Joint Economic Lot Size Research Articles

Quality improvement and setup reduction in the joint economic lot size model

The co-maker concept has become accepted practice in many successful global business organizations. This fact has resulted in a class of inventory models known as joint economic lot size (JELS) models. Heretofore such models assumed perfect quality production on the part of the vendor. This paper relaxes this assumption and proposes a quality-adjusted JELS model. In addition, classical optimization methods are used to derive models for the cases of setup cost reduction, quality improvement, and simultaneous setup cost reduction and quality improvement for the quality-adjusted JELS. Numerical results are presented for each of these models. Comparisons are made to the basic quality-adjusted model. Results indicate that all three policies exhibit significantly reduced total cost. However, the simultaneous model results in the lowest cost overall and the smallest lot size. This suggests a synergistic impact of continuous improvement programs that focus on both setup and quality improvement of the vendor's production process. Sensitivity analysis indicates that the simultaneous model is robust and representative of practice.

A fuzzy mathematical model for the joint economic lot size problem with multiple price breaks

This paper applies fuzzy mathematical programming to solve the joint economic lot size problem with multiple price breaks. In order to entice the buyer to increase the order quantity, it is a common practice for the seller to offer quantity discounts to the buyer. From the system viewpoint, the joint cost for the seller and buyer can be minimized only when the buyer increases his economic order quantity. The problem is how to determine the number of price breaks, as well as the quantity discount and order quantity at each price break, to achieve the optimal joint cost. Fuzzy mathematical programming provides a very efficient algorithm to solve the above problem simultaneously from the perspectives of the seller and the buyer. Another common problem in joint economic lot size model is how to split the system profit between the seller and the buyer. Whereas the traditional approach to this problem is to divide the profit based on a certain ratio determined by the bargaining power of both parties, fuzzy mathematical programming can achieve the same satisfaction level to both parties based on their respective cost functions.

A comparison of alternative joint vendor-purchaser lot-sizing models

Abstract This paper provides a comparative analysis of two sets of alternative joint lot-sizing models for the general one-vendor, many-nonidentical-purchasers case. Specifically, the basic joint economic lot size (irJELS) and individually responsible and rational decision (IRDD) models, and the simultaneous setup cost and order cost reduction versions are explored. Models for the latter situation are derived by the use of classical optimization techniques. A numerical example is presented which provides the basis for comparison of the models with the results of independent optimization (IO). For the basic models the previously reported advantages of IRRD are refuted. In the simultaneous investment case both the vendor and the purchasers realize significant savings over IO when the JELS policy is followed. This is not true for IRRD. This suggests that when an environment of co-operation between the parties has been established the JELS is a superior policy.

The Individually Responsible and Rational Decision Approach to Economic Lot Sizes for One Vendor and Many Purchasers

ABSTRACTBanerjee's [2] joint economic lot size (JELS) model, along with related works by Monahan [12] and Lal and Staelin [10], represents one approach to minimizing the total inventory carrying and ordering costs of a vendor and his purchaser(s). Noting that JELS philosophy requires a coordinated system and that its practical implementation is problematic, we present an alternative approach to the same problem: the individually responsible and rational decision (IRRD) approach. The IRRD approach is consistent with a free enterprise system and easy to implement. In order to show that the IRRD approach is also more economical than the JELS approach, we first build a more refined JELS model for the case of one vendor and many identical purchasers. Drawing on earlier criticisms of specific JELS models, our refinement relaxes the lot‐for‐lot assumption commonly used by JELS scholars. To be comparable with earlier works, we retain the assumption of deterministic conditions and demonstrate the economic advantages of IRRD over JELS through a numerical example. An algebraic proof of IRRD's superiority over JELS is offered in the more general and realistic case of a vendor dealing with K nonidentical purchasers with reasonably predictable annual demand but uncertain order quantities and timings.

Note—On “A Quantity Discount Pricing Model to Increase Vendor Profits”

Monahan (Monahan, James P. 1984. A quantity discount pricing model to increase vendor profits. Management Sci. 30 (June) 720–726.) develops a model for establishing an optimal quantity discount schedule from a vendor's viewpoint. In this note we show that this model is limited to the case where the vendor buys from another supplier. Incorporating vendor's inventory carrying costs, we develop a generalized version of Monahan's model and demonstrate its equivalence with the joint economic lot size approach suggested by Banerjee (Banerjee, Avijit. 1986. A joint economic lot size model for purchaser and vendor. Decision Sci. 17 (Summer) 292–311.).