A Multiple Items EPQ/EOQ Model for a Vendor and Multiple Buyers System with Considering Continuous and Discrete Demand Simultaneously

Jonrinaldi Jonrinaldi,E Wirdianto,T Rahman,D Z Zhang,Henmaidi Henmaidi

doi:10.1088/1757-899x/319/1/012037

Jonrinaldi Jonrinaldi, E Wirdianto + Show 3 more

Open Access

https://doi.org/10.1088/1757-899x/319/1/012037

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Abstract

This paper proposed a mathematical model for multiple items Economic Production and Order Quantity (EPQ/EOQ) with considering continuous and discrete demand simultaneously in a system consisting of a vendor and multiple buyers. This model is used to investigate the optimal production lot size of the vendor and the number of shipments policy of orders to multiple buyers. The model considers the multiple buyers’ holding cost as well as transportation cost, which minimize the total production and inventory costs of the system. The continuous demand from any other customers can be fulfilled anytime by the vendor while the discrete demand from multiple buyers can be fulfilled by the vendor using the multiple delivery policy with a number of shipments of items in the production cycle time. A mathematical model is developed to illustrate the system based on EPQ and EOQ model. Solution procedures are proposed to solve the model using a Mixed Integer Non Linear Programming (MINLP) and algorithm methods. Then, the numerical example is provided to illustrate the system and results are discussed.

Highlights

Inventory management is one of the vital competitive factors for industries [1,2,3]
Many of inventory models based on Economic Order Quantity (EOQ) or Economic Production Quantity (EPQ) due to their simplicity and robustness [6, 7, 8]
The basic EPQ model was proposed five years later after the basic EOQ model was presented and it used the same assumptions with EOQ model [11]

Summary

Introduction

Inventory management is one of the vital competitive factors for industries [1,2,3]. It used inventory model as decision-making tool to control the inventory [4] and have received a lot attention since the last past century till today [5]. The EOQ model is used to determine an optimal order size by balancing the setup cost and inventory holding cost [9] and EPQ model is used to determine the optimal replenishment lot size to produce [5] Due to their own assumptions and conditions, these models are bound to their applicability in real-world situations [1] so that it is extended by several academicians and researchers [10]. This research proposed a multiple items EPQ/EOQ model with considering continuous and discrete demand simultaneously in a vendor-multiple buyers system.

System characteristics

Notations and assumptions

Model formulation

The solution procedures

Numerical example and discussion

Conclusions