing rule, develop a secure protocol for this benefit sharing rule, and assess under which conditions stochastic benefit sharing can guarantee secure collaboration.

LOT SIZE DECISIONS IN A THREE-LEVEL SUPPLY CHAIN WITH FREIGHT RATE DISCOUNTS

ABSTRACT Previous research on the joint economic lot size (JELS) problem was focused on the decisions of lot sizes and batches delivered among players in the supply chain, assuming that transportation cost was independent of shipment amounts. Nevertheless, the transportation cost accounts for a major part of supply chain cost, especially when transportation companies offer freight rate discount schedules to the supply channel, shippers are able to claim over-declared shipment to lower their transportation costs. The impact of freight rate discount is significant and should not be overlooked. In this article, we address an integrated three-level JELS problem with freight rate discounts. Managerial insights of the model are illustrated in propositions and numerical examples are provided.

Managing level of consigned inventory with buyer's warehouse capacity constraint

In this article, we consider a single-manufacturer, single-buyer supply chain problem in which a manufacturer produces a single item product and periodically delivers it to the buyer on the basis of a consignment policy. An integrated inventory control model, making joint economic lot size decisions of the manufacturer's production batch and the replenishment lot subject to consignee's warehouse space capacity constraint, is constructed to minimise the manufacturer's total cost. The model developed is a general model from which known results in specific cases can be deduced. An algorithm that optimally solves the proposed model is presented along with a numerical illustration. The characteristics of the model and the impact of available consignee's warehouse space capacity constraint on the manufacturer's total cost, production batch, and replenishment lot sizes are also discussed.

Joint Economic Lot Sizing Optimization in a Supplier-Buyer Inventory System When the Supplier Offers Decremental Temporary Discounts

This research discuss es mathematical models of joint economic lot size optimization in a supplier-buyer inventory system in a situation when the supplier offer s decremental temporary discounts during a sale period. Here, the sale period consists of n phases and the phases of discounts offered descend as much as the number of phases. The highest discount will be given when orders are placed in the first phase while the lowest one will be given when they are placed in the last phase. In this situa t ion, the supplier attempts to attract the buyer to place orders as early as possible during the sale period. The buyers will respon these offers by ordering a special quantity in one of the phase. In this paper, w e propose such a forward buying model with discount-proportionally-distributed time phases. To examine the behaviour of the proposed model, we conducted numerical ex periments . We assumed that there are three phases of discounts during the sale period. We then compared the total joint cost s of special order placed in each phase for two scenarios. The first scenario is the case of independent situation – there is no coordination between the buyer and the supplie-, while the second scenario is the opposite one, the coordinated model. Our results showed the coordinated model outperform the independent model in term s of producing total joint cost s . We finally conducted a sensitivity analyzis to examine the other behaviour of the proposed model. Keywords: supplier-buyer inventory system, forward buying model, decremental temporary discounts, joint economic lot sizing, optimization.

An integrated vendor–buyer cooperative model under stochastic supply lead-time

This paper presents a single-vendor, single-buyer integrated inventory model. We relax the assumption of deterministic lead-time in the hitherto existing joint economic lot sizing (JELS) models and analyze the problem where the buyer lead-time is a stochastic variable. Moreover, we consider the situation in which shortage is allowed. The vendor produces the product in batches and periodically delivers final goods at a fixed lot size to the customer, who has a constant demand rate. The proposed model, based on the integrated expected total relevant costs of both buyer and vendor finds out optimal values of reorder point, order quantity, and number of shipments, using a solution procedure. Numerical examples are also used to analyze the savings in joint total cost over individually derived policies.

A note on “quality improvement and setup reduction in the joint economic lot size model”

In a recent paper, Affisco et al. [J.F. Affisco, M.J. Paknejad, F. Nasri, Quality improvement and setup reduction in the joint economic lot size model, European Journal of Operations Research 142 (2002) 497–508] propose a quality-adjusted joint economic lot size model that considers investments in quality improvement and setup cost reduction. In particular, they consider a single-vendor, single-buyer, deterministic demand economic lot-sizing problem, and they investigate the potential impact of economic investments in the vendor’s quality improvement and setup cost reduction efforts on the system-wide costs. However, the particular form of the investment function that they use to represent the cost of investments in quality improvement does not represent actual practice in many industries. Hence, in this note, we develop modified models for quality improvement and simultaneous quality improvement and setup cost reduction using a modified form of the investment function. Our fundamental results and conclusions are substantially different than those in Affisco et al. (2002).

A factual comment on “Joint economic lot size in distribution system with multiple shipment policy”

A factual comment on “Joint economic lot size in distribution system with multiple shipment policy”

A bargaining model with asymmetric information for a single supplier–single buyer problem

Banerjee’s joint economic lot size (JELS) model represents one approach to minimizing the joint total relevant cost of a buyer and a supplier by using a joint optimal order and production policy. The implementation of a jointly optimal policy requires coordination and cooperation. Should the buyer have the market power to implement his own optimal policy as that one to be used in the exchange process no incentive exists for him to choose a joint optimal policy. A joint policy can therefore only be the result of a bargaining process between the parties involved. The supplier may make some sort of concession such as a price discount or a side payment in order to influence the buyer’s order policy. A critical assumption made throughout in supply chain literature is that the supplier has complete knowledge about the buyer’s cost structure. Clearly, this assumption will seldom be fulfilled in practice. The research presented in this paper provides a bargaining model with asymmetric information about the buyer’s cost structure assuming that the buyer has the power to impose its individual optimal policy.

A joint economic-lot-size model for purchaser and vendor in fuzzy sense

This paper investigates a group of computing schemas for joint economic lot size as fuzzy values of the economic lot size model for purchaser and vendor. We express the fuzzy order quantity/production lot size for the purchaser/vendor as the normal triangular fuzzy number ( q 1, q 0, q 2) and then we solve the aforementioned optimization problem under the condition 0 < q 1 < q 0 < q 2. We find that, after defuzzification, the joint total relevant cost is slightly higher than in the crisp model.

Joint optimization of process improvement investments for supplier–buyer cooperative commerce

This research focuses on supporting the formation of strategic alliances through the concept of cooperative commerce, where suppliers and buyers work together to jointly optimize their business. The general goal of this research is to examine existing cooperative commerce models for obstacles that would hinder their successful implementation into modern industrial applications and to address those shortcomings. Total annual cost equations are formulated to capture the joint total relevant cost of cooperative commerce business relationships. These total joint relevant cost models will include terms that capture the ordering cost, holding cost, and cost of quality, as well as any applicable investment cost for process improvements, consistent with traditional economic order quantity and economic production quantity theory. This research corrects a modelling/computational error found in the literature that led to underestimation of the effectiveness of process improvements in joint economic lot size models by 5–12%. In addition, the models are expanded to accommodate a full range of product quality inspection policies, from 0 to 100% product inspections. Furthermore, the models are modified to account for the cost of scrap generation, as well as the effects of accepting non-conforming product and rejecting conforming product during quality inspections. Once the total cost models are expanded to account for these neglected costs, the joint total relevant cost equations are minimized to find the optimal batch sizes, and the effects of each model extension on the model solution are studied. Results indicate that these extensions have a significant impact on the model results, such as reduced optimal batch sizes and increased optimal fraction conforming product.

Joint economic lot size in distribution system with multiple shipment policy

This paper presents a new methodology to obtain the Joint Economic Lot size in the case where multiple buyers are demanding one type of item from a single vendor. The shipment policy is found and a new model is proposed to minimize the joint total relevant cost (JTRC) for both vendor and buyer(s). Considering the two-buyer and more than two-buyer cases, exact and approximate optimum solutions were obtained. The benefits of the new model were illustrated in term of two different ratios: production rate to demand rate, and transportation cost to holding cost. A sensitivity analysis was conducted to test the robustness of the new model.

A single-vendor multiple-buyer inventory model with a multiple-shipment policy

This paper presents a new methodology to obtain the joint economic lot size in the case where multiple buyers are demanding one type of item from a single vendor. The shipment policy is found and a new model is proposed to minimise the joint total relevant cost (JTRC) for both vendor and buyer(s). Considering the two-buyer and the more-than-two-buyer cases, an analytical solution and numerical solution are obtained. A significant savings in joint total relevant cost is achieved when the total demand rate is close to the production rate. A sensitivity analysis is also conducted to test the robustness of the new model .

A joint economic lot size model for raw material ordering, manufacturing setup, and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.