Wilson Adarme Jaimes¹, Martín Darío Arango Serna², Delio Alexander Balcázar³

¹ Industrial Engineer, Universidad Industrial de Santander. Specialist production management , Universidad Pedagógica y Tecnológica de Colombia-UPTC. Master of Engineering , Universidad de Valle. Ph.D. candidate , Universidad Nacional de Colombia. Assistant Professor , Universidad Nacional de Colombia, Colombia. wadarmej@unal.edu.co

² Industrial Engineer, Specialist in Finance, Master in Engineering, PhD in Industrial Engineering. Universidad Nacional de Colombia. Professor, Universidad Nacional de Colombia—Sede Medellín, Colombia. mdarango@unalmed.edu.co

³ Industrial Engineering, Masters Candidate in Industrial Engineering, Universidad Distrital Francisco José de Caldas. Business consultant and researcher at the line of logistics and supply chain group SEPRO, Universidad Nacional de Colombia, Colombia. alexefr@gmail.com

ABSTRACT

This paper presents the results of research carried out bythe GICO and SEPRO research groups affiliated to theUniversidad Nacional de Colombia regarding the Colombianshipbuilding industry to coordinate autonomousagents in a supply chain (SC), in a decentralised environment,where buyers (shipbuilders) have a project systemsetting production. An exact multi-criteria linear programmingmodel was developed for this purpose; it was aimedat reducing the deficit in meeting demand and minimisinglogistical costs incurred by all SC members, consideringautonomy as being inherent to them, and the need to coordinatelogistical operation through knowledge of customerdemand and suppliers' target planning ability. Theproposed model was able to reduce total costs by 0,047%monetary units, and explicitly identify logistical costs as achain complex.

Keywords: coordination, supply chain, decentralisation,planning.

Received: June 2th 2011

Accepted: July 24th 2011

Introduction

A logistics context (Simchi Levi, 2003) defines supply chain (SC)administration as the effective integration of suppliers, manufacturers,warehouses and stores, so that goods are produced anddistributed in the right quantities and locations at the right time,for minimising total system cost, while meeting customer servicerequirements. SC integration is nowadays considered an importanttool for ensuring competitive advantage (Yan et al, 2008).

SC agent coordination depends on managing dependenciesbetween activities within a SC, following essential prerequisitesfor its successful management (Lambert & Cooper, 2000). Other researchers, such as Speakman (Speakman et al., 1998) have argued that only through close collaborative linkages throughout an SC can the benefits of cost reduction and improved revenue performance be achieved. According to Arshinder (Arshinder et al., 2008), coordination in a SC leads to increased sales, lower lead times and excess inventory, thereby improving customer service, lowering costs, greater flexibility, higher income and increased customer retention (i.e. loyalty).

In the maritime industry, shipbuilding plays an essential role in providing services for constructing and repairing naval craft; nevertheless, no detailed methodologies and models are available for their SC member' s coordination, particularly in Colombia. This condition makes the proposal described here very significant, given that maritime transport is one of the main pillars of the Colombian economy, as trade by sea accounts for about 95% of global operations (Gómez, 2010)

The coordination model for shipbuilding industry agents assumes that shipbuilders are buyers, acting in a decentralised environment in which SC members make decisions independently, without considering other SC agents' activities.

Background

There is a need in Colombia to study shipbuilding sector SC logistical operation which is concentrated in Cartagena: Astivik S.A, Cotecmar, Ferroalquimar S.A and Navtech S.A. These organisations represent entities constructing or repairing naval craft, requiring them to purchase raw materials from national and international suppliers. Each entity is an agent in SC transformation, and each supplier is another agent in SC supply.

Each transformation level agent within the SC makes its decisions autonomously, considering external agents' constraints, and also autonomously at supply level. The investigation motivating this paper determined that strategic coordination between the agents involved is important and necessary, i.e. suppliers, capacities, fleet types, ways and means of transport, rules of negotiation and agreement between parties. This does not happen in the Colombian shipbuilding sector, generating higher costs and customer service deficiency. The complexity of these systems' operation and the lack of studies concerning the application of coordination models involving agents in its SC was the motivation for the research. An exact model is proposed aimed at coordinating autonomous agents within a system having finite capacity regarding both storage and transportation, where autonomy can be maintained and coordinated operation of the SC can be guaranteed.

The model provides the means for establishing policies, rules and negotiation mechanisms for creating an environment where projects (transformation level), suppliers (supplying level) and carriers (distribution level) operate autonomously and in a coordinated manner to improve logistics operational performance, achieving coordinated benefits in a production-based setting.

The following highlights such approach; Sucky (Sucky, 2006) coordinated negotiation models with asymmetric information, Jaber (Jaber et al., 2008) investigated coordination in order quantities in a three-level centralised SC and Romero (Romero et al., 2009) studied a coordination environment in a decentralised two-level SC.Coordination strategies would include joint order development (Banerjeé, 1986) (Lau et al., 1994), common replenishment epochs (CRE) (Viswanathan et al., 2001) and vendor -managed inventory (VMI) (Dong et al., 2002) (Yao et al., 2008) (Arango et al., 2010).

A rigorous literature review revealed no contributions regarding the state of the art about coordination models at strategic level applied to the Colombian shipbuilding industry. A model for this industry has thus been proposed to guide decision-making by jointly committing buyers, sellers and carriers.

Methodology

The research involved evaluating specific organisations within the Colombian shipbuilding area, located in the city of Cartagena (Colombia), through studies carried out during the past three years. This included employers, workers and researchers' participation through meetings, conducting surveys and direct observation of the shipbuilders' logistics system, using IIRSA procedures for SC characterisation (IIRSA, 2006). This led to determining parameters regarding cost and the skills required in the model. The relevant variables were order frequency and size, and the transportation means used.

Available national studies regarding the shipbuilding industry were evaluated as was the state of the art regarding coordination models, strategies, mechanisms and negotiation rules for companies operating in production area. It was determined that the models used for supply in these organisations consider classical inventory management systems such as economic order quantity (EOQ) and the Silver-Meal algorithm, assuming that the buyer weilds the power in the SC. There was an evident lack of proposals for agents' integration and coordination within the context of the shipbuilding industry in Latin-America and Colombia. The proposed model was thus designed and developed in GAMS code with a Visual Basic interface that allows multiple scenario analysis and evaluation. The parameters were deterministic and compared two instances of applying the proposed model to the model constructed here.

Proposed model

The model simulated a network in which suppliers i, supplied raw materials and input type p to k plants during t periods using transportation means type s. These plants did not engage in transformation, but purchased from and managed raw materials supplied to j customers. Classical mixed linear programming was used for minimising SC costs with 3 suppliers, 2 plants and 3 customers (2 served by plant 1 and by plant 2) demanding 3 products to be transported by 3 transportation types, over a planning horizon of 3 fortnights. The model was converted into a goal programming model to reduce demand fulfilment deviations.

The symbolism, nomenclature and their definition were as follows:

Index used in the model: i supplier index, i = 1,…,m; j customer index, j = 1,…,n; k plant index, k = 1,…,K. p product index , p = 1,…,q.; t consumption period index, t = 1,…,T. s transportation mean index , it is assumed that each transportation mean has unique associated capacity s = 1,…,S.

Model assumptions: There is a free flow of information between agents in the SC. Delivery times are considered in the strategic planning. It has been assumed that purchase prices remain constant over the planning horizon. Lead time is zero. The time period used in the model is half a month, covering a one year planning horizon. The model does not include reverse flows, durability and waste of products. There is no transformation of raw materials in the intermediate nodes of the SC. Fixed costs are associated with administrative activities needed to make deliveries, regardless of the number of units. There are volume restrictions on storage and transportation capacity.

Parameters:

i. Supplier parameters

CF_i,k,s Fixed cost from supplier i to plant k using means of transport having capacity s.

CV^pi,k,s variable cost of transporting one unit of each product type p from supplier i to plant k using means of transport type s.

ch^p_i holding cost of each unit of product type p assumed by supplier i in period t .

CO ^p_i,t supply capacity of supplier i for product type p in period t

ED _i,t total space available for inventory for supplier i in period t.

NV _i,k,t,smaximum number of trips per means of transport s from supplier i to plant k in period t.

ii. Plant parameters

CF _k,j,s Fixed cost of transportation from plant k to customer j using means of transport type s.

CV^p_k,j,s Variable cost of transporting one unit of each product type p from plant k to customer j using means of transport s.

Ch^p_k Holding cost of each product type p assumed by plant k in period t.

b_j,k Matrix j x k containing binary values [0,1] in customer asignation to plants

SS ^p_k,t Units of product type p to be kept as safety stock in plant k during period t.

ED_k,t Total space available for inventory for plant k during period t.

NV_k,j,t,s Maximum number of trips per means of transport s from plant k to customer j in period t.

iii. Customer parameters.

ch ^p_j Holding cost of each product type p assumed by customer j in period t

D^p_j,t Demand for product p by customer j in period t

SS ^p_j,t Units of product type p to be kept as safety stock by client j during period t.

pc ^p Purchasing price per unit of product type p

PD _j,t Total budget available by plant k in period t.

ED _j,t Total space available for inventory for customer j in period t.

iv. General parameters.

h^p cubic meters of space required to store one unit of product type p

a ^p cubic meters of space required to transport one unit of product type p

CC_s load capacity (volume) per unit of transportation type s

v. Decision variables

x ^p _i,k,t,s units of product type p shipped from supplier i to plant k in period t using mean of transport s.

y ^p _k,j,t,sunits of product type p shipped from plant k to customer j in period t using means of transport s.

I ^p _i,t inventory level of product type p held by supplier i during period t

I ^p_k,t inventory level of type p product held by plant k during period t

I ^p _j,t inventory level of product type p held by customer j during period t

U _k,j,t,snumber of trips to make from plant k to customer j using means of transport s during period t.

U_i,k,t,s number of trips to make from supplier i to plant k using means of transport s in period t

des_j,t^(-)deviation variable indicating investment deficit in products against available budget.

des_j,t⁽⁺⁾deviation variable indicating investment excess in products against available budget.

desct ⁽⁺⁾variable indicating minimum cost deviation.

desct ^(-)variable indicating above minimum cost deviation.

desdem_p,j,t^(-)variable indicating required demand deviation.

desdem_p,j,t⁽⁺⁾variable indicating above required demand deviation.

Basic model:

The basic supply chain management model was extended by the concept of joint planning integration with suppliers, including considerations of supplier inventory management, supplier transport and inventory costs, aimed at reducing joint SC costs.

i. Objective function

ii. Restrictions

Initial conditions:

I ^p_i,o = Kte    ∀i = 1,…, m,p = 1,…,q;I ^p_j,o = Kte2

∀j = 1;…, m ,p =1,…,q;I ^p _K,O = Kte3 ∀ =1,…,m,p = 1,…,q

Where Kte, Kte2 and Kte3 represented initial inventory levels

Subject to:

Final conditions:

I ^p_j,T = Kte4     ∀j =1,…,mp = 1,…,q ; Kte4 ≥ SS ^p_j,t

I ^p_k,T = Kte5     ∀k =1,…,mp = 1,…,q ; Kte5 ≥ SS ^p_k,t

Kte4 and Kte5 represented required inventory levels at the end of planning horizon T.

Model transformed to minimise deficit:

This linear goal programming model included the objective of minimising deficit, instead of coast minimisation. It also eliminated buyer inventory as a result of integrated and centralised planning through a collection centre. Restrictions (3), (5), (9), inventory conditions at beginning and end node j were removed.

i. Transformed objective function

ii. Additional restrictions:

Results

Developing a model for coordinating SC agents in the Colombian shipbuilding industry provided a tool for supporting integral management relationships between suppliers, carriers and buyers, thereby minimising the deficit in supply to entities considering the costs of all SC agents.

By applying the basic model to a particular instance total costs of 105,746,633 monetary units (MU) were obtained; the model aimed at minimising deficit (17) generated a cost of 105,696,939 MU, representing a 0.047% decrease regarding the basic model.

The main differences between results for both models concerned variation of inventory levels in plants (Table 1) and the period for sending orders to entities, despite the total amounts in both models being equal (Table 2). By eliminating project inventory, plants increased their levels from period to period to ensure compliance with demand. By applying both models there were no changes in the quantity shipped from suppliers to customers, or in shipment periods, or number of trips. Given the model' s structure and parameters used, the significant difference observed when comparing them lay in cost reduction due to eliminating inventories from the final node and changing inventory levels in plants.

Conclusions and Discussion

We have proposed an innovative mathematical model for strategic and tactical CS planning in the shipbuilding industry, involving a network of autonomous actors who interact in a decentralised environment, introducing also a coordination proposal for minimising the cost of all SC members, considering the strategy of distributing responsibility for inventory management in the beginning and intermediate nodes, aimed at reducing deficit in meeting demand.

This way of managing inventory in shipbuilding requires an accurate flow of information and a high level of commitment by SC members where elements such as contracts, status and power relationships, and the concept of shared benefits must be considered as they play a key role in the success of planning. Centralising inventory management in plant collection centres facilitates monitoring quantities, committed orders, disposal and waste and obsolete materials and supplies.

According to the results of the work done by research groups, the model presented led to proposing partial centralisation of SC by joint planning of global supply and distribution in an intermediate link in the SC, thereby generating the general supply, inventory and distribution plan to guide SC members' joint actions towards meeting end customers' estimated demand during the planning period, taking supply and demand data together, and conditions and restrictions concerning production, storage and capacity regarding the different nodes and arcs.

Future research

Further work may consider extending the model to compare the proposal to strategies like VMI. Currently, research groups are working on including logistics operation externality management. It is suggested using the model to support the inclusion of management returns and waste, as factors relevant to the shipbuilding industry.

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