Integrated Supply Chain Network Model for Allocating LPG in a Closed Distribution System
Amelia Santoso^{*}, Dina Natalia Prayogo, Joniarto Parung
Industrial Engineering Department, University of Surabaya, Surabaya, Indonesia
Email address:
To cite this article:
Amelia Santoso, Dina Natalia Prayogo, Joniarto Parung. Integrated Supply Chain Network Model for Allocating LPG in a Closed Distribution System. Automation, Control and Intelligent Systems. Vol. 3, No. 5, 2015, pp. 95-99. doi: 10.11648/j.acis.20150305.16
Abstract: This paper proposes a model of integrated supply chain network for allocating subsidized Liquefied Petroleum Gas (LPG) in a closed distribution system. Subsidized LPG is selected as a case study due to its specific product in Indonesia. Since 2007, the Indonesian government makes policy, namely energy conversion from kerosene to LPG. The main purpose of converting kerosene to LPG is to reduce subsidies on fuel oil. The distribution system consists of several filling stations, distributors and retailers. Currently, the distribution of subsidized LPG, does not flow smoothly because there will be a shortage or excess tubes in retailers mainly because it uses a closed distribution system. A closed distribution means that people who are eligible to buy subsidized LPG will be given a card for identifying them as a legal receiver of the LPG. The model is developed using mathematical approach with reference to previous transshipment study. Based on the developed model and by using a numerical example as a case study, the allocation of LPG from filling station to the distributors and from the distributor to the retailers with minimum distribution costs can be determined. LPG in some specific retailers is supplied by only one distributor which is authorized to distribute subsidized LPG on the retailers. However, this model has limitations to arrange the route filling and distribution route.
Keywords: Supply Chain Network, Subsidized LPG, Closed Distribution System
1. Introduction
Since 2007, the Indonesian government makes policy, namely energy conversion from kerosene to LPG. The main purpose of converting kerosene to LPG is to reduce subsidies on fuel oil. During this time, kerosene, which has a high production cost is consumed by the majority of low-income communities which are concentrated in rural areas. Therefore government provides subsidies to ease the burden of their energy costs.
LPG starter pack in the form of a gas stove, a tube with its accessories has been distributed in total of more than 56 million packs in 29 provinces in Indonesia. The problem faced now is when and where we doing the refill.
Smoothing material flow is one of the goals in the concept of supply chain, which consists of several echelons [1]. Likewise in the distribution system, if the flow of LPG distribution does not go smoothly, there will be a shortage or excess in retailers mainly because it uses a closed distribution system. A closed distribution means that people who are eligible to buy subsidized LPG will be given a card for identifying them as a legal receiver of the LPG [2].
The lack of proper LPG’s distribution can be caused by faulty allocation of LPG’s distribution under the authority and responsibility of filling depots or distributors. Hence, in order to overcome the problems, it is necessary to redesign distribution network system. This distribution network design serves as an input to the government in making policy on LPG distribution system based on the real conditions of the field. In other words, we need the concept of distribution network design to manage the allocation of multi LPG filling depot to distributor and from distributor to retailers.
Figure 1 below shows the current down-stream LPG supply chain (distribution). Government applies closed distribution system for distributing subsidized LPG tubes or canisters in order to ensure the subsidized LPG would reach the proper targets.
2. Related Work
There are many distribution network designs in the literatures which concern with interaction among member of supply chain. Most of the interaction treats each member of the supply chain as a separate system. As a result, many of the problems solved with minimum integrated [3]. Here, we present previous study which is associated with the main objective of the research.
The main objective of this closed distribution network design is to minimize the total distribution cost. The total distribution cost per year consists of total distribution cost from filling stations to distributors and from distributors to retailers. Generally, network design covers supply allocation, and selecting location of supply chain members in the public and private economic sectors. Distribution network design relates to real situations where an organization needs to get the most effective and efficient distribution facilities [4]. According to Meng, Huang, and Cheu, the integration of location decisions with other relevant decisions is a basic feature that distribution design has to capture in order to support decision-making involvement in strategic supply chain planning [5].
According to Melo et al, [6] a company’s distribution network must meet service goals at the lowest possible cost. In some instances, a company may be able to save millions of dollars in logistics costs and simultaneously improve service levels by redesigning its distribution network. To achieve this, an ideal network must have the optimum number, size, and location of facilities.
As already presented in the introduction, that because of the LPG distribution system does not run smoothly; it is necessary to redesign the distribution network of LPG. Distribution Networks is needed to be redesigned for the purpose of allocations from filling station to the distributor and from the distributor to the retailer. One of the main models that can be used is the transshipment models. Transshipment problem which was first introduced by Orden [7] refers to a development of the transportation problem by considering the possibility of transshipment. The point is that any shipping or receiving point is permitted as an intermediate point. At the transshipment problem, an origin or destination can transport subsidized LPG to another origin or destination [8].
Development models will take into consideration the concept of transshipment [9] the model uses the concept of fixed and variable costs that proposed by Chopra and Meindl. The design of this network distribution aims to produce low distribution costs as proposed by Watson et al. [10]. The model developed is composed of 1). LPG allocations from filling station to the distributor and from the distributor to the retailer. 2) the size of the vehicle and the number of orders by distributors to the filling station.
The next part will present the development model based on this transshipment problem.
3. Research Methodology
This research using analytical based methodology to answer the questions: how to allocate, and what are the number of allocation of filled tubes from multi filling station to certain multi distributor and from each distributor to certain retailers in order to minimize total distribution cost per year.
Method of building model is as follows: Firstly, previous related work namely transshipment is analyzed and then developed with mathematical approach to create a new mathematical model. Secondly, the new distribution network design is tested using numerical example with real data as single case study problem. Based on this approach, the research can make a conclusion about model and giving several suggestions for future research.
4. Development Model
The integrated supply chain network model is developed for distributing subsidized 3-kg LPG tubes from filling stations to distributors and from distributors to retailers. This model determines number of allocation from multi filling station to certain multi distributor and from each distributor to certain retailers.
In this model, a filling station supplies multi distributor and a distributor can be supplied by more than one filling station. A distributor supplies multi retailer but only a certain distributor can supply a retailer.
Each distributor has a number of trucks with a number of empty tubes in the truck that will be filled by a filling station according to quota. After all empty tubes in a truck are filled, the truck directly distributes the LPG tubes to multi certain retailers of the distributor.
4.1. Mathematical Notations
The mathematical notations are used in developing model as follows:
Indices
s: Filling station s=1..S
a: Distributor a=1..A
p: Retailer p=1..P
Decision Variables
: Number of LPG tubes that are supplied by filling station s to distributor a
: Number of LPG tubes that are supplied by distributor a to retailer p
: 1 if filling station s supplies distributor a, and 0 otherwise
: 1 if distributor a supplies retailer p, and 0 otherwise
: Number of day-trucks of subsidized LPG that are supplied from filling station s to distributor a
Variables/Parameters
: Capacity of filling station s
: Number of trucks owned by distributor a
: Monthly LPG demand of retailer p
: Fixed cost of distributing LPG from filling station s to distributor a
: Variable cost of distributing LPG per tubes from filling station s to distributor a
: fixed cost of distributing LPG from distributor a to retailer p
: Variable cost of distributing LPG per tubes from distributor a to retailer p
LO: the order size contract of subsidized LPG per day between certain distributor and specific filling station
JMLH: number of days per month
MINJHT: minimum number of day-trucks that are used from filling station to distributor
4.2. Mathematic Formulation
The objective function is to minimize total cost of LPG supply chain. The total cost consists of fixed cost and variable cost at fulfilling station, distributor and retailer.
(1)
This model was developed by considering some constraints to ensure the model according to the condition of the distribution of subsidized LPG.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
Constraint (2) ensures each filling station never distributes subsidized LPG tubes to their distributor more than its capacity. Constraint (3) ensures there is never a supply from the filling station to the distributor exceeds the capacity of all truck owned by the distributor. The next constraint (4) guarantees number of LPG tubes are filled and supplied from a filling station to a distributor must be a multiple of the vehicle capacity in accordance with their contracts (LO). Constraint (5) deals with the contract between a filling station and a distributor has to be equal to or greater than minimum day-trucks are used. Number of day-trucks is guaranteed not to be greater than total trucks per month that owned by each distributor (constraint 6). Constraint (7) guarantees the supply balance so that the distributor has no inventory. Constraint (8) ensures a retailer can only be supplied by a distributor that has been decided as suppliers while constraint (9) guarantees each retailer is only supplied by one certain distributor. Constraint (10) and (11) ensure the amount of allocation from a distributor to a retailer is equal to demand of the retailer and total of all allocation from a distributor to all retailer do not greater than its all vehicle capacity. Constraint (12) and (13) guarantee two decision variables are binary while constraint (14), (15) and (16) guarantee the last three decision variables have to be integer and always greater than zero.
5. Numerical Example
Supply chain structure of 3-kg subsidized LPG consists of two filling station, four distributors and 77 retailers. The capacity of filling stations and distributors can be seen in the following Table.
filling station | capacity | distributor | number of trucks | capacity of truck |
F1 | 84,000 | D1 | 2 | 28,000 |
F2 | 67,200 | D2 | 3 | 42,000 |
D3 | 2 | 28,000 | ||
D4 | 3 | 42,000 |
retailer | demand | retailer | demand | retailer | demand |
P1 | 2995 | P26 | 2643 | P51 | 2163 |
P2 | 2085 | P27 | 3199 | P52 | 827 |
P3 | 2228 | P28 | 2776 | P53 | 1514 |
P4 | 2497 | P29 | 2758 | P54 | 1020 |
P5 | 885 | P30 | 761 | P55 | 1610 |
P6 | 1931 | P31 | 3093 | P56 | 1441 |
P7 | 2683 | P32 | 3093 | P57 | 2378 |
P8 | 100 | P33 | 2115 | P58 | 763 |
P9 | 891 | P34 | 3343 | P59 | 1372 |
P10 | 943 | P35 | 979 | P60 | 2364 |
P11 | 113 | P36 | 3040 | P61 | 2450 |
P12 | 2189 | P37 | 179 | P62 | 2032 |
P13 | 1690 | P38 | 1680 | P63 | 1793 |
P14 | 2097 | P39 | 850 | P64 | 2623 |
P15 | 1442 | P40 | 246 | P65 | 2772 |
P16 | 2123 | P41 | 425 | P66 | 648 |
P17 | 1861 | P42 | 1988 | P67 | 2388 |
P18 | 2655 | P43 | 1777 | P68 | 1778 |
P19 | 1396 | P44 | 2887 | P69 | 3245 |
P20 | 2485 | P45 | 334 | P70 | 2254 |
P21 | 3061 | P46 | 702 | P71 | 2643 |
P22 | 1254 | P47 | 2875 | P72 | 1036 |
P23 | 1640 | P48 | 2841 | P73 | 189 |
P24 | 1346 | P49 | 3113 | P74 | 917 |
P25 | 2523 | P50 | 100 | P75 | 1223 |
P76 | 1734 | ||||
P77 | 1517 |
D1 | D2 | D3 | D4 | |
F1 | 144,000,000 | 142,000,000 | 129,000,000 | 143,000,000 |
F2 | 145,000,000 | 141,000,000 | 143,000,000 | 127,000,000 |
D1 | D2 | D3 | D4 | |
F1 | 78,000 | 77,000 | 57,000 | 52,000 |
F2 | 51,000 | 58,000 | 59,000 | 69,000 |
With fixed and variable cost from distributor to retailer, the following result is obtained.
D1 | D2 | D3 | D4 | |
F1 | 0 | 11200 | 28000 | 42000 |
F2 | 28000 | 30800 | 0 | 0 |
TOTAL | 28000 | 42000 | 28000 | 42000 |
JHT | Distributor | |||
1 | 2 | 3 | 4 | |
F1 | 0 | 20 | 50 | 75 |
F2 | 50 | 55 | 0 | 0 |
TOTAL | 50 | 75 | 50 | 75 |
Filling station | QSA | Distributor | QAP | retailer |
F1 | 42000 | Dist 4 | 2189 | P12 |
1442 | P15 | |||
2123 | P16 | |||
1861 | P17 | |||
3093 | P31 | |||
3093 | P32 | |||
3040 | P36 | |||
179 | P37 | |||
1777 | P43 | |||
334 | P45 | |||
2841 | P48 | |||
100 | P50 | |||
1514 | P53 | |||
1020 | P54 | |||
1441 | P56 | |||
2032 | P62 | |||
1793 | P63 | |||
2772 | P65 | |||
3245 | P69 | |||
2254 | P70 | |||
917 | P74 | |||
1223 | P75 | |||
1517 | P77 | |||
TOTAL | 41800 | 23 | ||
F 1 | 28000 | Dist 3 | 2085 | P2 |
100 | P8 | |||
891 | P9 | |||
113 | P11 | |||
2097 | P14 | |||
1396 | P19 | |||
2776 | P28 | |||
761 | P30 | |||
3343 | P34 | |||
425 | P41 | |||
2887 | P44 | |||
3113 | P49 | |||
1372 | P59 | |||
2364 | P60 | |||
648 | P66 | |||
1778 | P68 | |||
1734 | P76 | |||
TOTAL | 27883 | 17 | ||
F 1 | 11200 | dist 2 | 2497 | P4 |
2683 | P7 | |||
943 | P10 | |||
1690 | P13 | |||
3061 | P21 | |||
F 2 | 30800 | Dist 2 | 1254 | P22 |
2643 | P26 | |||
3199 | P27 | |||
2115 | P33 | |||
979 | P35 | |||
850 | P39 | |||
246 | P40 | |||
702 | P46 | |||
2875 | P47 | |||
2163 | P51 | |||
827 | P52 | |||
2378 | P57 | |||
763 | P58 | |||
2450 | P61 | |||
2623 | P64 | |||
2388 | P67 | |||
2643 | P71 | |||
42000 | TOTAL | 41972 | 22 | |
F 2 | 28000 | Dist 1 | 2995 | P1 |
2228 | P3 | |||
885 | P5 | |||
1931 | P6 | |||
2655 | P18 | |||
2485 | P20 | |||
1640 | P23 | |||
1346 | P24 | |||
2523 | P25 | |||
2758 | P29 | |||
1680 | P38 | |||
1988 | P42 | |||
1610 | P55 | |||
1036 | P72 | |||
189 | P73 | |||
TOTAL | 27949 | 15 |
6. Conclusion
Based on the developed model, and by using a numerical example as a case study, the allocation of LPG from filling station to the distributor and from the distributor to the retailer with minimum distribution costs can be determined. Every retailer can be supplied by only one distributor which is authorized to distribute subsidized LPG on the retailer. It means retailers cannot be supplied by other distributors. Distributors can only fill an empty tube on the filling station that is authorized to supply distributor.
The developed model has been able to establish the allocation of filling stations that will supply a particular distributor. The model has also been able to establish which distributor that will supply a particular retailer. Based on the developed model, and by using a numerical example as a case study, the allocation of LPG from filling station to the distributor and from the distributor to the retailer with minimum distribution costs can be determined. LPG in some specific retailers is supplied by only one distributor which is authorized to distribute subsidized LPG on the retailers.
The model has been able to establish the allocation of filling stations that will supply a particular distributor. The model has also been able to establish which distributor that will supply particular retailers. However, this model has limitations to arrange the route filling and distribution route. This initial model will be developed in further research to establish the fleet distributors’ route.
Acknowledgements
We would like to thank the Ministry of Research, Technology and Higher Education, which provides financial grants so that our research can be done.
References