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Optimal production allocation and distribution supply chain networks
ARTICLE IN PRESS
Int. J. Production Economics 111 (2008) 468–483 www.elsevier.com/locate/ijpe
Optimal production allocation and distribution supply chain networks Panagiotis Tsiakisa,, Lazaros G. Papageorgioub a
Process Systems Enterprise Limited, 107a Hammersmith Bridge Road, London W6 9DA, UK Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, London WC1E 7JE, UK
b
Received 31 March 2006; accepted 9 February 2007 Available online 24 March 2007
Abstract Enterprise optimisation can rapidly strip significant ‘‘bottom line’’ costs out of global operations, giving companies a real competitive edge. The benefits of managing supply chain networks by integrating operational, design and financial decisions have been acknowledged by the industrial and academic community. The objective of this work is to determine the optimal configuration of a production and distribution network subject to operational and financial constraints. Operational constraints include quality, production and supply restrictions, and are related to the allocation of the production and the work-load balance. Financial constraints include production costs, transportation costs and duties for the material flowing within the network subject to exchange rates. As a business decision the out-sourcing of production is considered whenever the organisation cannot satisfy the demand. A mixed integer linear programming (MILP) model is proposed to describe the optimisation problem. A case study for the coatings business unit of a global specialty chemicals manufacturer is used to demonstrate the applicability of the approach in a number of scenarios. r 2007 Elsevier B.V. All rights reserved. Keywords: Production allocation; Duties; Mixed integer linear programming; Optimisation; Supply chain
1. Introduction A global production and supply network can de defined as a set of existing or potential, manufacturing facilities, warehouses and distribution centres with multiple supply configurations and customers with demands. All these facilities can be located in
Corresponding author. Current address: IBM UK Ltd, 76-78 Upper Ground, South Bank, London SE1 9PZ, UK. Tel.: +44 20 8563 088; fax: +44 20 8563 0999. E-mail addresses: [email protected], [email protected] (P. Tsiakis).
different countries where different tax breaks and currencies apply. In today’s rapidly changing economic and political conditions global corporations face a continuous challenge to constantly evaluate and optimally configure their supply chain operations to achieve key performance indices (KPIs), either it is profitability, cost reduction or customer service. In this environment operations managers and planners need to address accurately questions such as which plants to operate, what product mix per plant, which distribution centre supplies which customer, what inventory levels are necessary to maintain service levels, which suppliers are to be used.
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2007.02.035
ARTICLE IN PRESS P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483
Beamon (1998) identified the increasing attention placed on the performance, design, and analysis of the supply chain as a whole and provided an analysis of the available modelling methods categorising them to heuristic and mathematical programming approaches. Mathematical programming approaches are further categorised into (1) deterministic, (2) stochastic, (3) economic and (4) simulation. The necessity to develop strategic and tactical level supply chain planning models in order to address issues in a quantitative manner rather than the qualitative approaches used till now is acknowledged by the industry (Shapiro, 2004) and still remains an active research area. This has created many challenges both for researchers and practitioners who wish to successfully implement supply chain support systems. In a recent literature survey, Bilgen and Ozkarahan (2004) analyse previous research and review models for the production and distribution problem. A classification scheme was employed to categorise and compare strengths and weaknesses as they are reported in a table at the end of the review. Klose and Drexl (2005) review the status of research in facility location models for the design of distribution systems. Their work reviews state-of-the-art model formulations on strategic planning, distribution system design, facility location and mixed integer programming. Previous attempts to improve the performance of supply chain networks have mainly focused on the logistic aspects rather than the business decisions associated with the plant operation and production for the design of such networks. In an early attempt Arntzen et al. (1995) developed a mixed integer linear programming (MILP) ‘‘global supply chain model’’ (GSCM) aiming to determine: (1) the number and location of distribution centres, (2) customer-distribution centre assignment, (3) number of echelons, and (4) the product-plant assignment. The objective of the model is to minimise a weighted combination of total cost (including production, inventory, transportation, and fixed costs) and activity days as a bill of material problem. To the same direction and as supply chains become increasingly global, additional aspects such as differences in tax regimes, duty drawback and avoidance, and fluctuations in exchange rates also become important (Vidal and Goetschalckx, 1997). Tsiakis et al. (2001) have addressed a large number of the production and
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logistics issues reported by Bilgen and Ozkarahan in a comprehensive work that models supply chain networks under demand uncertainty focusing on the production and transportation issues. The resulting MILP problem is solved to optimality using decomposition methods to reduce the computational effort required. The model reported does not include financial aspects such as duties and exchange rates. Guinet (2001) examines the economics of multi-site production systems using a two-level approach to allocate production to sites and address the workshop scheduling problem. A primal–dual heuristic approach was used to solve cases of this problem aiming to minimise variable and fixed costs. Goetschalckx et al. (2002), review the area of modelling and design of global logistics and propose two models, one for a global case where the aim is to calculate the transfer prices and a second one for a single country where the focus is on tackling efficiently seasonality in the demand. The focus is on the logistic aspects with the plants assumed multi-product without limitations. Kaihara (2003) uses an agent based approach to manage supply chains in terms of product allocation and resource distribution. The proposed model has the form of a discrete resource allocation problem under dynamic environment. The design of a supply chain network is characterised as a complex issue and the methods used to perform such an analysis vary depending on the problem type and the scope Ballou (2001). The author supports the idea that location analysis is most likely sufficient for most supply chain problems. Arguably, in a continuous changing environment and dynamic economic conditions such as costs, exchange rates, transportation structures and duties detail modelling is required to manage the data available and achieve expected performance. Harrison (2001) identifies the issues related to global supply chain design and operation while he points out the benefits of optimisation. Supply chain design needs to address issues such as manufacturing strategy, supplier base selection, outsourcing policies and new product and process design. Fandel and Stammen (2004) define strategic supply chain management as the long-term part of supply chain management, where product allocation and supply chain network configuration are determined. They propose a general linear mixed integer model for the design of business processes to include product life cycle.
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P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483
The key business issue of supply chain partnership was investigated by Gjerdrum et al. (2002). In their work, a mathematical programming formulation is presented for fair, optimised profit distribution between members of multi-enterprise supply chains based on a novel approach applying game theoretical Nash-type models to find the optimal profit level for each enterprise subject to given minimum profit requirements. Model decision variables include inter-company transfer prices, production and inventory levels, resource utilisation, and flows of products between echelons, subject to a deterministic sales profile, minimum profit requirements for each enterprise. Based on the work of Papageorgiou et al. (2001) on the strategic design of pharmaceutical supply chains, Levis and Papageorgiou (2004) extended the model to study the long-term capacity planning problem under uncertainty. The problem was formed as a mathematical programming model (MILP) to determine both product portfolio and plant capacity taking into account the uncertainty of clinical trials to develop a new product. The resulting large scale MILP problem was solved using two-stage, multi-scenario hierarchical algorithm, and the applicability was demonstrated through illustrative examples. The current paper proposes a strategic planning model for multi-echelon supply chain networks, integrating components associated with production, facility location and distribution along side with financial and business issues such as import duties, plant utilisation, exchange rates and plant maintenance. The network comprises a number of manufacturing sites, each using a set of flexible, shared resources for the production of a number of products. The manufacturing sites already exist at given locations, so do the customer zones. Although the location of distribution facilities is given, the design in terms of capacity of each distribution centre and its connectivity is considered as part of the optimisation problem. The model developed and presented in the next sessions is more generic and can be used to address design issues of the supply chain such as production plant location and distribution centre location. Section 2 of this paper presents the problem statement and description, while in Section 3 we present an MILP formulation of the problem for the optimal design and operation of global supply chain networks, and Section 4 presents an industrial case study. Section 5 concludes by summarising the
results and highlights directions for further research. 2. Problem description This work considers the optimal design and operation of multi-product, multi-echelon global production and distribution networks. The network consists of a number of existing multi-product manufacturing sites at fixed locations, a number of distribution centres, and finally a number of customer zones at fixed locations. In general, each product can be produced at several plants at different locations. The production capacity of each manufacturing site is modelled in terms of a set of linear constraints relating the mean production rate per product to the availability of the plant and the number of change-overs between campaigns. Distribution centres are described by upper and lower bounds on their material handling capacity and they can be supplied from more than one manufacturing plants and can supply more than one customer zone. However, ‘‘single sourcing’’ constraints requiring that a distribution centre be supplied by a single plant can also be accommodated. Each customer zone places demands for one or more products. These demands may be assumed to be known a priori. A customer may be served by more than one distribution centre. Alternatively, single sourcing constraints, according to which a customer zone must be served by a single distribution centre, may be imposed by modifying the constraints. Operational costs include those associated with production, handling of material at distribution centres, transportation and duties. Transportation costs are assumed to be linear functions of the actual flow of the product from the source stage to the destination stage. Additionally to transportation costs we have taxes and duties. The decisions to be determined include the product portfolio per production plant, production amounts, utilisation level, and transportation links to establish in the network along side with material flows. The objective is the minimisation of the total annualised cost of the network, taking into account both infrastructure and operating costs. This paper considers a steady-state form of the above problem according to which demands are time-invariant and all production and transportation flows determined by the optimisation are considered to be timeaveraged quantities.
ARTICLE IN PRESS P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483
3. Optimal design of global production and distribution network The above problem is formulated mathematically as an MILP optimisation problem. We aim to obtain an optimal design of this network. 3.1. Notation The notation to be used in this section is described below: Indices/sets I J K L
products plants possible distribution centres customer demand zone Parameters
C DH ik C D;e k C D;s k C dijk C dikl C P;e j C P;s j C Pij C Si C Tijk C Tikl Dmin k , Dmax k Dil Hj Mj
unit handling cost for product i at distribution centre k annualised fixed cost of establishing a distribution centre at location k annualised fixed cost of shutting down a distribution centre at location k unit duty cost for product i leaving production plant j to distribution centre k unit duty cost for product i leaving distribution centre k to customer l annualised fixed cost of establishing a production plant at location j annualised fixed cost of shutting down a production plant at location j unit production cost for product i at plant j unit production cost for product i supplied to the network from third parties unit transport cost for product i from plant j to distribution centre k unit transport cost for product i from distribution centre k to customer zone l minimum/maximum distribution centre capacity demand for product i in customer zone l operating horizon of production site j in days per annum annual days of maintenance of production site j
N cij max Pmin ij , Pij
Qmin jk , Qmax jk Qmin kl , Qmax kl max T min ij =T ij
rdj ajk akl b g dik
z t
471
number of campaigns of product i at production plant j minimum/maximum production capacity of plant j for product i minimum/maximum rate of flow of materials transferred from plant j to distribution centre k minimum/maximum rate of flow of materials transferred from distribution centre k to customer zone l minimum/maximum availability of plant j for the production of product i per annum in days expected daily production rate of plant j duty coefficient relating production plant j to distribution centre k duty coefficient relating distribution centre k to customer l coefficient applied to production cost for duty purposes coefficient applied to transportation cost for duty purposes coefficient relating capacity of distribution centre k to flow of product i handled utilisation parameter in days change-over coefficient in days
Continuous variables Dk Oik Pij Qijk Qikl Tij Uj DU
capacity of distribution centre k out-sourced product i delivered to distribution centre k production rate of product i in plant j rate of flow of product i transferred from plant j to distribution centre k rate of flow of product i transferred from distribution centre k to customer zone l days allocated for the production of product i in plant j utilisation of production plant j as production days per year maximum allowed difference in utilisation between plants
Binary variables Yj Yk
1 if production plant j is to be established, 0 otherwise 1 if distribution centre k is to be established, 0 otherwise
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Xjk Xkl Wij
1 if production plant j is assigned to distribution centre k, 0 otherwise 1 if distribution centre k is assigned to customer zone l, 0 otherwise 1 if production plant j is to produce product i, 0 otherwise
The mathematical model proposed for this problem is an MILP problem as described below. 3.2.1. Network structure constraints A link between a production plant j and a distribution centre k may exist only if production plant j is established: 8j; k.
(3.1)
If a distribution centre k is established, it can then be served by more than one production plant j: X X jk XY k ; 8k. (3.2) j
This constraint can be transformed into a single source constraint for case where this restriction applies. In this case the constraint has to be written as X X jk ¼ Y k ; 8k. (3.20 ) j
The link between a distribution centre k and a customer zone l may exist only if the distribution centre is established: X kl pY k ;
8k; l.
(3.5)
i
Flow of material from distribution centre k to customer zone l can take place only if the corresponding connection exists: X Qikl pQmax 8i; k; l. (3.6) Qmin kl X kl p kl X kl ; i
3.2. Mathematical formulation of deterministic problem
X jk pY j ;
corresponding connection exists: X X p Qijk pQmax 8i; j; k. Qmin jk jk jk X jk ;
(3.3)
Each customer can be supplied by more than one distribution centres to satisfy demand: X X kl X1; 8l. (3.4) k
In accordance with the ‘‘single sourcing’’, each customer zone can be served by exactly one distribution centre and the constraint has to be modified as follows: X X kl ¼ 1; 8l. (3.40 ) k
3.2.2. Logical constraints for transportation flows Flow of material from production plant j to distribution centre k can take place only if the
max appearValues for the upper bounds Qmax jk , Qkl ing on the right-hand sides of constraints (3.5) and (3.6) are determined by contracts in place for the transportation of materials. The bounds apply on the total amount sent to each destination.
3.2.3. Material balances The actual rate of production of product i by plant j must equal the total flow of this product from plant j to all distribution centres k: X Pij ¼ Qijk ; 8i; j. (3.7) k
Assuming that there is no stock accumulation or depletion (i.e. steady-state operation), the total rate of flow of each product leaving a distribution centre must equal the total rate of flow entering this node of the supply chain network: X X Qijk þ Oik ¼ Qikl ; 8i; k. (3.8) j
l
Ideally the total rate of flow of each product i received by each customer zone l from the distribution centres must be equal to the corresponding market demand. In the case where this amount is not sufficient to cover the demand this is partially filled by out-sourced material which is supplied to the distribution centres: X Qikl ¼ Dil ; 8i; l. (3.9) k
3.2.4. Production constraints An important issue in designing the distribution network is the ability of the manufacturing plants to cover the demands of the customers as expressed through the orders received from the warehouses. The rate of production of each product at any plant cannot exceed certain limits. Thus, there is always a maximum production capacity for any product; moreover, there is often a minimum production rate that must be maintained while the
ARTICLE IN PRESS P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483
(i.e. Yk ¼ 1):
plant is operating: max Y j Pmin ij pPij pPij Y j ;
8i; j.
(3.10)
Production is restricted by the number of change-overs and number of campaigns performed at a site. Also maintenance has to be taken into account: X X T ij pðH j M j ÞY j t N cij W ij ; 8j. (3.11)
max Dmin k Y k pDk pDk Y k ;
The number of days available for the production of product i in production site j is limited by the total availability of the plant, subject to the plant producing this product: max T min ij W ij pT ij pT ij W ij ;
8i; j.
(3.12)
The production per site is organised in terms of campaigns due to the seasonal nature of the business, the demand patterns and the portfolio of products which require long cleaning periods of the production lines between products. Therefore the production capacity is reduced based on the number of change-overs. We assume that on average the same length of cleaning is required between products. The total production of each product depends on the daily production capability of the plant and the number of days allocated per year: 8i; j.
(3.13)
The utilisation of each plant is equal to the number of production days per year and is given by X Uj ¼ T ij ; 8j. (3.14)
where dik is a given coefficient that relates product and distribution centre capacity. 3.2.6. Objective function In general, a distribution network involves both capital and operating costs. The former are one-off costs associated with the establishment of the infrastructure of the network, and in particular its warehouses and distribution centres. On the other hand, operating costs are incurred on a daily basis and are associated with the cost of production of material at plants, the handling of material at warehouses and distribution centres, and the transportation of material through the network. 3.2.6.1. Fixed infrastructure costs. The infrastructure costs considered by our formulation are related to the establishment or shut-down of a production plant or a distribution centre at a candidate location. These costs are expressed in the following objective function terms: X P;e X P;s Cj Y j þ C j ð1 Y j Þ j
þ
DU XU j U j0 ;
8j; j 0 aj,
DU XU j0 U j ;
8j 0 ; jaj 0 ,
DU pz.
(3.15)
3.2.5. Capacity of distribution centres The capacity of a distribution centre k generally has to lie between given lower and upper bounds, Dmin and Dmax provided, of course, that k k , the distribution centre is actually established
(3.16)
i;l
i
Due to multi-site production we want to ensure that production is distributed evenly between sites, therefore utilisation per site should be similar with the difference limited to a specified range. The following constraints ensure that the total utilisation per site remains close:
8k.
We generally assume that the capacities of the distribution centres are related linearly to the flows of materials that they handle. This is expressed via the constraints: X Dk X dik Qikl ; 8k, (3.17)
i
Pij ¼ rdj T ij ;
473
X k
j
C D;e k Yk
þ
X
C D;s k ð1 Y k Þ.
k
If we assume that the production plants are already established, we need to provide the option of expansion. Therefore, we do consider the capital cost associated with their re-design and construction. We ignore any infrastructure cost associated with customer zones. 3.2.6.2. Production cost. The production cost is given by the product of the production rate Pij of product i in plant j, with the unit production cost C Pij . The corresponding term in the objective function is of the form X C Pij Pij . i;j
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The production cost C Pij is expressed in terms of local currency. As part of the production cost we have to account the cost of change-overs as lost production X t C Pij N cij W ij . ij
As production costs we account for the material out-sourced to third parties to satisfy excess demand: X C Si Oik . i;k
3.2.6.3. Material handling costs at distribution centres. Handling costs can usually be approximated as linear functions of the total throughput. They can be expressed as follows: ! X X DH C ik Qikl : i;k
l
The unit duty cost is a function of the handling and transportation costs between the source (distribution centre) and destination (customer). It is applied as a coefficient on the combined material handling and transportation cost: DH T CD ikl ¼ aikl ðbC ik þ gC ikl Þ.
The contribution to the objective function is given by X CD ikl Qikl . i;k;l
3.2.6.6. Overall objective function. By combining the cost terms derived in Sections 3.2.6.1–3.2.6.5, we obtain the total cost of the supply chain network, which is to be determined by the optimisation: min
production plant infrastructure costs P P;e P C j Y j þ C jP;s ð1 Y j Þ j
j
Handling and temporary storage costs at production plants are included in the production cost.
þdistribution centre infrastructure costs P D;e P C k Y k þ C D;s k ð1 Y k Þ
3.2.6.4. Transportation cost. The unit transportation cost is constant independent of the product transported and depends only on the source and destination node. Transportation costs that we include are those between production plant to distribution centres and distribution centres to customers. Therefore the following term needs to be added to the objective function: X X C Tijk Qijk þ C Tikl Qikl .
þproduction cost P P P P C ij Pij þ C Si Oik þ t C Pij N cij W ij
k
i;j;k
i;k;l
i;j
i;k
i;j
þmaterial handling cost at distribution centres P DH P C ik Qikl i;k
l
þtransportation costs P T P T C ijk Qijk þ C ikl Qikl
i;j;k
i;k;l
þduties cost P D P D C ijk Qijk þ C ikl Qikl : i;j;k
3.2.6.5. Duties. In the specific model duties apply to the material transferred from the production sites to the distribution centres and is calculated in currency of the importing country. The unit duty cost is a function of the production and transportation costs between the source and destination. It is applied as a coefficient on the combined production and transportation costs:
k
ð3:18Þ
i;k;l
The above minimisation is subject to all the constraints presented in Sections 3.2.1–3.2.5. The objective function can be modified to define a maximisation problem based on the profit by satisfying the product demand at a specific product price.
P T CD ijk ¼ ajk ðbC ij þ gC ijk Þ.
4. Case study
The contribution to the objective function is given by X CD ijk Qijk .
To demonstrate the applicability of the proposed model we examine the performance of a global organisation with a supply chain extending in many countries in different continents where multiple currencies and taxes apply.
i;j;k
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The model was applied on a network consisting of six manufacturing plants located at different countries on different continents. Each plant can produce six types of products using a number of shared production resources, therefore only one product may be produced at a time. A number of possible distribution centres are considered to handle the material based on the market demand placed by the customer zones. Customer zones comprise eight large geographical areas. The network superstructure is given in Fig. 1. The superstructure assumes complete connectivity between all sites which is subject to constraints regarding material transfers. We examine different scenarios of operation to demonstrate the benefits of optimisation over decisions imposed by practice or heuristics. These scenarios are:
The model described above is implemented in GAMS (Brooke et al., 1998) and CPLEX is the solver used to solve the MILP problem. Other solvers were used such as (Xpress-MP, GLPK and LP-Solve) with similar results.
4.1. Problem description This section describes the data required by the model to set values for the parameters. All available data used to produce the results are presented in Sections 4.1.1–4.1.3 and Tables 1–8.
4.1.1. Production plants The theoretical maximum production capacity of each plant with respect to each product (i.e. the parameter Pmax of the formulation) is given as a ij result of Table 1 and the maximum availability of the plant. The corresponding minimum production rates Pmin are taken to be zero unless the product is ij selected. The production per plant in term of tonnes of product per day is given in Table 1. This is the bulk product capacity. The operating horizon is 365 days per plant and maintenance duration per production site is 10 days except plants 5 and 6 where we have 7 days.
free optimisation where all decisions are determined by the model subject to the constraints; optimise network flows when product allocation decisions and network structure has been fixed; optimise the network when each plant can manufacture up to three allocated products; examine the network sensitivity by changing some of the parameters such as utilisation constraint.
Production plant PL1
Distribution centre Customer zone Possible connection C8
PL2
DC1
DC2
PL3
C2 DC3 C1 C6
C3
PL5 DC5
PL4 C5 PL6 C7 DC4
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C4 DC6 Fig. 1. A typical supply chain representation.
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Table 1 Daily production rate per production site (tonnes/day) PL1 73.4
PL2 12.7
PL3 35.1
PL4 34.4
PL5 11.0
PL6 10.0
Table 5 Costs associated with the distribution centres upon establishment
Table 2 Unit production cost per product per plant (rmua/kg) Product
P1 P2 P3 P4 P5 P6 a
Maximum production for each product per site is T max ¼ 365 days, while the minimum campaign ij length is T min ¼ 7 days. ij The change-over duration is assumed to be t ¼ 1 day and we assume that the utilisation coefficient is z ¼ 10 days.
Distribution centre costs
Production site PL1
PL2
PL3
PL4
PL5
PL6
4.68 3.23 4.18 2.48 1.43 2.15
4.53 3.17 4.19 2.71 1.49 2.15
5.17 3.21 5.17 2.54 1.55 2.22
5.04 3.87 4.35 2.74 1.41 2.40
4.27 3.12 3.71 2.43 1.28 2.07
4.26 3.97 3.70 2.42 1.27 2.06
rmu: relative money units.
Table 3 Transportation cost between production sites and distribution centres (rmu/kg)
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
0.053 0.077 0.141 0.00 0.038 0.117
0.051 0.071 0.125 0.143 0.00 0.038
0.056 0.077 0.119 0.144 0.038 0.00
0.062 0.089 0.126 0.138 0.236 0.178
0.081 0.127 0.00 0.182 0.117 0.236
DC2
DC3
DC4
Fixed infrastructure cost (,000 rmu) 4,300 2,900 3,100 2,200 Material handling cost per product (rmu/kg) P1 0.07 0.068 0.077 0.076 P2 0.048 0.048 0.048 0.058 P3 0.063 0.063 0.077 0.065 P4 0.037 0.041 0.038 0.041 P5 0.021 0.022 0.024 0.021 P6 0.032 0.032 0.033 0.036
DC5
DC6
1,300
1,500
0.064 0.047 0.056 0.036 0.019 0.031
0.064 0.060 0.056 0.036 0.019 0.031
Table 6 Customer zone demand per product (tonnes) Product Customer zone
From/to Distribution centre production site DC1 DC2 DC3 0.00 0.065 0.083 0.107 0.183 0.168
DC1
C1 P1 P2 P3 P4 P5 P6
C2
C3
C4
C5
C6
C7
C8
5,701 3,665 3,398 2,686 1,342 2,310 2,436 1,819 2,116 365 1,468 1,355 910 630 1,049 748 3,246 887 1,369 1,353 609 410 1,219 679 2,582 295 3,016 466 556 700 1,436 906 3,683 437 2,284 922 794 690 1,578 844 294 64 311 1,173 130 110 172 323
Table 4 Values of coefficient aijk to apply on duties structure (%) From/to production site
PL1 PL2 PL3 PL4 PL5 PL6
Product group
P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
0.0 0.0 0.0 0.0 6.5 6.5 0.0 0.0 0.0 0.0 6.5 6.5
0.0 0.0 0.0 0.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0
7.1 3.8 7.1 3.8 0.0 0.0 4.1 0.3 7.1 3.8 4.1 0.3
53.1 53.1 53.1 53.1 53.1 53.1 0.0 0.0 53.1 53.1 53.1 53.1
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 0.0 0.0 10.0 10.0
5.0 12.5 5.0 12.5 5.0 12.5 5.0 12.5 5.0 12.5 0.0 0.0
ARTICLE IN PRESS P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483 Table 7 Transportation cost between distribution centre and customers (in rmu/kg) Distribution centre
DC1 DC2 DC3 DC4 DC5 DC6
Customer zone C1
C2
C3
C4
C5
C6
C7
C8
0.00 0.65 0.90 1.13 1.89 1.74
0.62 0.00 1.40 1.52 2.16 1.78
0.81 1.27 0.0 1.82 2.61 2.36
0.53 0.77 1.41 0.0 1.66 1.17
0.51 0.73 1.25 1.43 0.00 0.00
0.56 0.77 1.19 1.44 0.57 0.59
1.31 1.38 1.35 1.93 1.57 1.36
1.66 1.77 1.29 1.54 1.34 1.23
Table 8 Duty coefficient for material transferred between distribution centre and customer aikl (%) Distribution centre
DC1 DC2 DC3 DC4 DC5 DC6
Customer zone C1
C2
C3
C4
C5
C6
C7
C8
0.0 0.0 6.5 6.5 6.5 6.5
0.0 0.0 9.0 9.0 9.0 9.0
7.1 7.1 0.0 4.1 7.1 4.1
53.1 53.1 53.1 0.0 53.1 53.1
12.5 12.5 12.5 12.5 0.0 12.5
11.0 11.0 11.0 11.0 11.0 11.0
17.0 17.0 17.0 17.0 17.0 17.0
15.0 15.0 15.0 15.0 15.0 15.0
The unit production costs per product for each plant are given in Table 2. Note that all costs displayed have been converted to relative money units based on certain exchange rates for confidentiality reasons. Sensitivity analysis was performed on the exchange rate fluctuation and the average price was used. 4.1.2. Distribution centres The distribution centres to be designed are assumed to have sufficient capacity to handle the material received and distributed and the logistics management is not an issue at this level. In order for a connection between a production plant and distribution centre to exist that must be at least for a total flow of 1,000 tonnes (i.e. Qmin jk ¼ 1; 000 8j; k). The transportation costs from the production plants to the distribution centres are given in Table 3. This is the unit transportation cost and is independent of the product type and the amount transported. The amount transported to the distribution centres is subject to duties as they have been defined
477
in Section 3.2.6.5. Table 4 describes the coefficients used between production sites and distribution centres. For this case parameter b ¼ 1.1 and g ¼ 1.0. The relationship can then be written as aijk ð1:1 C Pij þ C Tijk Þ. The establishment of a distribution centre occurs at fixed costs for the organisation. These amounts have been amortised to annual amounts. Depending on the materials stored there is a handling cost per product. Both costs are given in Table 5. 4.1.3. Customer zones The customer zones are located close to the distribution centres and the allocation for the specific problem is considered fixed, therefore distribution costs can be ignored. The demand per product and customer zone is given in Table 6. The transportation costs from distribution centres to customer demand zones are given in Table 7. The amount transported to the customer demand zones is subject to duties as they have been defined in Section 3.2.6.5. Table 8 describes the coefficients used between distribution centres and customers. For this case parameter b ¼ 1.0 and g ¼ 1.0. The relationship can then be written as T aikl ðC DH ik þ C ikl Þ.
4.2. Network optimization—base scenario The first case is a free optimisation exercise where the model is allowed to determine all the decisions required such as product allocation per plant and production level, establishment of distribution centres and customer allocation, material flows and distribution centre capacity. The optimal solution for the network is given in Fig. 2. Table 9 shows the product allocation per plant and the number of days of production per product. Out-sourced material is purchased to cover demand that cannot be satisfied by internal production and is presented as the last column of the same table. This material is directly supplied to the distribution centres and from there to the customer zones assigned. The total material supplied from the production plants to distribution centres is shown in Table 10. This is subject to the material flow constraint that
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PL1
PL2
DC1 PL3
DC2
C8
C2
DC3
C6 C1
PL5
C3 DC5 PL4 C7
C5 PL6
DC4 C4
Fig. 2. Optimal network configuration for base case.
Table 9 Product allocation per plant and production days allocated Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
148 54 69 0 58 0
321 0 0 0 0 14
0 61 50 124 95 0
173 42 66 0 0 50
131 108 0 0 0 96
133 0 58 48 94 0
Utilisation Total
329
335
330
331
335
333
applies for an established link. At the bottom of the table the total material handling capacity of each distribution centre is given. This includes the amount received by third parties as out-sourced production. Material flows from a distribution centre, where it has been established to the assigned customers, is equal to the total demand placed by the customer. The flow per arc equals to the total product demand per customer since we enforce single source constraints. The total annual cost of operation for this case is 311,681,000 rmu. Individual contributions to the objective function are given in Table 17.
0 0 0 5,097 0 2,289
Table 10 Material flow from production plants to distribution centres (in tonnes) From/to production site
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
20,765 2,096 1,000 3,258 1,000 0 1,418 0 1,000 0 1,000 0
1,000 0 0 0 10,538 0 3,656 6,316 0 0 1,337 0
0 0 0 0 2,340 1,315
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
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4.3. Fixed product allocation and customer assignment
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plants can produce the whole range of products and the optimisation is used to determine product allocation, material flows within the network, and the connections between plants, distribution centres and customer zones. The actual production per site in terms of days is given in Table 13. Material which is out-sourced and supplied directly to the distribution centres by third parties is given in as the last column of the same table. The flow of material in the network is given in Table 14. Fig. 4 shows the optimal network configuration and the customer allocation to distribution centres, while the associated cost is 343,218,000 rmu. The cost analysis is given in Table 17. Comparing this network structure with the configuration of the base case we can see that the connections between plants and distribution centres have changed. This is due to the different product portfolio.
This case assumes that production allocation and network configuration in terms of customer allocation to distribution centres are decisions already taken. Product allocation is made according to plant capabilities and bidding process from the plants. Secondary, customer demands are assigned to the nearest possible geographical site. These decisions are based on the planning experience—can also be characterised as rules of thumb or heuristics. As a result the model size is reduced in terms of number of decision variables need to be determined since Xkl and Wij are fixed. The model is allowed to optimise the production levels (as days per year and campaigns) and flows within the network as well as connections between plants and distribution centres. Table 11 shows the activity levels for each plant based on the preallocation of products. Out-sourced material purchased for this case is given as the last column of Table 11. More products are out-sourced and its total is higher than the base case. The flow of material between plants and distribution centres is given in Table 12. The total cost of operation in this case is 327,049,000 rmu. The break-down of individual costs is given in Table 17. The solution of the problem is given in Fig. 3 which also shows the customer assignment to distribution centres. These connections were fixed.
Table 12 Material flow between production plants and distribution centres (in tonnes) From/to production site
Distribution centre DC1
4.4. Maximum allocation of three products per plant In this case it is assumed that each plant is allowed to manufacture up to three products. All
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
19,869 2,197 1,000 3,156 0 0 1,000 0 0 0 0 0
0 0 0 0 9,482 0 1,000 6,316 0 0 0 0
0 0 0 0 3,260 0
1,353 0 1,634 2,936 0 3,583
Total handling capacity
22,362 5,713
11,846 7,955
4,341
13,209
Table 11 Production per plant as days per product Product
P1 P2 P3 P4 P5 P6 Utilisation Total
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
91 50 62 42 74 0
327 0 0 0 0 0
84 60 42 56 75 0
165 42 70 0 49 0
69 91 59 28 80 0
133 42 58 28 66 0
319
327
317
326
327
327
1,711 0 134 4,323 0 2,467
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480
PL1
PL2
DC1
DC2
PL3
C2 DC3
C6 C1
PL5
C3 DC5 PL4 C5 PL6
DC6 C7
DC4 C4
C8 Fig. 3. Network configuration for second case.
Table 13 Production levels in days per plant Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
131 0 82 0 86 0
283 0 0 0 0 16
84 0 0 125 90 0
145 74 70 0 0 0
118 109 0 0 72 0
98 107 0 0 94 0
Utilisation Total
289
289
289
289
289
289
Table 14 Material flow between production plants and distribution centres (in tonnes) From/to production site
0 3,840 1,344 5,574 0 2,269
4.5. Sensitivity analysis on utilisation factor and change-over duration
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
19,319 1,615 1,000 2,797 1,000 0 0 0 1,000 0 0 0
1,000 0 0 0 9,477 0 4,620 5,316 0 0 1,274 1,000
0 0 0 0 1,978 1,000
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
The base scenario case (case 1) was resolved for different values of utilisation factor z. As a result of these change no modification to the solution of the base case was observed. This is primarily to the fact that there is no spare capacity in the production plants and they are utilised to the maximum available rate. Many companies identify the change-overs as one of the major factors limiting the production capacity and flexibility of the plants. We are
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PL1
PL2
DC1 PL3
481
DC2
C8
C2 DC3 C1
PL5
C6
C3
DC5 PL4
C7
C5 PL6
DC4 C4
Fig. 4. Network configuration when product allocation has been fixed.
Table 15 Production per plant in days per year Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
128 48 82 0 82 0
334 0 0 0 0 14
84 60 0 120 75 0
116 42 70 0 50 62
131 109 59 49 0 0
133 42 58 28 84 0
Utilisation Total
340
348
339
340
347
345
examining the case where the change-over duration is halved to 12 h instead of one day. The reduction of change-over duration results to a change of product portfolio per plant. This is summarised in Table 15. Out-sourced material is purchased to cover demand that cannot be satisfied by internal production. The amount of material purchased is smaller than the material bought in the base case as a result of the increased utilisation. The flow of material in the network is given in Table 16. The total cost of operation for this case is 295,714,000 rmu and a cost analysis is given in
0 0 122 4,957 0 130
Table 17. The network structure remains the same as that in Fig. 2. 4.6. Result analysis The results obtained demonstrate clearly the savings of optimisation against heuristic decisions that dictate part of the network structure. The savings are significant to justify the re-design of the supply chain to comply with the results obtained design. The benefits are a result of a better utilisation of the plants by selecting suitable product portfolios, minimisation of the out-sourced material and
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savings on total transportation and duties. Savings also result from infrastructure decisions since only five distribution centres are needed to serve the customer basis. Although the plants are multi-purpose it is beneficial for the organisation to operate specific plants in a dedicated mode. This reduces switches between products and production costs. Comparing cases 3 and 1 it is obvious that there is an optimal product portfolio per plant thus reducing outsourced material. It is clear from case 4 that further savings are possible if the plant is re-engineered to reduce the duration of change-overs. The additional savings result from the reduction of out-sourced purchased material. 5. Conclusions This paper has proposed an integrated model based on a detailed mathematical programming Table 16 Material flow between production plants and distribution centres (in tonnes) From/to production site
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
20,068 1,894 1,000 3,423 1,000 0 1,236 0 1,000 0 0 0
1,000 0 0 0 10,888 0 2,974 7,489 0 0 2,302 0
0 0 0 0 2,461 1,478
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
formulation that addresses some of the complex issues related to the design and operation of global supply chain networks. The focus is on financial and tactical operational aspects within the organisation taking into account production balancing amongst sites. Between other business benefits is the operational and distribution efficiency of the network, visibility and control of the supply chain and capability to perform towards KPIs such as operational cost, customer satisfaction and product quality. Moreover, the impact of decisions on the design and tactical operation can be quantified and evaluated. The data used are extracted directly from ERP systems making such approaches easy to use and easy to update every time the application is used. The proposed MILP model aims to assist senior operations management to decisions about production allocation, production capacity per site, purchase of raw materials and network configuration taking into account financial aspects (exchange rates, duties, etc.) and costs. Currently, the organisation under study employs a number of spreadsheet where ERP data are manipulated using Excel formulas to calculate average costs and plant capacities. The model proposed is packaged as an add-in tool which imports data from Excel but uses an MILP formulation to optimise network configuration and minimise operating costs as described. The results are reported in Excel or text reports. The purpose of the model is to be used not as frequent as an Advanced Planning Scheduling (APS) system (daily, weekly or monthly) but for longer periods (such as quarterly, six months or yearly) to address strategic and tactical supply design aspects. Its
Table 17 Cost analysis and comparison of cases (,000 rmu) Cost analysis Case 1
Case 2
Case 3
Case 4
Global production costs Global distribution costs Global duties paid Global out-sourcing cost Infrastructure costs Material handling cost
225,641 22,060 4,503 42,230 13,800 3,447
223,558 21,397 5,942 57,458 15,300 3,394
206,798 21,923 5,197 92,053 13,800 3,447
222,863 21,979 4,392 29,233 13,800 3,447
Total costs
311,681
327,049
343,118
295,714
Difference (%)
0.00
+4.93
+10.08
5.12
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allocation decisions are set as production targets for the APS systems to optimise production sequences.
References Arntzen, B.C., Brown, G.G., Harrison, T.P., Trafton, L.L., 1995. Global supply chain management at digital equipment corporation. Interfaces 25, 69–93. Ballou, R.H., 2001. Unresolved issues in supply chain network design. Information Systems Frontiers 3 (4), 417–426. Beamon, B.M., 1998. Supply chain design and analysis: models and methods. International Journal of Production Economics 55, 281–294. Bilgen, B., Ozkarahan, I., 2004. Strategic tactical and operational production–distribution. International Journal of Technology Management 28, 151–171. Brooke, A., Kendrick, D., Meeraus, A., Raman, R., 1998. GAMS: A User’s Guide. GAMS Development Corporation. Fandel, G., Stammen, M., 2004. A general model for extended strategic supply chain management with emphasis on product life cycles including development and recycling. International Journal of Production Economics 89, 293–308. Gjerdrum, J., Shah, N., Papageorgiou, L.G., 2002. Fair transfer price and inventory holding policies in two-enterprise supply chains. European Journal of Operational Research 143, 582–599. Goetschalckx, M., Vidal, C.J., Dogan, K., 2002. Modeling and design of global logistics systems: a review of integrated
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strategic and tactical models and design algorithms. European Journal of Operational Research 143, 1–18. Guinet, A., 2001. Multi-site planning: a transhipment problem. International Journal of Production Economics 74, 21–32. Harrison, T.P., 2001. Global supply chain design. Information Systems Frontiers 3 (4), 413–416. Kaihara, T., 2003. Multi-agent based supply chain modelling with dynamic environment. International Journal of Production Economics 85, 263–269. Klose, A., Drexl, A., 2005. Facility location models for distribution system design. European Journal of Operational Research 162, 4–29. Levis, A., Papageorgiou, L.G., 2004. A hierarchical solution approach for multi-site capacity planning under uncertainty in the pharmaceutical industry. Computers & Chemical Engineering 28, 707–725. Papageorgiou, L.G., Rotstein, G.E., Shah, N., 2001. Strategic supply chain optimization for the pharmaceutical industries. Industrial Engineering and Chemistry Research 40, 275–286. Shapiro, J.F., 2004. Challenges of strategic supply chain planning and modeling. Computers & Chemical Engineering 28, 855–861. Tsiakis, P., Shah, N., Pantelides, C.C., 2001. Design of multiechelon supply chain networks under demand uncertainty. Industrial Engineering and Chemistry Research 40, 3585–3604. Vidal, C., Goetschalckx, M., 1997. Strategic production–distribution models: a critical review with emphasis on global supply chain models. European Journal of Operational Research 98, 1–18.
Int. J. Production Economics 111 (2008) 468–483 www.elsevier.com/locate/ijpe
Optimal production allocation and distribution supply chain networks Panagiotis Tsiakisa,, Lazaros G. Papageorgioub a
Process Systems Enterprise Limited, 107a Hammersmith Bridge Road, London W6 9DA, UK Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, London WC1E 7JE, UK
b
Received 31 March 2006; accepted 9 February 2007 Available online 24 March 2007
Abstract Enterprise optimisation can rapidly strip significant ‘‘bottom line’’ costs out of global operations, giving companies a real competitive edge. The benefits of managing supply chain networks by integrating operational, design and financial decisions have been acknowledged by the industrial and academic community. The objective of this work is to determine the optimal configuration of a production and distribution network subject to operational and financial constraints. Operational constraints include quality, production and supply restrictions, and are related to the allocation of the production and the work-load balance. Financial constraints include production costs, transportation costs and duties for the material flowing within the network subject to exchange rates. As a business decision the out-sourcing of production is considered whenever the organisation cannot satisfy the demand. A mixed integer linear programming (MILP) model is proposed to describe the optimisation problem. A case study for the coatings business unit of a global specialty chemicals manufacturer is used to demonstrate the applicability of the approach in a number of scenarios. r 2007 Elsevier B.V. All rights reserved. Keywords: Production allocation; Duties; Mixed integer linear programming; Optimisation; Supply chain
1. Introduction A global production and supply network can de defined as a set of existing or potential, manufacturing facilities, warehouses and distribution centres with multiple supply configurations and customers with demands. All these facilities can be located in
Corresponding author. Current address: IBM UK Ltd, 76-78 Upper Ground, South Bank, London SE1 9PZ, UK. Tel.: +44 20 8563 088; fax: +44 20 8563 0999. E-mail addresses: [email protected], [email protected] (P. Tsiakis).
different countries where different tax breaks and currencies apply. In today’s rapidly changing economic and political conditions global corporations face a continuous challenge to constantly evaluate and optimally configure their supply chain operations to achieve key performance indices (KPIs), either it is profitability, cost reduction or customer service. In this environment operations managers and planners need to address accurately questions such as which plants to operate, what product mix per plant, which distribution centre supplies which customer, what inventory levels are necessary to maintain service levels, which suppliers are to be used.
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2007.02.035
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Beamon (1998) identified the increasing attention placed on the performance, design, and analysis of the supply chain as a whole and provided an analysis of the available modelling methods categorising them to heuristic and mathematical programming approaches. Mathematical programming approaches are further categorised into (1) deterministic, (2) stochastic, (3) economic and (4) simulation. The necessity to develop strategic and tactical level supply chain planning models in order to address issues in a quantitative manner rather than the qualitative approaches used till now is acknowledged by the industry (Shapiro, 2004) and still remains an active research area. This has created many challenges both for researchers and practitioners who wish to successfully implement supply chain support systems. In a recent literature survey, Bilgen and Ozkarahan (2004) analyse previous research and review models for the production and distribution problem. A classification scheme was employed to categorise and compare strengths and weaknesses as they are reported in a table at the end of the review. Klose and Drexl (2005) review the status of research in facility location models for the design of distribution systems. Their work reviews state-of-the-art model formulations on strategic planning, distribution system design, facility location and mixed integer programming. Previous attempts to improve the performance of supply chain networks have mainly focused on the logistic aspects rather than the business decisions associated with the plant operation and production for the design of such networks. In an early attempt Arntzen et al. (1995) developed a mixed integer linear programming (MILP) ‘‘global supply chain model’’ (GSCM) aiming to determine: (1) the number and location of distribution centres, (2) customer-distribution centre assignment, (3) number of echelons, and (4) the product-plant assignment. The objective of the model is to minimise a weighted combination of total cost (including production, inventory, transportation, and fixed costs) and activity days as a bill of material problem. To the same direction and as supply chains become increasingly global, additional aspects such as differences in tax regimes, duty drawback and avoidance, and fluctuations in exchange rates also become important (Vidal and Goetschalckx, 1997). Tsiakis et al. (2001) have addressed a large number of the production and
469
logistics issues reported by Bilgen and Ozkarahan in a comprehensive work that models supply chain networks under demand uncertainty focusing on the production and transportation issues. The resulting MILP problem is solved to optimality using decomposition methods to reduce the computational effort required. The model reported does not include financial aspects such as duties and exchange rates. Guinet (2001) examines the economics of multi-site production systems using a two-level approach to allocate production to sites and address the workshop scheduling problem. A primal–dual heuristic approach was used to solve cases of this problem aiming to minimise variable and fixed costs. Goetschalckx et al. (2002), review the area of modelling and design of global logistics and propose two models, one for a global case where the aim is to calculate the transfer prices and a second one for a single country where the focus is on tackling efficiently seasonality in the demand. The focus is on the logistic aspects with the plants assumed multi-product without limitations. Kaihara (2003) uses an agent based approach to manage supply chains in terms of product allocation and resource distribution. The proposed model has the form of a discrete resource allocation problem under dynamic environment. The design of a supply chain network is characterised as a complex issue and the methods used to perform such an analysis vary depending on the problem type and the scope Ballou (2001). The author supports the idea that location analysis is most likely sufficient for most supply chain problems. Arguably, in a continuous changing environment and dynamic economic conditions such as costs, exchange rates, transportation structures and duties detail modelling is required to manage the data available and achieve expected performance. Harrison (2001) identifies the issues related to global supply chain design and operation while he points out the benefits of optimisation. Supply chain design needs to address issues such as manufacturing strategy, supplier base selection, outsourcing policies and new product and process design. Fandel and Stammen (2004) define strategic supply chain management as the long-term part of supply chain management, where product allocation and supply chain network configuration are determined. They propose a general linear mixed integer model for the design of business processes to include product life cycle.
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The key business issue of supply chain partnership was investigated by Gjerdrum et al. (2002). In their work, a mathematical programming formulation is presented for fair, optimised profit distribution between members of multi-enterprise supply chains based on a novel approach applying game theoretical Nash-type models to find the optimal profit level for each enterprise subject to given minimum profit requirements. Model decision variables include inter-company transfer prices, production and inventory levels, resource utilisation, and flows of products between echelons, subject to a deterministic sales profile, minimum profit requirements for each enterprise. Based on the work of Papageorgiou et al. (2001) on the strategic design of pharmaceutical supply chains, Levis and Papageorgiou (2004) extended the model to study the long-term capacity planning problem under uncertainty. The problem was formed as a mathematical programming model (MILP) to determine both product portfolio and plant capacity taking into account the uncertainty of clinical trials to develop a new product. The resulting large scale MILP problem was solved using two-stage, multi-scenario hierarchical algorithm, and the applicability was demonstrated through illustrative examples. The current paper proposes a strategic planning model for multi-echelon supply chain networks, integrating components associated with production, facility location and distribution along side with financial and business issues such as import duties, plant utilisation, exchange rates and plant maintenance. The network comprises a number of manufacturing sites, each using a set of flexible, shared resources for the production of a number of products. The manufacturing sites already exist at given locations, so do the customer zones. Although the location of distribution facilities is given, the design in terms of capacity of each distribution centre and its connectivity is considered as part of the optimisation problem. The model developed and presented in the next sessions is more generic and can be used to address design issues of the supply chain such as production plant location and distribution centre location. Section 2 of this paper presents the problem statement and description, while in Section 3 we present an MILP formulation of the problem for the optimal design and operation of global supply chain networks, and Section 4 presents an industrial case study. Section 5 concludes by summarising the
results and highlights directions for further research. 2. Problem description This work considers the optimal design and operation of multi-product, multi-echelon global production and distribution networks. The network consists of a number of existing multi-product manufacturing sites at fixed locations, a number of distribution centres, and finally a number of customer zones at fixed locations. In general, each product can be produced at several plants at different locations. The production capacity of each manufacturing site is modelled in terms of a set of linear constraints relating the mean production rate per product to the availability of the plant and the number of change-overs between campaigns. Distribution centres are described by upper and lower bounds on their material handling capacity and they can be supplied from more than one manufacturing plants and can supply more than one customer zone. However, ‘‘single sourcing’’ constraints requiring that a distribution centre be supplied by a single plant can also be accommodated. Each customer zone places demands for one or more products. These demands may be assumed to be known a priori. A customer may be served by more than one distribution centre. Alternatively, single sourcing constraints, according to which a customer zone must be served by a single distribution centre, may be imposed by modifying the constraints. Operational costs include those associated with production, handling of material at distribution centres, transportation and duties. Transportation costs are assumed to be linear functions of the actual flow of the product from the source stage to the destination stage. Additionally to transportation costs we have taxes and duties. The decisions to be determined include the product portfolio per production plant, production amounts, utilisation level, and transportation links to establish in the network along side with material flows. The objective is the minimisation of the total annualised cost of the network, taking into account both infrastructure and operating costs. This paper considers a steady-state form of the above problem according to which demands are time-invariant and all production and transportation flows determined by the optimisation are considered to be timeaveraged quantities.
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3. Optimal design of global production and distribution network The above problem is formulated mathematically as an MILP optimisation problem. We aim to obtain an optimal design of this network. 3.1. Notation The notation to be used in this section is described below: Indices/sets I J K L
products plants possible distribution centres customer demand zone Parameters
C DH ik C D;e k C D;s k C dijk C dikl C P;e j C P;s j C Pij C Si C Tijk C Tikl Dmin k , Dmax k Dil Hj Mj
unit handling cost for product i at distribution centre k annualised fixed cost of establishing a distribution centre at location k annualised fixed cost of shutting down a distribution centre at location k unit duty cost for product i leaving production plant j to distribution centre k unit duty cost for product i leaving distribution centre k to customer l annualised fixed cost of establishing a production plant at location j annualised fixed cost of shutting down a production plant at location j unit production cost for product i at plant j unit production cost for product i supplied to the network from third parties unit transport cost for product i from plant j to distribution centre k unit transport cost for product i from distribution centre k to customer zone l minimum/maximum distribution centre capacity demand for product i in customer zone l operating horizon of production site j in days per annum annual days of maintenance of production site j
N cij max Pmin ij , Pij
Qmin jk , Qmax jk Qmin kl , Qmax kl max T min ij =T ij
rdj ajk akl b g dik
z t
471
number of campaigns of product i at production plant j minimum/maximum production capacity of plant j for product i minimum/maximum rate of flow of materials transferred from plant j to distribution centre k minimum/maximum rate of flow of materials transferred from distribution centre k to customer zone l minimum/maximum availability of plant j for the production of product i per annum in days expected daily production rate of plant j duty coefficient relating production plant j to distribution centre k duty coefficient relating distribution centre k to customer l coefficient applied to production cost for duty purposes coefficient applied to transportation cost for duty purposes coefficient relating capacity of distribution centre k to flow of product i handled utilisation parameter in days change-over coefficient in days
Continuous variables Dk Oik Pij Qijk Qikl Tij Uj DU
capacity of distribution centre k out-sourced product i delivered to distribution centre k production rate of product i in plant j rate of flow of product i transferred from plant j to distribution centre k rate of flow of product i transferred from distribution centre k to customer zone l days allocated for the production of product i in plant j utilisation of production plant j as production days per year maximum allowed difference in utilisation between plants
Binary variables Yj Yk
1 if production plant j is to be established, 0 otherwise 1 if distribution centre k is to be established, 0 otherwise
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Xjk Xkl Wij
1 if production plant j is assigned to distribution centre k, 0 otherwise 1 if distribution centre k is assigned to customer zone l, 0 otherwise 1 if production plant j is to produce product i, 0 otherwise
The mathematical model proposed for this problem is an MILP problem as described below. 3.2.1. Network structure constraints A link between a production plant j and a distribution centre k may exist only if production plant j is established: 8j; k.
(3.1)
If a distribution centre k is established, it can then be served by more than one production plant j: X X jk XY k ; 8k. (3.2) j
This constraint can be transformed into a single source constraint for case where this restriction applies. In this case the constraint has to be written as X X jk ¼ Y k ; 8k. (3.20 ) j
The link between a distribution centre k and a customer zone l may exist only if the distribution centre is established: X kl pY k ;
8k; l.
(3.5)
i
Flow of material from distribution centre k to customer zone l can take place only if the corresponding connection exists: X Qikl pQmax 8i; k; l. (3.6) Qmin kl X kl p kl X kl ; i
3.2. Mathematical formulation of deterministic problem
X jk pY j ;
corresponding connection exists: X X p Qijk pQmax 8i; j; k. Qmin jk jk jk X jk ;
(3.3)
Each customer can be supplied by more than one distribution centres to satisfy demand: X X kl X1; 8l. (3.4) k
In accordance with the ‘‘single sourcing’’, each customer zone can be served by exactly one distribution centre and the constraint has to be modified as follows: X X kl ¼ 1; 8l. (3.40 ) k
3.2.2. Logical constraints for transportation flows Flow of material from production plant j to distribution centre k can take place only if the
max appearValues for the upper bounds Qmax jk , Qkl ing on the right-hand sides of constraints (3.5) and (3.6) are determined by contracts in place for the transportation of materials. The bounds apply on the total amount sent to each destination.
3.2.3. Material balances The actual rate of production of product i by plant j must equal the total flow of this product from plant j to all distribution centres k: X Pij ¼ Qijk ; 8i; j. (3.7) k
Assuming that there is no stock accumulation or depletion (i.e. steady-state operation), the total rate of flow of each product leaving a distribution centre must equal the total rate of flow entering this node of the supply chain network: X X Qijk þ Oik ¼ Qikl ; 8i; k. (3.8) j
l
Ideally the total rate of flow of each product i received by each customer zone l from the distribution centres must be equal to the corresponding market demand. In the case where this amount is not sufficient to cover the demand this is partially filled by out-sourced material which is supplied to the distribution centres: X Qikl ¼ Dil ; 8i; l. (3.9) k
3.2.4. Production constraints An important issue in designing the distribution network is the ability of the manufacturing plants to cover the demands of the customers as expressed through the orders received from the warehouses. The rate of production of each product at any plant cannot exceed certain limits. Thus, there is always a maximum production capacity for any product; moreover, there is often a minimum production rate that must be maintained while the
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(i.e. Yk ¼ 1):
plant is operating: max Y j Pmin ij pPij pPij Y j ;
8i; j.
(3.10)
Production is restricted by the number of change-overs and number of campaigns performed at a site. Also maintenance has to be taken into account: X X T ij pðH j M j ÞY j t N cij W ij ; 8j. (3.11)
max Dmin k Y k pDk pDk Y k ;
The number of days available for the production of product i in production site j is limited by the total availability of the plant, subject to the plant producing this product: max T min ij W ij pT ij pT ij W ij ;
8i; j.
(3.12)
The production per site is organised in terms of campaigns due to the seasonal nature of the business, the demand patterns and the portfolio of products which require long cleaning periods of the production lines between products. Therefore the production capacity is reduced based on the number of change-overs. We assume that on average the same length of cleaning is required between products. The total production of each product depends on the daily production capability of the plant and the number of days allocated per year: 8i; j.
(3.13)
The utilisation of each plant is equal to the number of production days per year and is given by X Uj ¼ T ij ; 8j. (3.14)
where dik is a given coefficient that relates product and distribution centre capacity. 3.2.6. Objective function In general, a distribution network involves both capital and operating costs. The former are one-off costs associated with the establishment of the infrastructure of the network, and in particular its warehouses and distribution centres. On the other hand, operating costs are incurred on a daily basis and are associated with the cost of production of material at plants, the handling of material at warehouses and distribution centres, and the transportation of material through the network. 3.2.6.1. Fixed infrastructure costs. The infrastructure costs considered by our formulation are related to the establishment or shut-down of a production plant or a distribution centre at a candidate location. These costs are expressed in the following objective function terms: X P;e X P;s Cj Y j þ C j ð1 Y j Þ j
þ
DU XU j U j0 ;
8j; j 0 aj,
DU XU j0 U j ;
8j 0 ; jaj 0 ,
DU pz.
(3.15)
3.2.5. Capacity of distribution centres The capacity of a distribution centre k generally has to lie between given lower and upper bounds, Dmin and Dmax provided, of course, that k k , the distribution centre is actually established
(3.16)
i;l
i
Due to multi-site production we want to ensure that production is distributed evenly between sites, therefore utilisation per site should be similar with the difference limited to a specified range. The following constraints ensure that the total utilisation per site remains close:
8k.
We generally assume that the capacities of the distribution centres are related linearly to the flows of materials that they handle. This is expressed via the constraints: X Dk X dik Qikl ; 8k, (3.17)
i
Pij ¼ rdj T ij ;
473
X k
j
C D;e k Yk
þ
X
C D;s k ð1 Y k Þ.
k
If we assume that the production plants are already established, we need to provide the option of expansion. Therefore, we do consider the capital cost associated with their re-design and construction. We ignore any infrastructure cost associated with customer zones. 3.2.6.2. Production cost. The production cost is given by the product of the production rate Pij of product i in plant j, with the unit production cost C Pij . The corresponding term in the objective function is of the form X C Pij Pij . i;j
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The production cost C Pij is expressed in terms of local currency. As part of the production cost we have to account the cost of change-overs as lost production X t C Pij N cij W ij . ij
As production costs we account for the material out-sourced to third parties to satisfy excess demand: X C Si Oik . i;k
3.2.6.3. Material handling costs at distribution centres. Handling costs can usually be approximated as linear functions of the total throughput. They can be expressed as follows: ! X X DH C ik Qikl : i;k
l
The unit duty cost is a function of the handling and transportation costs between the source (distribution centre) and destination (customer). It is applied as a coefficient on the combined material handling and transportation cost: DH T CD ikl ¼ aikl ðbC ik þ gC ikl Þ.
The contribution to the objective function is given by X CD ikl Qikl . i;k;l
3.2.6.6. Overall objective function. By combining the cost terms derived in Sections 3.2.6.1–3.2.6.5, we obtain the total cost of the supply chain network, which is to be determined by the optimisation: min
production plant infrastructure costs P P;e P C j Y j þ C jP;s ð1 Y j Þ j
j
Handling and temporary storage costs at production plants are included in the production cost.
þdistribution centre infrastructure costs P D;e P C k Y k þ C D;s k ð1 Y k Þ
3.2.6.4. Transportation cost. The unit transportation cost is constant independent of the product transported and depends only on the source and destination node. Transportation costs that we include are those between production plant to distribution centres and distribution centres to customers. Therefore the following term needs to be added to the objective function: X X C Tijk Qijk þ C Tikl Qikl .
þproduction cost P P P P C ij Pij þ C Si Oik þ t C Pij N cij W ij
k
i;j;k
i;k;l
i;j
i;k
i;j
þmaterial handling cost at distribution centres P DH P C ik Qikl i;k
l
þtransportation costs P T P T C ijk Qijk þ C ikl Qikl
i;j;k
i;k;l
þduties cost P D P D C ijk Qijk þ C ikl Qikl : i;j;k
3.2.6.5. Duties. In the specific model duties apply to the material transferred from the production sites to the distribution centres and is calculated in currency of the importing country. The unit duty cost is a function of the production and transportation costs between the source and destination. It is applied as a coefficient on the combined production and transportation costs:
k
ð3:18Þ
i;k;l
The above minimisation is subject to all the constraints presented in Sections 3.2.1–3.2.5. The objective function can be modified to define a maximisation problem based on the profit by satisfying the product demand at a specific product price.
P T CD ijk ¼ ajk ðbC ij þ gC ijk Þ.
4. Case study
The contribution to the objective function is given by X CD ijk Qijk .
To demonstrate the applicability of the proposed model we examine the performance of a global organisation with a supply chain extending in many countries in different continents where multiple currencies and taxes apply.
i;j;k
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The model was applied on a network consisting of six manufacturing plants located at different countries on different continents. Each plant can produce six types of products using a number of shared production resources, therefore only one product may be produced at a time. A number of possible distribution centres are considered to handle the material based on the market demand placed by the customer zones. Customer zones comprise eight large geographical areas. The network superstructure is given in Fig. 1. The superstructure assumes complete connectivity between all sites which is subject to constraints regarding material transfers. We examine different scenarios of operation to demonstrate the benefits of optimisation over decisions imposed by practice or heuristics. These scenarios are:
The model described above is implemented in GAMS (Brooke et al., 1998) and CPLEX is the solver used to solve the MILP problem. Other solvers were used such as (Xpress-MP, GLPK and LP-Solve) with similar results.
4.1. Problem description This section describes the data required by the model to set values for the parameters. All available data used to produce the results are presented in Sections 4.1.1–4.1.3 and Tables 1–8.
4.1.1. Production plants The theoretical maximum production capacity of each plant with respect to each product (i.e. the parameter Pmax of the formulation) is given as a ij result of Table 1 and the maximum availability of the plant. The corresponding minimum production rates Pmin are taken to be zero unless the product is ij selected. The production per plant in term of tonnes of product per day is given in Table 1. This is the bulk product capacity. The operating horizon is 365 days per plant and maintenance duration per production site is 10 days except plants 5 and 6 where we have 7 days.
free optimisation where all decisions are determined by the model subject to the constraints; optimise network flows when product allocation decisions and network structure has been fixed; optimise the network when each plant can manufacture up to three allocated products; examine the network sensitivity by changing some of the parameters such as utilisation constraint.
Production plant PL1
Distribution centre Customer zone Possible connection C8
PL2
DC1
DC2
PL3
C2 DC3 C1 C6
C3
PL5 DC5
PL4 C5 PL6 C7 DC4
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C4 DC6 Fig. 1. A typical supply chain representation.
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Table 1 Daily production rate per production site (tonnes/day) PL1 73.4
PL2 12.7
PL3 35.1
PL4 34.4
PL5 11.0
PL6 10.0
Table 5 Costs associated with the distribution centres upon establishment
Table 2 Unit production cost per product per plant (rmua/kg) Product
P1 P2 P3 P4 P5 P6 a
Maximum production for each product per site is T max ¼ 365 days, while the minimum campaign ij length is T min ¼ 7 days. ij The change-over duration is assumed to be t ¼ 1 day and we assume that the utilisation coefficient is z ¼ 10 days.
Distribution centre costs
Production site PL1
PL2
PL3
PL4
PL5
PL6
4.68 3.23 4.18 2.48 1.43 2.15
4.53 3.17 4.19 2.71 1.49 2.15
5.17 3.21 5.17 2.54 1.55 2.22
5.04 3.87 4.35 2.74 1.41 2.40
4.27 3.12 3.71 2.43 1.28 2.07
4.26 3.97 3.70 2.42 1.27 2.06
rmu: relative money units.
Table 3 Transportation cost between production sites and distribution centres (rmu/kg)
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
0.053 0.077 0.141 0.00 0.038 0.117
0.051 0.071 0.125 0.143 0.00 0.038
0.056 0.077 0.119 0.144 0.038 0.00
0.062 0.089 0.126 0.138 0.236 0.178
0.081 0.127 0.00 0.182 0.117 0.236
DC2
DC3
DC4
Fixed infrastructure cost (,000 rmu) 4,300 2,900 3,100 2,200 Material handling cost per product (rmu/kg) P1 0.07 0.068 0.077 0.076 P2 0.048 0.048 0.048 0.058 P3 0.063 0.063 0.077 0.065 P4 0.037 0.041 0.038 0.041 P5 0.021 0.022 0.024 0.021 P6 0.032 0.032 0.033 0.036
DC5
DC6
1,300
1,500
0.064 0.047 0.056 0.036 0.019 0.031
0.064 0.060 0.056 0.036 0.019 0.031
Table 6 Customer zone demand per product (tonnes) Product Customer zone
From/to Distribution centre production site DC1 DC2 DC3 0.00 0.065 0.083 0.107 0.183 0.168
DC1
C1 P1 P2 P3 P4 P5 P6
C2
C3
C4
C5
C6
C7
C8
5,701 3,665 3,398 2,686 1,342 2,310 2,436 1,819 2,116 365 1,468 1,355 910 630 1,049 748 3,246 887 1,369 1,353 609 410 1,219 679 2,582 295 3,016 466 556 700 1,436 906 3,683 437 2,284 922 794 690 1,578 844 294 64 311 1,173 130 110 172 323
Table 4 Values of coefficient aijk to apply on duties structure (%) From/to production site
PL1 PL2 PL3 PL4 PL5 PL6
Product group
P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5 P1–P6 P5
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
0.0 0.0 0.0 0.0 6.5 6.5 0.0 0.0 0.0 0.0 6.5 6.5
0.0 0.0 0.0 0.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0
7.1 3.8 7.1 3.8 0.0 0.0 4.1 0.3 7.1 3.8 4.1 0.3
53.1 53.1 53.1 53.1 53.1 53.1 0.0 0.0 53.1 53.1 53.1 53.1
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 0.0 0.0 10.0 10.0
5.0 12.5 5.0 12.5 5.0 12.5 5.0 12.5 5.0 12.5 0.0 0.0
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DC1 DC2 DC3 DC4 DC5 DC6
Customer zone C1
C2
C3
C4
C5
C6
C7
C8
0.00 0.65 0.90 1.13 1.89 1.74
0.62 0.00 1.40 1.52 2.16 1.78
0.81 1.27 0.0 1.82 2.61 2.36
0.53 0.77 1.41 0.0 1.66 1.17
0.51 0.73 1.25 1.43 0.00 0.00
0.56 0.77 1.19 1.44 0.57 0.59
1.31 1.38 1.35 1.93 1.57 1.36
1.66 1.77 1.29 1.54 1.34 1.23
Table 8 Duty coefficient for material transferred between distribution centre and customer aikl (%) Distribution centre
DC1 DC2 DC3 DC4 DC5 DC6
Customer zone C1
C2
C3
C4
C5
C6
C7
C8
0.0 0.0 6.5 6.5 6.5 6.5
0.0 0.0 9.0 9.0 9.0 9.0
7.1 7.1 0.0 4.1 7.1 4.1
53.1 53.1 53.1 0.0 53.1 53.1
12.5 12.5 12.5 12.5 0.0 12.5
11.0 11.0 11.0 11.0 11.0 11.0
17.0 17.0 17.0 17.0 17.0 17.0
15.0 15.0 15.0 15.0 15.0 15.0
The unit production costs per product for each plant are given in Table 2. Note that all costs displayed have been converted to relative money units based on certain exchange rates for confidentiality reasons. Sensitivity analysis was performed on the exchange rate fluctuation and the average price was used. 4.1.2. Distribution centres The distribution centres to be designed are assumed to have sufficient capacity to handle the material received and distributed and the logistics management is not an issue at this level. In order for a connection between a production plant and distribution centre to exist that must be at least for a total flow of 1,000 tonnes (i.e. Qmin jk ¼ 1; 000 8j; k). The transportation costs from the production plants to the distribution centres are given in Table 3. This is the unit transportation cost and is independent of the product type and the amount transported. The amount transported to the distribution centres is subject to duties as they have been defined
477
in Section 3.2.6.5. Table 4 describes the coefficients used between production sites and distribution centres. For this case parameter b ¼ 1.1 and g ¼ 1.0. The relationship can then be written as aijk ð1:1 C Pij þ C Tijk Þ. The establishment of a distribution centre occurs at fixed costs for the organisation. These amounts have been amortised to annual amounts. Depending on the materials stored there is a handling cost per product. Both costs are given in Table 5. 4.1.3. Customer zones The customer zones are located close to the distribution centres and the allocation for the specific problem is considered fixed, therefore distribution costs can be ignored. The demand per product and customer zone is given in Table 6. The transportation costs from distribution centres to customer demand zones are given in Table 7. The amount transported to the customer demand zones is subject to duties as they have been defined in Section 3.2.6.5. Table 8 describes the coefficients used between distribution centres and customers. For this case parameter b ¼ 1.0 and g ¼ 1.0. The relationship can then be written as T aikl ðC DH ik þ C ikl Þ.
4.2. Network optimization—base scenario The first case is a free optimisation exercise where the model is allowed to determine all the decisions required such as product allocation per plant and production level, establishment of distribution centres and customer allocation, material flows and distribution centre capacity. The optimal solution for the network is given in Fig. 2. Table 9 shows the product allocation per plant and the number of days of production per product. Out-sourced material is purchased to cover demand that cannot be satisfied by internal production and is presented as the last column of the same table. This material is directly supplied to the distribution centres and from there to the customer zones assigned. The total material supplied from the production plants to distribution centres is shown in Table 10. This is subject to the material flow constraint that
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PL1
PL2
DC1 PL3
DC2
C8
C2
DC3
C6 C1
PL5
C3 DC5 PL4 C7
C5 PL6
DC4 C4
Fig. 2. Optimal network configuration for base case.
Table 9 Product allocation per plant and production days allocated Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
148 54 69 0 58 0
321 0 0 0 0 14
0 61 50 124 95 0
173 42 66 0 0 50
131 108 0 0 0 96
133 0 58 48 94 0
Utilisation Total
329
335
330
331
335
333
applies for an established link. At the bottom of the table the total material handling capacity of each distribution centre is given. This includes the amount received by third parties as out-sourced production. Material flows from a distribution centre, where it has been established to the assigned customers, is equal to the total demand placed by the customer. The flow per arc equals to the total product demand per customer since we enforce single source constraints. The total annual cost of operation for this case is 311,681,000 rmu. Individual contributions to the objective function are given in Table 17.
0 0 0 5,097 0 2,289
Table 10 Material flow from production plants to distribution centres (in tonnes) From/to production site
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
20,765 2,096 1,000 3,258 1,000 0 1,418 0 1,000 0 1,000 0
1,000 0 0 0 10,538 0 3,656 6,316 0 0 1,337 0
0 0 0 0 2,340 1,315
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
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4.3. Fixed product allocation and customer assignment
479
plants can produce the whole range of products and the optimisation is used to determine product allocation, material flows within the network, and the connections between plants, distribution centres and customer zones. The actual production per site in terms of days is given in Table 13. Material which is out-sourced and supplied directly to the distribution centres by third parties is given in as the last column of the same table. The flow of material in the network is given in Table 14. Fig. 4 shows the optimal network configuration and the customer allocation to distribution centres, while the associated cost is 343,218,000 rmu. The cost analysis is given in Table 17. Comparing this network structure with the configuration of the base case we can see that the connections between plants and distribution centres have changed. This is due to the different product portfolio.
This case assumes that production allocation and network configuration in terms of customer allocation to distribution centres are decisions already taken. Product allocation is made according to plant capabilities and bidding process from the plants. Secondary, customer demands are assigned to the nearest possible geographical site. These decisions are based on the planning experience—can also be characterised as rules of thumb or heuristics. As a result the model size is reduced in terms of number of decision variables need to be determined since Xkl and Wij are fixed. The model is allowed to optimise the production levels (as days per year and campaigns) and flows within the network as well as connections between plants and distribution centres. Table 11 shows the activity levels for each plant based on the preallocation of products. Out-sourced material purchased for this case is given as the last column of Table 11. More products are out-sourced and its total is higher than the base case. The flow of material between plants and distribution centres is given in Table 12. The total cost of operation in this case is 327,049,000 rmu. The break-down of individual costs is given in Table 17. The solution of the problem is given in Fig. 3 which also shows the customer assignment to distribution centres. These connections were fixed.
Table 12 Material flow between production plants and distribution centres (in tonnes) From/to production site
Distribution centre DC1
4.4. Maximum allocation of three products per plant In this case it is assumed that each plant is allowed to manufacture up to three products. All
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
19,869 2,197 1,000 3,156 0 0 1,000 0 0 0 0 0
0 0 0 0 9,482 0 1,000 6,316 0 0 0 0
0 0 0 0 3,260 0
1,353 0 1,634 2,936 0 3,583
Total handling capacity
22,362 5,713
11,846 7,955
4,341
13,209
Table 11 Production per plant as days per product Product
P1 P2 P3 P4 P5 P6 Utilisation Total
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
91 50 62 42 74 0
327 0 0 0 0 0
84 60 42 56 75 0
165 42 70 0 49 0
69 91 59 28 80 0
133 42 58 28 66 0
319
327
317
326
327
327
1,711 0 134 4,323 0 2,467
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PL1
PL2
DC1
DC2
PL3
C2 DC3
C6 C1
PL5
C3 DC5 PL4 C5 PL6
DC6 C7
DC4 C4
C8 Fig. 3. Network configuration for second case.
Table 13 Production levels in days per plant Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
131 0 82 0 86 0
283 0 0 0 0 16
84 0 0 125 90 0
145 74 70 0 0 0
118 109 0 0 72 0
98 107 0 0 94 0
Utilisation Total
289
289
289
289
289
289
Table 14 Material flow between production plants and distribution centres (in tonnes) From/to production site
0 3,840 1,344 5,574 0 2,269
4.5. Sensitivity analysis on utilisation factor and change-over duration
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
19,319 1,615 1,000 2,797 1,000 0 0 0 1,000 0 0 0
1,000 0 0 0 9,477 0 4,620 5,316 0 0 1,274 1,000
0 0 0 0 1,978 1,000
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
The base scenario case (case 1) was resolved for different values of utilisation factor z. As a result of these change no modification to the solution of the base case was observed. This is primarily to the fact that there is no spare capacity in the production plants and they are utilised to the maximum available rate. Many companies identify the change-overs as one of the major factors limiting the production capacity and flexibility of the plants. We are
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PL1
PL2
DC1 PL3
481
DC2
C8
C2 DC3 C1
PL5
C6
C3
DC5 PL4
C7
C5 PL6
DC4 C4
Fig. 4. Network configuration when product allocation has been fixed.
Table 15 Production per plant in days per year Product
Actual production per production site (days)
Out-sourced (tonnes)
PL1
PL2
PL3
PL4
PL5
PL6
P1 P2 P3 P4 P5 P6
128 48 82 0 82 0
334 0 0 0 0 14
84 60 0 120 75 0
116 42 70 0 50 62
131 109 59 49 0 0
133 42 58 28 84 0
Utilisation Total
340
348
339
340
347
345
examining the case where the change-over duration is halved to 12 h instead of one day. The reduction of change-over duration results to a change of product portfolio per plant. This is summarised in Table 15. Out-sourced material is purchased to cover demand that cannot be satisfied by internal production. The amount of material purchased is smaller than the material bought in the base case as a result of the increased utilisation. The flow of material in the network is given in Table 16. The total cost of operation for this case is 295,714,000 rmu and a cost analysis is given in
0 0 122 4,957 0 130
Table 17. The network structure remains the same as that in Fig. 2. 4.6. Result analysis The results obtained demonstrate clearly the savings of optimisation against heuristic decisions that dictate part of the network structure. The savings are significant to justify the re-design of the supply chain to comply with the results obtained design. The benefits are a result of a better utilisation of the plants by selecting suitable product portfolios, minimisation of the out-sourced material and
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savings on total transportation and duties. Savings also result from infrastructure decisions since only five distribution centres are needed to serve the customer basis. Although the plants are multi-purpose it is beneficial for the organisation to operate specific plants in a dedicated mode. This reduces switches between products and production costs. Comparing cases 3 and 1 it is obvious that there is an optimal product portfolio per plant thus reducing outsourced material. It is clear from case 4 that further savings are possible if the plant is re-engineered to reduce the duration of change-overs. The additional savings result from the reduction of out-sourced purchased material. 5. Conclusions This paper has proposed an integrated model based on a detailed mathematical programming Table 16 Material flow between production plants and distribution centres (in tonnes) From/to production site
Distribution centre DC1
DC2
DC3
DC4
DC5
DC6
PL1 PL2 PL3 PL4 PL5 PL6
20,068 1,894 1,000 3,423 1,000 0 1,236 0 1,000 0 0 0
1,000 0 0 0 10,888 0 2,974 7,489 0 0 2,302 0
0 0 0 0 2,461 1,478
0 0 0 0 0 0
Total handling capacity
30,252 5,713
17,165 7,955
4,341
0
formulation that addresses some of the complex issues related to the design and operation of global supply chain networks. The focus is on financial and tactical operational aspects within the organisation taking into account production balancing amongst sites. Between other business benefits is the operational and distribution efficiency of the network, visibility and control of the supply chain and capability to perform towards KPIs such as operational cost, customer satisfaction and product quality. Moreover, the impact of decisions on the design and tactical operation can be quantified and evaluated. The data used are extracted directly from ERP systems making such approaches easy to use and easy to update every time the application is used. The proposed MILP model aims to assist senior operations management to decisions about production allocation, production capacity per site, purchase of raw materials and network configuration taking into account financial aspects (exchange rates, duties, etc.) and costs. Currently, the organisation under study employs a number of spreadsheet where ERP data are manipulated using Excel formulas to calculate average costs and plant capacities. The model proposed is packaged as an add-in tool which imports data from Excel but uses an MILP formulation to optimise network configuration and minimise operating costs as described. The results are reported in Excel or text reports. The purpose of the model is to be used not as frequent as an Advanced Planning Scheduling (APS) system (daily, weekly or monthly) but for longer periods (such as quarterly, six months or yearly) to address strategic and tactical supply design aspects. Its
Table 17 Cost analysis and comparison of cases (,000 rmu) Cost analysis Case 1
Case 2
Case 3
Case 4
Global production costs Global distribution costs Global duties paid Global out-sourcing cost Infrastructure costs Material handling cost
225,641 22,060 4,503 42,230 13,800 3,447
223,558 21,397 5,942 57,458 15,300 3,394
206,798 21,923 5,197 92,053 13,800 3,447
222,863 21,979 4,392 29,233 13,800 3,447
Total costs
311,681
327,049
343,118
295,714
Difference (%)
0.00
+4.93
+10.08
5.12
ARTICLE IN PRESS P. Tsiakis, L.G. Papageorgiou / Int. J. Production Economics 111 (2008) 468–483
allocation decisions are set as production targets for the APS systems to optimise production sequences.
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