OPTIMIZATION MODEL OF SUPPLY CHAIN ON A PALM OIL PLANTATION Mario Ernesto Martínez Avella[1] Rafael Guillermo Garcia Cáceres Edgar Gutierrez Franco Maria Margarita Cervantes
Universidad de La Sabana, Bogotá, Colombia
[1] Address: Autopista Norte Kilómetro 21 puente del común – Chía, Cundinamarca. E-mails:
[email protected],
[email protected],
[email protected],
[email protected]
Index • Proposal of research: objectives • Context: optimization of supply chains. • Problematic situation in a plantation of oil palm. • Elements of the theoretical frame on IO. • A hypothetical model. • Conclusions.
OPTIMIZATION OF THE AGROINDUSTRIAL SUPPLY CHAIN IN COLOMBIA
Proposal: support the process of tactical planning of the agro-industrial companies by application of mathematical models, and to promote the knowledge of the advantages and possibilities for the application of IO tools.
Objectives • To analyze the present situation of Colombian Agroindustria, by the study of generic models. • To implement models of mathematical programming for tactical planning. • To spread with base in cases of reference and specific results, the benefits of use methodologies and technologies associated to • the research.
Actual Supply Chain Plantations – Plots -
Internal gathering center
External Gathering Center. Trucks Elevators
Trucks
Download in plant
THEORETICAL FRAME
BENEFITS OF THE MATHEMATICAL MODELS • • • •
•
1. Reduction in costs or increase in the earnings. 2. More rational and systematic processes of planning. 3. Improvements in the communication process 4. Clarification of the goals of the organization, the options of decision, and the restrictions of the surroundings. 5. Better approach of the harvesting process and data processing.
Jeremy F. Shapiro
BENEFITS OF THE MATHEMATICAL MODELS
The models reveals relations that are not evident at first sight. Once constructed the mathematical model is possible to extract properties and characteristics of the relations between the elements that could remain hidden
Interests of all the People The optimal solution maximizes the value if three types of variables are consider: • The probabilities of election action courses. • The efficiencies of each one of those courses. • The values of each one of those results.
Hypothetic Model • It is a lineal mathematical scheduling model to study the supply chain of a palm oil industry at the gather-production stage. It has been designed to be an alternative hypothesis to the actual condition of supply chain and learn about the process. • Its objective is to get knowledge over the model, and its outputs will be used as a reference to study the actual conditions of the chain.
Problem Statement • The difficult conditions of worker´s cooperatives are of particular importance to the logistic relationships in this kind of enterprise. • It is important to determine the number of trucks and gathering groups for planning the supply chain. At the end, this model is a new asset to tactical planning.
Hypothetical Chain i
Wijt
Groups
Xjkt j
k
trucks Internal Gathering External gathering Centers centers
Plots
Factory
What it looking for The model attempts: – To provide support to decisions about the number of groups to harvest in every plantation’s plot. – The number of trucks owned by the company and those belonging to individual contractors (outsourcing) to transport from the internal gathering centers to external gathering centers.
What it looking for • The model permits – To define periodic planning horizons, that minimize the operative costs. – To determinate the material transported from gathering centers to the production center.
• The model allows – An estimation of production – The inventory in the gathering center and – The inventory of raw materials and finished products.
Constraints • Production, collecting, pick up, transporting and storing capacities. • Mass balance and minimal historic demand constrains, beginning from scheduling and whole fruit gathering in the planning period.
We Obtain Based on this model and its implementation with real and hypothetic data, we can obtain: • A better understanding of supply chain behavior in a broad base for the study of the real chain of the company. • Better decision in tactical planning and help the design of new models.
MODEL FORMULATION Primary indices and index sets • • • • • • • • • •
t = Day i = Plantation’s plot j = Internal gathering center k = External gathering center (cross docking) and the gathering center SCAIP(i)= Internal gathering center set j, supplied by plantation’s plot i. SCAICAE(k)= Internal gathering center set j, providers to external gathering center k. SPCAE(k)= Plantation’s plot set i, providers to external gathering center k. CLPCAI(i,j)= Logistic connection between the plantation’s plot i and the internal gathering center j. CLCAICAE(j,k)= Logistic connection between the internal gathering center j and the external gathering center k. CLPCAICAE(i,j,k)= Logistic connection between the plantation’s plot i and the external gathering center k.
Parameters: • • • • • • • • •
d = Estimated minimal request to the planning horizon oi t = Harvest rate offer at the plantation’s plot i the day t. rend = Relationship between raw material ton / product ton s = Storing capacity at the finished store room u = Storing capacity at the raw material store room on the production center c = Production capacity fj = Storing capacity at the raw material store room on the internal gathering center j. ek = Storing capacity at the raw material store room on the external gathering center k. h = Carried capacity of the harvest group
Parameters: • • • • • • •
b = Trucks owned by the company ton capacity. b´ = Trucks belonging to individual contractors ton capacity. nij = Number of daily trips carried out by a group between a plantation’s plot i to the internal gathering center j. njk = Number of daily trips carried out by a truck owned by the company between an internal gathering center j to the external gather center k. nk = Number of daily trips carried out by a truck owned by the company between the external gathering center k to the production center. njk’ = Number of daily trips carried out by a truck belonging to individual contractors between a internal gathering center j to the external gather center k. nk’ = Number of daily trips carried out by a truck belonging to individual contractors between the external gathering center k to the production center.
Parameters: • • • • • • • • • • •
a = Number of available harvesting groups r = Number of trucks owned by the company r´ = Number of trucks belonging to individual contractors cr = Gathering ton cost cci = Internal carried ton cost cce = External carried ton cost cp = Produced ton cost cgi = Internal derrick cost cge = External derrick cost cim = Raw material inventory cost cip = Finished products cost
Variables: • • • • • • •
Wijt = Raw material transported between the plantation’s plot i to the internal gathering center j at the day t. Xjkt = Raw material ton transported between the internal gathering center j to the external gathering center k at the day t. Z t = Produced ton at the day t. Aij t = Number of groups used at day t to gather plantation’s plot i that unload the raw material at the internal gathering center j. Ij t = Raw material inventory in the internal gathering center j at day t. Ik t= Raw material inventory in the external gathering center k at day t. JM t= Raw material inventory available in the production center at day t.
Variables: • • • • • •
JP t= Finished product available on the production center at day t. Ykt = Raw material transported between the external gathering center k to the production center at day t. Ljkt = Number of trucks owned by the company used at day t between the internal gathering center to the external gathering center k. Ljk´t = Number of trucks belonging to individual contractors used at day t between the internal gathering center to the external gathering center k. Mkt = Number of trucks owned by the company used at day t between the external gathering center k to the production center. Mk´t = Number of trucks belonging to individual contractors used at day t between the external gathering center k to the production center.
Objective Function MIN: ∑(cp)Z t + ∑∑(cge+ cce)Ykt + ∑∑ ∀t
∀t ∀k
∑(cr)W + ∑∑ ∑(cci+ cgi) X
∀t ∀i j∈SCAIP(i )
t ij
∀t ∀k j∈SCAICAE( k )
t t t t ( cim ) I + ( cim ) I + ( cim ) JM + ( cip ) JP ∑∑ ∑∑ ∑ ∑ j k ∀t ∀i
∀t ∀i
∀t
∀t
• Minimizes the addition of produced tons cost at the period, plus the addition of derrick cost (internal and external), plus the addition of the gathering ton cost, plus the addition of carried ton costs (internal and external), plus the addition of raw material inventory cost, plus the addition of the final product inventory cost.
t jk
+
Constrains The offer of the plantation i at time t:
∑W
t ij j∈SCAIP(i,k)
= o ∀i , ∀t t i
• The addition of raw material tons transported from each plantation’s plot to internal gathering centers is equal to the harvest rate offer at every period.
Capacity Constrain: Carried Capacity between the plantation’s plots i to the internal gathering center j: t t W ≤ ( h )( n ) A ∑ ij ij ij ∀ i , ∀ t
j∈SPCAI(i, k)
• The addition of raw material tons transported from the plantation’s plots to the internal gathering center have to be less or equal to the number of the carried harvest group, times the carried capacity of each harvest group, times number of daily trips done by the group
Production Center Capacity:
Z ≤ c __∀t t
• Produced tons have to be less or equal than the production center capacity.
Finished product storeroom inventory capacity:
JP ≤ s ∀ t t
• The finished product storeroom inventory available at the production center has to be less or equal than finished product storeroom storing capacity.
Raw material storeroom inventory capacity:
JM ≤ u ∀ t t
• Raw material storeroom inventory available at the production center has to be less or equal to the raw material product storeroom capacity.
Raw material inventory capacity at the internal gathering center j:
I j ≤ f j __∀ j,∀t t
• Raw material inventory at the internal gathering center has to be less or equal to the raw material product store capacity at the internal gathering center.
Raw material inventory capacity at the external gathering center k
I k ≤ ek __ ∀k , ∀t t
• Raw material inventory at the external gathering center has to be less or equal to the raw material product store capacity at the external gathering center.
Maximum carried capacity transported between carried areas to an external gathering center at period t:
∑X
t jk j∈SCAICAE(k)
≤
∑ (b )(n
∑ (b)(n
j∈SCAICAE(k) '
'
j∈SCAICAE(k)
•
jk
jk
)L + t jk
) L __∀k , ∀t 't jk
The addition of the raw material tons transported between internal gathering center to the external gathering center have to be less or equal to the addition of number of trucks owned by the company, times its ton capacity, times the number of daily trips used by gathering centers. Furthermore, the addition of the number of trucks belonging to individual contractors, times its ton capacity, times number of daily trips used by gathering centers.
Maximum loaded capacity transported between external gathering centers to the production center at the period t:
Y ≤ (b)(nk )M + (b )(nk )Mk't __∀k,t t k
•
t k
'
'
The addition of raw material transported between external gathering center has to be less or equal than the number of trucks owned by the company used, times truck capacity, times the number of trips, plus the number of trucks belonging to individual contractors, times truck capacity, times number of trips completed.
Mass balance constrains: Finished product mass balance constrains on the finished room store: t −1
JP + Z = JP __∀t t
t
• Finished product inventory available at the room store at the preceding period, plus produced tons at the period have to be equals to the finished product inventory available on the process center at the end of the period t.
Raw material mass balance on the raw material room store: t −1 t t ( ) Y + JM − rend Z = JM __ ∀t ∑k t
k
•
This is the sum of raw material transported from the external gathering center, plus the raw material inventory at the gathering center storeroom at the preceding period, minus the tons produced at the period. This is multiplied by the proportion of raw material tons to the product tons have to be equal to the raw material inventory available at the external gathering center storeroom at the period.
Mass balance on the external gathering center k: t−1 k
I +
•
−Y =I __∀k,∀t
t t jk k j∈SCAICAE(k)
∑X
t k
Raw material inventory at the external gathering center at the preceding period, plus the raw material tons transported from the internal gathering center at the period subtracted the raw material tons transported to the production center at the period should be equal to he raw material inventory on the room store of the external gathering center at the end of the period.
Mass balance on the internal gathering center j: t−1
I j + ∑Wijt −∑ Xtjk = I j __∀j ,∀t t
∀i
•
∀k
This is the raw material inventory at the internal gathering center at the preceding period, plus the addition of raw material tons transported from the plantation’s plot to the internal gathering center subtracted the addition of the raw material transported from the internal gathering center to the external gathering center at the period should be equal to the inventory of raw material on the room store on the internal gathering center at the end of the period.
Gathering and distribution constrains: Maximum number of gathering groups available:
∑ ∑A
t ij ∀i j∈SPCAI ( i )
≤ a __ ∀ t
• The sum of the groups number used at the period to gathering the plantation’s plot that unload the raw material on the internal gathering center have to be less or equal than the number of available groups.
Maximum number of trucks owned by the company available :
t t ( L + M ∑ k k ) ≤ r __∀t ∀k
•
The sum of trucks owned by the company used at the period between the associated internal gathering center to the associated external gathering center. Added to this is the number of trucks owned by the company used at the period of transporting from the external gathering center to the production center have to be less or equal than the number of trucks owned by the company.
Maximum number of trucks belonging to individual contractors available:
∑ (L' ∀k
•
t k
+ M ' ) ≤ r __ ∀ t t k
'
This is the sum of trucks belonging to the individual contractors used at the period between the associated internal gathering centers, and the associated external gathering centers. Added to this is the number of trucks belonging to individual contractors used at the period to transporting from the external gathering center to the production center, have to be less or equal to the number of trucks belonging to individual contractors.
Demand constrain:
∑
Z
t
≥ d
t • The addition of produced tons at each period has to be greater or equal than the estimated minimal request to the planning horizon*n.
Decision variables limits: Zt ≥ 0
∀t
Ykt ≥ 0
∀t
Wijt ≥ 0
∀CLPCAI(i, j), ∀ t
X tjk ≥ 0
∀CLCAICAE(j, k), ∀ t
I tj ≥ 0
∀t
I kt ≥ 0
∀t
JM t ≥ 0
∀t
JP ≥ 0 t
∀t
Decision variables limits: A ijt ≥ 0 Ltk ≥ 0 L'kt ≥ 0 M kt ≥ 0
M 'kt ≥ 0
And entire value
CONCLUTIONS • Based on this model, the research group have a first level of understanding of the supply chain. It had opened possibilities to develop new models and proposals to appropriate design the Chain. Suited to the enterprise, according to optimization, cost polices and the harvest job by cooperatives. • This model has been a learning device at the initial stage of the research. • From an academic perspective, we hope that it help as a study tool on the enterprise or other supply chain with similar conditions.
CONCLUTIONS • The modeled process has allowed in one first stage to development learning capacity in the research group. • For the future models the enterprise will be consider - in addition to the outputs of optimization of this model- the intentions of the mangers awaited of the model and the interests of cooperative´s people.
