In this paper, the PIDRP is modelled as a one-to-many distribution system, in which a single warehouse or production facility is responsible for restocking a set of customers whose demands are deterministic and time-varying. The demand can be satisfied from either inventory held at the customer sites or from daily production. A fleet of homogeneous capacitated vehicles for making the deliveries is also considered. Capacity constraints for the inventory are given for each customer and the demand must be fulfilled on time, without delay. The aim of solving the PIDRP model is to minimize the overall cost of coordinating the production, inventory and transportation over a finite planning horizon. We propose an iterative procedure commonly known as MatHeuristic algorithm, an optimization algorithm designed by the interpolation of metaheuristics and mathematical programming techniques, to solve the model. In Phase 1, we construct routes in each period with the assumption that all the demands are satisfied in the given period by Variable Neighborhood Search, then the mixed integer programming is solved in Phase 2 to obtain the production schedules, quantity to be delivered and the inventory levels at the production facility and the customer sites. Based on the output from Phase 2, the routes are improved and the algorithm iterates until some stopping criteria is met. The model is solved by using Concert Technology of CPLEX 12.5 Optimizers with Microsoft Visual C++ 2010. Computational experiment is conducted to test the effectiveness of the algorithm. We observed that our algorithm performs better compared to the best integer solution obtained from CPLEX.

1.
J. F.
Bard
and
N.
Nananukul
,
Computers & Operations Research
37
(
12
),
2202
2217
(
2010
).
2.
Y.
Adulyasak
and
M. M.
Dessouky
,
Computers & Operations Research
55
,
141
152
(
2015
).
3.
P.
Chandra
,
Journal of the Operational Research Society
,
44
(
7
),
681
692
(
1993
).
4.
P.
Chandra
and
M.
Fisher
,
European Journal of Operational Research
,
72
(
3
),
503
517
(
1994
).
5.
L.
Lei
,
S.
Liu
,
A.
Ruszczynski
and
S.
Park
,
IIE Transactions on Scheduling & Logistics
,
38
(
11
),
955
970
(
2006
).
6.
M.
Boudia
,
M. A. O.
Louly
, and
C.
Prins
,
Computers & Operations Research
,
34
(
11
),
3402
3419
(
2007
).
7.
J. F.
Bard
and
N.
Nananukul
,
Journal of Scheduling
,
12
(
3
),
257
280
(
2009
).
8.
V. A.
Armentano
,
A. L.
Shiguemoto
and
A.
Lokketagen
,
Computers & Operations Research
,
195
,
703
715
(
2009
).
9.
M.
Boudia
and
C.
Prins
,
Computers & Operations Research
,
38
(
8
),
1199
1209
(
2011
).
10.
Y.
Adulyasak
,
J. -F.
Cordeau
and
R.
Jans
,
INFORMS Journal on Computing
,
26
(
1
),
103
120
(
2014
).
11.
N.
Nananukul
, “
Lot-sizing and inventory routing for a production-distribution supply chain
”, PhD dissertation,
The University of Texas
,
Austin
,
2008
.
12.
C-G.
Lee
,
Y.A.
Bozer
and
C.C.
White
 III
, “
A heuristic approach and properties of optimal solutions to the dynamic inventory routing problem
”,
Working paper
,
2003
.
13.
N.
Mladenovic
and
P.
Hansen
,
Computers & Operations Research
,
24
,
1097
1100
(
1997
).
14.
B.E.
Gillett
and
L.R.
Miller
,
Operations Research
,
22
,
1974
,
340
344
(
1974
).
15.
A.
Imran
,
S.
Salhi
and
N.A.
Wassan
,
European Journal of Operational Research
,
197
(
2
),
509
518
(
2009
).
16.
N.H.
Moin
and
Y.
Titi
,
Mathematical Problems in Engineering
,
2015
,
1
11
(
2015
).
This content is only available via PDF.