Optimization model for the new coordinated replenishment and delivery problem with multi-warehouse

• Date: 08 May 2017
• DOI: https://doi.org/10.1108/IJLM-11-2015-0217
• Published date: 08 May 2017
• Pages: 290-310
• Author: Rui Liu,Shan Liu,Yu-Rong Zeng,Lin Wang
• Subject Matter: Management science & operations,Logistics

Optimization model

for the new coordinated

replenishment and delivery

problem with multi-warehouse

Rui Liu

School of Management,

Huazhong University of Science and Technology,

Wuhan, China

Shan Liu

School of Management,

Xi’an Jiaotong University, Xi’an, China

Yu-Rong Zeng

School of Information Engineering,

Hubei University of Economics, Wuhan, China, and

Lin Wang

School of Management,

Huazhong University of Science and Technology,

Wuhan, China

Abstract

Purpose –The purpose of this paper is to investigate a new and practical decision support model of the

coordinated replenishment and delivery (CRD) problem with multi-warehouse (M-CRD) to improve

the performance of a supply chain. Two algorithms, tabu search-RAND (TS-RAND) and adaptive hybrid

different evolution (AHDE) algorithm, are developed and compared as to the performance of each in solving

the M-CRD problem.

Design/methodology/approach –The proposed M-CRD is more complex and practical than classical

CRDs, which are non-dete rministic polynomia l-time hard problems. Acc ording to the structure o f the

M-CRD, a hybrid algorit hm, TS-RAND, and AHDE are designed to solve t he M-CRD.

Findings –Results of M-CRDs with different scales show that TS-RAND and AHDE are good candidates for

handling small-scale M-CRD. TS-RAND can also find satisfactory solutions for large-scale M-CRDs. The total

cost (TC ) of M-CRD is apparently lower than that of a CRD with a single warehouse. Moreover, the TC is

lower for the M-CRD with a larger number of optional warehouses.

Practical implications –The proposed M-CRD is helpful for managers to select the suitable warehouse and

to decide the delivery scheduling with a coordinated replenishment policy under complex operations

management situations. TS-RAND can be easily used by practitioners because of its robustness, easy

implementation, and quick convergence.

Originality/value –Compared with the traditional CRDs with one warehouse, a better policy with

lower TC can be obtained by the new M-CRD. Moreover, the proposed TS-RAND is a good candidate for solving

the M-CRD.

Keywords Decision making, Supply chain management, Transportation management, Purchasing,

Hybrid different evolution algorithm, TS-RAND algorithm

Paper type Research paper

The International Journal of

Logistics Management

Vol. 28 No. 2, 2017

pp. 290-310

© Emerald PublishingLimited

0957-4093

DOI 10.1108/IJLM-11-2015-0217

Received 13 February 2015

Revised 15 November 2015

16 November 2015

2 January 2016

Accepted 4 January 2016

The current issue and full text archive of this journal is available on Emerald Insight at:

www.emeraldinsight.com/0957-4093.htm

The authors are grateful for the constructive comments of Professor Benjamin T. Hazen and three

referees. This research is partially supported by National Natural Science Foundation of China

(Nos: 71371080; 71531009), and Humanities and Social Sciences Foundation of Chinese Ministry of

Education (No. 15YJA630095).

290

IJLM

28,2

Nomenclature

Sets and parameters

D

i,m

demand rate of item idistributed

through warehouse m(deliver to

retailer i)

hR

iinventory holding cost of item iin

retailer iper unit per unit time

hW

i;minventory holding cost of item iin

warehouse mper unit per unit time

iindex of item or retailer, i¼1, 2, …,n

mindex of warehouse, m¼1, 2, …,M

q

i,m

the quantity of item ifor retailer i

distributed through warehouse m

received in every k

i,m

T/f

i,m

interval

Q

i,m

the ordering quantity of item i

distributed through warehouse m,

and Q

i,m

¼k

i,m

TD

i,m

Swarehouses’major ordering cost

sR

i;moutbound transportation cost of item

idistributed through warehouse m

(deliver to retailer i)

sW

i;mminor ordering cost of item i

distributed through warehouse m

T

i,m

the replenishment cycle of item i

when item idistributed through

warehouse m, and T

i,m

¼k

i,m

T

Decision variables

f

i,m

integer number that decides the

outbound schedule of item i

distributed through warehouse m;

the upper and lower bounds of

f

i,m

are fUB

i;mand fLB

i;m; the matrix for

all f

i,m

is F

k

i,m

integer number that decides the

replenishment schedule of item i

distributed through warehouse m;

the upper and lower bounds of k

i,m

are kUB

i;mand kLB

i;m; the matrix for all

k

i,m

is K

Tbasic cycle time; the upper and lower

bounds of Tare Tmax and Tmin

x

i,m

0-1 variable, if x

i,m

¼1, the path

of item idistributed through

warehouse mexists; otherwise, 0

Notations of TS

TL tabu list

Bneighborhood solution

K

max

the maximum iteration

Y_best current best solution

pmutation probability

CR a random number in [0, 1]

1. Introduction

Over the past few years, the coordinated replenishment problem (CRP) has been heavily

studied (Zeng et al., 2016). For a CRP procedure, the cost of placing an order for a number of

different items comprises two parts: a major ordering cost incurred whenever an order is

placed, and this cost is independent of the number of different items in the order; and a

minor ordering cost, which is decided by the number of different items in the order.

Grouping items into the same order when making purchasing decisions may be performed

for two reasons (Moon et al., 2008; Qu et al., 1999; Wang et al., 2015). First, a larger order may

be eligible for a quantity discount from the supplier. Second, in case a high major ordering

cost for placing an order is involved, grouping items into the same order can considerably

reduce the total of the major ordering cost (Tsao and Teng, 2013).

In a global purchasing environment, an increasing number of corporations have realized

that the coordinated replenishment and delivery (CRD) strategy can considerably save costs

(Sindhuchao et al., 2005). In fact, Blumenfeld et al. (1987) had already studied the adoption of

CRD policy in General Motors. Currently, single warehouse and n-retailer CRDs have still

received much attention from researchers (Ganeshan, 1999; Cha et al., 2008; Kang and Kim,

2010; Cui et al., 2014). With the rapid development of e-commerce, Moon et al. (2011) discussed

the CRD problem for a third-party warehouse while customers ordered in an e-marketplace.

However, multi-warehouse CRD strategy is few. In reality, a CRD policy is used by many

corporations with multiple warehouses. In many cases, an item from a supplier can cross

different warehouses with different costs. This may result in cost savings compared with a

291

Optimization

model for the

new CRD

problem