Go Bac
Dynamic Logistics Model for Optimal Delivery
Sutanto Soehodho
Department of Civil Engineering
University of Indonesia
Depok 16424, Indonesia.
Abstract
This paper deals with the development of dynamic based logistics model aims at
optimal delivery. A total logistics model covering five sub-models, namely raw
material stock, production process, production stock, production order, and
delivery, are proposed. Such models would, in general, require a firm control of the
availability of each production components in any of in-flow stage (e.g., raw
materials), processing stage (e.g., production), and outflow stage (e.g., production
stock, order process, and delivery), to achieve customer satisfaction. It is, however,
realized that equilibrium among the three stages is the key success of good logistic
systems, but in reality discrepancies among them are hard to avoid. In this research
a near-equilibrium situation may be achieved through a dynamic simulation
process of the sub-models characterizing their performance as well as their
interrelations. This sort of simulation can be considered further as an optimal
control for delivery through which a sensitivity trends may provide strategies to
producer of how to manage resource with best service. In this very early approach
formulation of an objective function that maximizes revenue of sales is determined
to cover the market demand. Furthermore, in the form of dynamic simulation
model various strategies may be exposed to decide the best policy of delivery.
1. Introduction
Many logistic processes are concemed with the balance among the sub-systems of
how to get sufficient raw materials put in the stock, how to guarantee production
process composed by the availability of raw materials and readiness of production
tools, of how to keep production in secure place and ready to be delivered, of how
to manage customer orders and provide them with tolerable service level of
delivery [Ballou, 1999]. Failure to maintain such equilibrium would create late
delivery at front-end of logistic system and customer dissatisfaction (i.e., late
delivery). There have been eminent ideas of how to solve such logistic problem in
many research works, but none has discussed the interrelations among the sub-
systems in dynamic manners. The system dynamic approach to control logistic
systems is very important in order to represent its interrelation, and how a feedback
from one sub-system to the other(s) could be elaborated to search optimal
performance.
In this research the dynamic based logistics model aims at optimal delivery is
developed. A total logistics model covering five sub-models, namely raw material
stock, production process, production stock, production order, and delivery, are
proposed. Such models would be determined as control system for the availability
of each production components in any of in-flow stage (e.g., raw materials),
processing stage (e.g., production), and outflow stage (e.g., production stock, order
process, and delivery), to achieve customer satisfaction. This proposed model is
then transformed in the dynamic simulation to represent the characteristics and
interrelation of the sub-models through sensitivity or discrepancies of the sub-
models can be learnt and elaborated. This elaboration may further provide
producer to introduce his/her strategy in satisfying customer with good delivery.
Indeed there might be plenty of possibilities in the determining the objective of
delivery strategy, however, in this very early formulation the objective function is
defined as to maximize the revenue of sales to cover the market demand.
In the ensuing sections, paper would discuss the rationale of model in section 2,
development of dynamic logistics model in section 3, and some simulation expose
through which a trend of certain scenario of delivery may result in is discussed
section 4. Finally section 5 would conclude the discussion.
2. Rationale of the Model
The proposed model has embedded from the emerging paradigm of designing the
transportation systems in a dynamic manner [Ran and Boyce, 1999]. In the
structure Ran and Boyce discussed that the equilibrium within the transportation
network that represents somehow the choice behavior of road users may require
dynamic control systems. Furthermore, as complete system transportation may
evolve from the socio-economic activities as suggested by Manheim [1979], by
which the flow of vehicles in the road network can be indicated as indicator of
performance of the system. As part of transportation systems, logistics eminently
represent the intact sub-systems of models explained in section 1, and in more
explicit term it does represent the fabrication of raw materials, production machine
and human characteristics in performing the socio-economic activity discussed by
Manheim.
In this section implication of such rationale would be explained in two stages that
is by the macro level of dynamic interaction and socio-economic activities, and the
relevant derivation of such rationale at micro level of logistic system.
2.1, System Dynamics in Socio-Economic Activities and Transport Systems
As illustrated in Figure 1, the dynamic interrelation between socio-economic
activities and transportation system in the context of physical distribution or
logistics can be determined as continuous model in which the interaction would
result in flow of freight in tonnages of commodities or vehicles.
Socio-Economic Activities
Distribution Systems
Figure 1: Dynamic Interrelation of Socio-Economic Activities
and Distribution Systems
Freight flow in some extent may denote performance or service level of the
distribution systems. If the performance is good then activities may likely increase
their quantity and quality which may further require more capacity of distribution
systems, and so on. If, however, the distribution systems do not perform as what
expected by the increase of socio-econmic activities it may create reduction impact
to the activities. Such more and less movement would achieve certain level of
equilibrium which may be understood that none of the sub-systems mentioned
above could develop unlimitedly.
The interesting phenomenom in the interaction above is that level of service
provides feedback to the both sub-systems either to move forward or to remain,
and this evolves by time. So it is obvious that such phenomenom can only be
handled or controled with dynamic approach as expected. It is also realized that the
distribution systems comprise several sub-systems as what refered in introduction,
so to provide any delivery service would involve those sub-systems
2.2. Dynamic Simulation for Logistics Model
To be more specific with the proposed logistics model Figure 2 illustrates possible
implication for which the distribution systems explained in Figure 1 exists. Figure
2 clearly denotes the interrelation among the logistic components (e.g., orders
received, inventory, shipment, and their possible adjustments), wherein the causal
loop may further indicate the balance, and hence arrow adjusts its feedback with
opposing or supporting manners. More comprehensive discussion on the system
dynamics can be found in Forrester [1969, 1971].
ORDERS a ogg a
RECEIVED |~ SHIPMENT |
B1 \
4 o Se, /
{ -
INVENTORY DESIRED
ORDERS AD] USMENT R1 INVENTORY
ne KU
NS R2
s
AVERAGE
SHIPMENT _—
Figure 2: Causal Loop Diagram for Logistics Model
Having the causal loop as represented in Figure 2, any simulation can be made for
certain resources or strategies of expected situation. What should be emphasized
further in the analysis is that accuracy may not be performed very well rather than
indicating the trends of impacts. This is the aim of the research to propose a tool to
logistic business manager to formulate best policy or strategy satisfying producer
and consumer at all time. Next section discusses the logistics model development
and its sub-system simulation.
3. Model Development
As a mathematical programming the proposed logistics model is determined to
maximize the revenue of sales subject to its limited resources, and such
programming can be written as;
Max Z[Q] = 3: Qi (ts)
Subject to,
2iQi (ts) SQcar
DaRa (ta)= Qilte) V ain
ti<h<ts <y..u.<ty=T
With state of dynamics, for order fulfillment, as
Qi (te) = Qi (tr )+ AQi(tar) Vin sere (5)
Where;
Qi (ta) = quantity of commodity ordered at region i at instant ta
U; — =unit price of commodity at region i
Qcap =maximum production quantity
Ra (ta) = raw material a that composes the commodity Q at instant t,
ty = T =Nth discrete time or end of time period
Besides the model derived in equations (1) - (5), the other significant underlying
assumption is that the delivery has unlimited capacity of fleet. It is also worth-
noting that quantity to be fulfilled in instant (t,) should be the accumulation of
undelivered quantity prior to instant (t,), (t:.1) plus the quantity ordered in time (t,)
slice determined. The model is linear in general, however the solution form is not
closed because it deals with time dependency. Further discussion on linearity can
be found in de Neufville [1990].
The followings are the sub-models developed for each level of logistic process that
would simulate performance of model (1) to (5) based on certain availability of
resources.
3.1, Raw Material Stock Sub-Model
This sub-model is responsible with the availability of raw materials to compose the
produced commodity. Figure 3 illustrates the sub-model of raw material stock in
the form of dynamic simulation. In this sub-model the stock is determined by both
inflow (e.g., absorbed) and outflow (e.g., expired and used) materials, which are
further decided by their composition.
Expired_Raw_Material
Capacity_of_Infow Raw Naterial
‘aw_Mateyél_Stock
Absorbed_Raw_Material
/_of_ Raw_Material
Composition_of_Raw_Material
NA
Total_Raw_Material
Figure 3: Raw Material Stock Sub-Model
3.2. Production Process Sub-Model
This sub-model is responsible in the production process in wherein various raw
materials are composed to produce the intended quantity and quality of
commodity. In this particular research a single commodity is assumed with a fixed
production capacity. Furthermore, Figure 4 illustrates the dynamic simulation
model for the production process. The net production in the process is somehow
determined by its gross production, net factor, raw material availability,
fabrication capacity of production machines/tools.
and
Fabrication_Capacity
Total_Raw_Material
Net_Production_Factor
Lt
Raw_Material_Stock
Nett_Production_Capacity
Figure 4: Production Process Sub-Model
3.3, Production Stock Sub-Model
As a buffer for distribution a logistic system may require a stock for production as
results of manufacturing, assembling or else. This may not necessarily be available
rather dependent upon the nature of produced commodity. However for the
completeness of logistics model, a production stock model is provided
illustrated in Figure 5.
and
t™~
jet_Production_Capacity
a Production_Stock
Inflow_Production
Outflow_Production
Expjréd_Production
A
Expired_P roduction_Factor Orders_Delivery
Figure 5: Production Stock Sub-Model
It can be seen in Figure 5 that production stock is determined by both inflow and
outflow production, which is further described by the orders delivered and expired
production. As for the inflow production, its magnitude can be simply derived
from the net production capacity. And similar case can be made for the expired
production, which is influenced by the expired production factor.
3.4, Customer Order Sub-Model
This sub-model is responsible in managing the orders of customers. This part may
come up quite complex since quantity of orders are used to exceed the production
capacity, so delay of deliveries is inevitably. This sub-model is in charge to decide
the customers to be satisfied and their priority, and how best unsatisfied customers
be treated, would be coordinated with production process as well as distribution
capacity. Figure 6 illustrates briefly the customer order sub-model.
Order_r1 Total_Orders
NA
Orders_Receivéd_by Region
Orders_Received_by Region
=
a
NA \
Delivered_r3 Delivered_r4 Delayed_Orders
Figure 6: Customer Order Sub-Model
In this particular model number of regions is limited to four, although in the large-
scale model this number is flexibly higher. It can be expected too within the model
that delayed delivery could be handled | the following delivery for the same
region.
3.5. Distribution Sub-Model
This last sub-model is responsible in managing strategies of delivery to the
customers within certain limited resources such as fleet, production quantity and so
forth. Furthermore Figure 7 illustrates the sub-model.
Fleet_Cost_1
Number_of Fleet
Fleet Cost
Fleet Budget
Fleet Capacity
\
Fleet Capacity Fleet Cost_1
a
Oistibution_ Fleet Capacity
Production_Distribution Capacity
Budget_Op_Armada
Figure 7: Distribution Sub-Model
In this distribution model it is explained that its capacity is determined with
product and fleet availability. Furthermore, the distribution cost would in some
extent derive the sale price as composed by transport and production costs.
4. Some Simulation Results
In order to comprehend the performance of the model a case is made for some
production and distribution capacities along with the availability of raw materials.
Suppose a cement factory with the following quantity and cost components (i.e.,
some are following pseudo random variables and normal distribution);
Budget allocation for machine, human resource, and fleet are 100, 4, 120 million
Rp respectively (e.g., Rp is the Indonesian currency). Costs spent for machine,
human resource, owned fleet, rent fleet respectively are 10,000,000, 20,000,
85,000, 400,000 Rp. Number of machines, human, fleet, and operators are 20, 200,
400, and 800 respectively. Production capacity per day for each of machine, human
and fleet are 1,200, 100, and 15 tons/day respectively. While for delivery region
1,2,3,and 4 have the following distance 30, 80, 400, 2000 kms, and can be
delivered in expectedly 3, 4, 6, and 6 days respectively. Finally their potential
order for each region is recorded as 40,000, 40,000, 40,000 and 30,000 tons/day
respectively.
In this case a strategic delivery of high utilization rate of fleet is exposed, in which
it may mean that priority of delivery is given to the nearest distance of regions. So
the nearer the region the higher the priority is. To evaluate impacts of such strategy
expected orders from region to region [pesanan (1)-(4)] were simulated by time of
days as shown in Figure 8.
8 —-Pesanan(1)
g ~2-Pesanan(2)
—3—Pesanan(3)
~q—Pesanan(4)
0 10 20 30 40 50 60
Days
Figure 8: Expected Orders from Regions by Days
Such expected demands or orders might affect total production stock and delivered
order as could be reflected in Figure 9. Eventually, how far chosen strategy may
satisfy the customers can be reflected by the expected recovery or fulfillment of
delayed orders in the ensuing days. To conclude such strategy performance Figure
10 represents the delayed order recovery [pemenuhan tunda - (1)-(4)] by region by
days.
6,00 \
4,000 —z-Pesanan_Total
5608 —7-Stok_Produk
vr
0. +
10 20 30 40 50 60
T
0
Days
Figure 9: The Expected Total Production Stock & Delivered Orders by Days
, 500
g 8 400
5 8 500, —-Pemenuhan_Tunda(1)
Bee —y~Pemenuhan_Tunda(2)
3 ‘fo —3~Pemenuhan_Tunda(3)
—a—Pemenuhan_Tunda(4)
Otes4—t2s4—tose 't234— 2534 —_ 43344
0” 10 2 «30 640 «50S 60
Days
Figure 10: Delayed Orders Recovery by Region by Days
5. Conclusions
A comprehensive logistics model based on dynamic simulation is proposed in this
research. The model is formulated in mathematical programming with objective
function of maximizing the sales revenue subject to various operational constraints.
And five sub-models (e.g., raw material stock, production process, production
stock, customer order, and distribution) are developed to solve the formulated
logistics model. To comprehend the performance of model, a case is made and
various outcomes of simulation are discussed. Eventually, it is expected that the
model could be enhanced for larger scale and higher complexities to deal with
some operational parameters of good logistic systems.
References
1. Ballou H. Ronald, Business Logistics Management, Prentice-Hall Inc., 1999.
2. Bin Ran and David Boyce, Modeling Dynamic Transportation Networks,
Springer Verlag, 1996.
3. Forrester, J, Urban Dynamics, MIT Press, 1969.
4. Forrester, J, Industrial Dynamics, MIT Press, 1971.
5. Manheim, M.L., Fundamentals of Transportation System Analysis, MIT Press,
1979.
6. Neufville, R., Applied Systems Analysis: Engineering Planning and
Technology Management, Mc Graw-Hill, 1990.
CC BY-NC-SA 4.0