Inventory control model for a supply chain system with multiple types of items and minimum order size requirements

• Published date: 01 November 2018
• Author: Jong Soo Kim,Jun Hyeong Park,Ki Young Shin
• Date: 01 November 2018
• DOI: http://doi.org/10.1111/itor.12262

Intl. Trans. in Op. Res. 25 (2018) 1927–1946

DOI: 10.1111/itor.12262

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RESEARCH

Inventory control model for a supply chain system with

multiple types of items and minimum order size requirements

Jun Hyeong Park, Jong Soo Kim∗and Ki Young Shin

Department of Industrial and Management Engineering, Hanyang University,Erica Campus, Ansan, South Korea

E-mail: common123@nate.com [Park];pure@hanyang.ac.kr [Kim]; kiyoungshin21@gmail.com [Shin]

Received 24 June2015; received in revised form 21 October 2015; accepted 28 December 2015

Abstract

This paper considers a replenishment problem for a single buyer who orders multiple types of items from

two or more heterogeneous suppliers in order to sell to end customers. The buyer periodically orders each

type of item from the suppliers according to a select inventory control policy. Processing the order, each

supplier enforces the policy thatan order from the buyer must meet a predetermined minimum order quantity

(MOQ). Therefore, the buyer must decide how much to order from each supplier considering the current

inventory level, demand forecast, and MOQ requirement. The buyer’s problem is formulated as an integer

programmingmodel and an efficient implementation strategy is suggested to apply the model to real problems.

Numerical experiments are performed to test the validity of the proposedmodel as well as the efficiency of the

implementation strategy. The experimental results show that this model combined with the implementation

method yields a considerable cost reduction compared to the most efficient policy currently available.

Keywords:inventory control; minimum order quantity; integer programming model

1. Introduction

This paper deals with a system in which a single buyer regularly orders multiple types of items from

heterogeneous suppliers and sells to end customers. For this type of logistics system, it is a common

practice for suppliers to ensure that an ordermeets predeter mined minimumorder quantity (MOQ)

requirement, or the total purchase amount exceeds a certain monetary value, which is referred to as

MOQ and minimum purchase amount (MPA) requirement (Porras and Dekker, 2005; Kiesm¨

uller

et al., 2011). A well-known example of MOQ is the fashion ski-wear distributor Sport Obermeyer,

Inc. It outsources almost all of its production to Hong Kong and China. Due to economy of scale,

the company requires an MOQ of 600 garments in Hong Kong and 1200 garments in China per

∗Corresponding author.

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1928 J.H. Park et al. / Intl. Trans.in Op. Res. 25 (2018) 1927–1946

order. In United States., Home Depot and Walmart honor the MOQs specified by the suppliers

(Zhao and Katehakis, 2006).

Manufacturing companies in various industries enforce both MOQ and MPA requirements

together. For example, K&J Magnetics, Inc. (http://www.kjmagnetics.com/), which manufac-

tures and sells different types of custom magnets, requires the MOQ ranging from 10 to 500

pieces per product and the MPA of $150 per order. Another example is Sac-Ace Electronics Ltd.

(http://www.sanace.com/sanace/index.php) selling electronics parts and components. The com-

pany requires the MOQ ranging up to 40 units and the MPA of $200 per order.

Even though the MOQ and MPA are frequently used in practice, it is not properly taken into

account in the basic inventory models. Up to now, little effort has been devoted to the modeling

and analysis of inventory systems working with the MOQ or MPA requirements (Kiesm¨

uller et al.,

2011). It has been proven that the optimal policy structure for this kind of system is complex (Zhao

and Katehakis, 2006). In this regard, an extensive research on the optimal policy and efficient

implementation method for an inventory system with the requirements is necessary.

In the system, the suppliers are differentiated from each other by the type and transfer prices of

the items they carry, minimum order or purchase amount requirements, and delivery lead times.

The buyer, who periodically replenishes inventory to economically meet the demand of the end

customers, must decide how much of each item to buy from which supplier at the start of each

period. Basic information considered in the decision process includes the current inventory level

and demand forecast for future periods, as well as information on proponent suppliers. Herein, the

decision problem of the buyer is formulated as an integer programming model, and an efficient

implementation method is suggested for easy application of the model.

Previous research directly related to our study can be divided into two categories of problems:

a replenishment problem with multiple suppliers and replenishment problem with minimum order

requirements. Research focusing on the first category can be summarized as follows. Chiang and

Gutierrez (1998) analyzed a periodic-review inventory system with stochastic demand and multiple

suppliers. They developed a dynamic programming model and suggested a method to obtain opti-

mal values for operation parameters. Rosenblatt et al. (1998) studied an inventory system with two

suppliers under deterministic demand and lead times. They proposed algorithms enabling efficient

operation of the system. Later, Fong et al. (2000) considered a multiple-supplier inventory prob-

lem with stochastic demand and lead time. Assuming a continuous-review inventory policy, they

proposed a method for determining the optimal reorder point and total order quantity that would

minimize the average stock level.

Fox et al. (2006) studied a periodic-review inventory problem in which there were two suppliers

with different variable and fixed costs. They suggested three possible optimal policies to minimize

costs. Nenes et al. (2010) considered a multiple-item stochastic inventory system with multiple

suppliers. They developed an efficient procedure for determining the optimal base stock level for a

periodic-review control policy. Chen et al. (2012) analyzed a periodic-review inventory system with

one main supplier and an additional backup supplier that charges higher unit costs and has higher

fixed-order costs than the regular supplier.They proposed an algorithm for finding the optimal order

quantities for each supplier. Zhou and Chao (2014) considered a periodic-review inventory system

with two supply modes: a regular supply mode and an expedited supply mode that is faster, but

also more expensive than the regular mode. They proposed a mixed-integer nonlinear programming

model for determining optimal inventory replenishment.

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2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies