# Design of Hybrid Multimodal Logistic Hub Network with Postponement Strategy

Imane Essaadi, Bernard Grabot, Pierre Fenies

► To cite this version:

Imane Essaadi, Bernard Grabot, Pierre Fenies. Design of Hybrid Multimodal Logistic Hub Network with Postponement Strategy. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2017, Hamburg, Germany. pp.40-48, 10.1007/978-3-319-66926-7_5 . hal-01707244

HAL Id: hal-01707244

https://inria.hal.science/hal-01707244

Submitted on 12 Feb 2018

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Design of hybrid multimodal logistic hub network with postponement strategy

I. Essaadi¹,², B. Grabot¹,³, P. Féniès¹,²

¹ Mohammed VI Polytechnic University – EMINES, 43140 Benguerir, Maroc,

²Paris Ouest Nanterre University, 92001 Nanterre Cedex, France

³LGP/INP-ENIT – Toulouse University, 31000 Toulouse, France

Imane.essaadi@emines.um6p.ma, bernard.grabot@enit.fr, pierre.fenies@u-paris10.fr

**Abstract.** This paper suggests a method allowing to design a hybrid logistic hub network in the context of mass customization, postponement being performed in hubs having industrial capabilities in addition to logistic ones. We propose a two-stage mathematical mixed integer linear programming model for: 1) logistic hub network design 2) postponement location in the designed network. The suggested model manages characteristics not yet taken into account simultaneously in the literature: hierarchical logistic structure, postponement strategy, multi-commodity, multi-packaging of goods (raw materials or components vs. final products), multi-period planning. The solutions are compared through service level and logistic costs.

**Keywords:** hybrid logistic hub, postponement, mass customization, service level, hierarchical logistic structure, multi-period, multi-commodity.

## 1 Introduction

The implementation of networks of logistic hubs usually allows to decrease transportation costs and delivery delays in comparison with direct source/destination transportation [1]. Within logistic hubs, material flows coming from different origins are sorted, consolidated according to their destination then transported using unimodal or multimodal transport. Two families of hubs can be distinguished: pure logistic hubs, providing standard logistic services (warehousing, inventory management, packaging, labeling, orders preparation or cross-docking, sorting and transport /distribution) and combined logistic / industrial hubs, offering high added-value services on logistics (such as co-packing) and/or industrial functionalities allowing the final customization of the product.

Late customization of products (often called "postponement") was considered for many years by some industries such as computers, printers, medical products and fertilizers [2]. Pushing this logic to its limits, multinational firms now attempt to customize their products within their distribution centers, like Hewlett-Packard producing DeskJet printers in its factory in Singapore and customizing them for the European and Asian markets within its European distribution center near Stuttgart. In
that new context, this paper aims at defining the optimal design of a network of logistic hubs with postponement strategy integration, in a context of mass customization. The distribution network has four levels: production plants, regional logistic hubs, sub-regional logistic hubs, and urban/rural distribution centers. The network processes goods with possibly different packaging (raw materials/components and finished products). The main originality of this study is that the joint location of logistic hub and postponement units was rarely addressed in the literature on supply chain network design. This original concept challenges the classical production-distribution model where a clear distinction is made between production and distribution networks [3].

## 2 State of the art

The hub network design problem, also known as the distribution network design problem, was intensively studied in the literature on global distribution networks [1, 4]. An analysis of this literature is summarized in Figure 1.

<table><caption>Figure 1. Logistic hub network review analysis</caption><thead><tr><th></th><th></th><th>Paper</th><th>Proposal</th><th>Medo and Stefan (2006)</th><th>Rodriguez et al (2007)</th><th>Gelareh et al (2010)</th><th>Contreras et al (2011)</th><th>Alumur et al (2012 a)</th><th>Alumur et al (2012 b)</th><th>Albareh et al (2012)</th><th>Graek et al (2014)</th><th>Alibeyg et al (2015)</th><th>Gelareh et al (2015)</th></tr></thead><tbody><tr><td rowspan="2">Hub network structure</td><td>Single level</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Multiple levels</td><td></td><td>X</td><td>X</td><td></td><td></td><td>X</td><td>X</td><td>X</td><td>X</td><td></td><td></td><td></td></tr><tr><td rowspan="6">Hub Features</td><td rowspan="2">Uncapacitated hub</td><td></td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fixed</td><td></td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Hub capacity</td><td>Based on known capacity</td><td></td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>To be determined</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Hub services</td><td>Logistical hubs</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Industrial hubs</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Allocation strategy</td><td>Static (S)/ Dynamic (D)</td><td></td><td>S</td><td>D</td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>D</td></tr><tr><td>Single (S)/Multiple (M)</td><td></td><td>M</td><td>S</td><td></td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>S</td><td>M</td><td>M</td></tr><tr><td rowspan="10">Transport Organization</td><td rowspan="4">Means of transportation</td><td>Transport Mode</td><td>Uni-modal</td><td>X</td><td></td><td>X</td><td>X</td><td>X</td><td></td><td>X</td><td>X</td><td>X</td><td></td></tr><tr><td>Type of fleet of vehicles</td><td>Multi-modal</td><td>X</td><td></td><td>X</td><td></td><td>X</td><td></td><td>X</td><td></td><td></td><td></td></tr><tr><td rowspan="2">Vehicles capacity</td><td>Homogenous</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Heterogenous</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Transport packaging</td><td>Uncapacitated</td><td></td><td></td><td>X</td><td></td><td>X</td><td>X</td><td>X</td><td>X</td><td></td><td></td></tr><tr><td>Determined</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Commodity information</td><td>To be determined</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Identical containers</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Service level</td><td>Heterogeneous containers</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Unity type</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2"></td><td>Multi-commodity</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Time</td><td>X</td><td>X</td><td>X</td><td></td><td>X</td><td>X</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2"></td><td>Distance</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
Few authors consider a multi-level network [4], while no paper addresses the integration of industrial services. Origin and destination nodes might be either allocated to a unique hub or to multiple ones: [5] considers multiple allocation of clients to located hubs while [6] studies multiple allocation of plants and customers to intermediate hubs. Service level can be addressed through the definition of a maximum distance between distribution center and market zone [7] or through a delivery delay [8, 9]. Many papers assume that demand is deterministic, which is seldom true. Multiple commodity, allowing to consider products using different transportation means, is only considered by few researchers (cf. Figure 1).

To our best knowledge, no paper considers a physical transformation of goods while transiting a hub (from bulk material to packs or pallets for instance). [10] states that one of the main characteristics of supply chain network design models is their multi-period nature. Many studies have analyzed the advantages and disadvantages of various postponement strategies [11, 12, 13]. However, quantitative models for postponement implementation decisions are scarce: [14] considers decisions on where to implement assembly and packaging functions in a distribution network while [15] addresses the problem of facility location-allocation (plants, warehouses) considering commonality and postponement strategies in the logistic network.

This quick analysis of the literature shows that no study gathers yet all the characteristics we have chosen to address in order to answer to present real problems, summarized by the "Proposal" column in Fig. 1.

## 3 Problem formulation

The problem is to determine simultaneously the location of the logistic hubs and of the postponement services, while minimizing the total logistics costs. Postponement units will have as inputs raw materials and components coming from international plants, based on their specialization and logistic costs, and will provide bagged/assembled products in response to the requirements of the market zones. These requirements may differ in terms of packaging preferences and required response time. We assume that postponement units hold sufficient component inventories for meeting the customer deterministic demands. The capacities (processing and storage) will be determined a posteriori (through simulation) by considering the expected levels of service. Market zones are allocated to a unique hub based on logistic costs.

In this problem, the interdependence of the decisions makes it difficult to instantiate all the decision variables simultaneously: the location of postponement units will impact the management of the logistic flow, as they constitute decoupling points. On the other hand, their location depends on the location of the logistic hubs and of the allocated demand (volume, response time and product preferences). For addressing this problem, we have chosen as a first approach to decouple the initial problem in two sub problems: definition of the logistic network, then location of the postponements facilities, even if the network structure may in theory be set into question by the positioning of the postponement units. Each sub-problem will be modeled by a deterministic mixed integer linear programming models (cf. 3.1 and 3.2).
### 3.1. First Sub-problem: logistic hub location problem

Within this sub-problem we have to decide: 1) The location of hub h among potential locations H using the $z_h$ binary variable 2) The allocation of the origin and destination nodes to the located hubs, using transport mode m represented by the $y_{o,d}^m$ binary variable defined only if a modal link between node “o” and “d” exists (Link (o, d, m) =1) and 3) The flow routing within the network $x_{o,d}^{m,k,t}$ i.e. the amount of final product k originated from plant p and transported from node “o” to node “d” using vehicle mode m and under packaging n at period t. The generated solution must provide the max benefit considering the initial investment to open hubs, the total transportation costs including customs, the external handling cost with seaport terminal or rail terminals and the internal handling cost within opened hubs (Eq. 1):

$$ 
\begin{aligned}
\text{Min}(\text{Cost}) = & \sum_{h \in H} c o_h \times A m \times z_h + \sum_{m \in M, t \in T, o \in O, d \in D} (c t_m + c d_{o,d}^m) \times N V_{o,d}^{m,t} + \\
& + \sum_{m \in M, n \in N, j \in T, k \in K_p, o \in O, h \in H, d \in D} c m_h^m \times (N V_{o,h}^{m,t} + N V_{h,d}^{m,t}) + c m^n \times \text{int}_h \times (x_{o,h}^{m,k,t,n} + x_{h,d}^{m,k,t,n}) \times f^n
\end{aligned}
\quad (1) $$

Subject to:

$$ \sum_{m \in M, h \in H} y_{h,z}^m = z_h \quad \forall h \in H \wedge z \in Dz \wedge \text{Link}(h, z, m) = 1 \quad (2) $$

$$ \sum_{m \in M, h_1 \in H} y_{h_1, h_2}^m = z_{h_2} \quad \forall h_2 \in H \wedge \text{Link}(h_1, h_2, m) = 1 \quad (3) $$

$$ \sum_{m \in M, h_i \in H} y_{h_i, h_2}^m = z_{h_2} \quad \forall h_2 \in H \wedge \text{Link}(h_1, h_2, m) = 1 \quad (4) $$

$$ y_{p,h}^1 + y_{p,h}^2 \le 2 \times z_h \quad \forall h \in H_1 \wedge p \in P \wedge m \in \{1, 2\} \wedge \text{Link}(p, h, m) = 1 \quad (5) $$

$$ y_{h_1, h_2}^m \le z_{h1} \quad \forall m \in \{2, 3\} \wedge h_1, h_2 \in H \wedge \text{Link}(h_1, h_2, m) = 1 \wedge \text{Dist}(h_1, h_2, m) \le D(m) \quad (6) $$

$$ y_{h_1, h_2}^{m} \le z_{h2} \quad \forall m \in \{2, 3\} \wedge h_1, h_2 \in H \wedge \text{Link}(h_1, h_2, m) = 1 \wedge \text{Dist}(h_1, h_2, m) \le D(m) \quad (7) $$

$$ y_{h,z}^3 \le z_h \quad \forall h \in H \wedge z \in Dz \wedge \text{Link}(h, z, 3) = 1 \wedge \text{Dist}(h, z, 3) \le D(3) \quad (8) $$

$$ x_{p,h}^{1,k,n,t,p} \le \text{BigM} \times z_h \quad \forall h \in H_1 \wedge p \in P_k \wedge k \in K_p \wedge t \in T \quad (9) $$

$$ x_{h_1, h_2}^{m,k,t,p} \le \text{BigM} \times z_{h_1} \quad \forall t \in T \wedge m \in \{2, 3\} \wedge k \in K_p \wedge h_1 \in H \wedge \text{Dist}(h_1, h_2, m) \le D(m) \quad (10) $$

$$ x_{h,z}^{3,k,t,p} \le \text{BigM} \times z_h \quad \forall t \in T \wedge h \in H \wedge z \in Dz \wedge k \in K_p \wedge \text{Dist}(h, z, 3) \le D(3) \quad (11) $$

$$ \sum_{p \in P_k} x_{o,d}^{m,k,n,t,p} \le \text{BigM} \times y_{o,d}^m \quad \forall m \in M \wedge n \in N \wedge t \in T \wedge k \in K_p \wedge o \in O \wedge d \in D \wedge \text{Link}(o, d, m) = 1 \quad (12) $$

$$ y_{o,d}^m \le \sum_{p \in P_k} x_{o,d}^{m,k,n,t,p} \quad \forall m \in M \wedge n \in N \wedge t \in T \wedge k \in K_p \wedge o \in O \wedge d \in D \wedge \text{Link}(o, d, m) = 1 \quad (13) $$

$$ \sum_{m \in M, p \in P_k} x_{p,h}^{m,k,n,t,p} = \sum_{m \in M, z \in D, h' \in H} x_{h,z}^{m,k,n,t+\Delta(p,h)+\theta,p} + x_{h,h'}^{m,k,n,t+\Delta(p,h)+\theta,p} \quad \forall k \in K \wedge h \in H \wedge t \in T \quad (14) $$
$$ \sum_{\substack{h \in H, \\ m \in M}} x_{h_1, h_2}^{m,k,n,t,p} = \sum_{z \in D_z, m \in M} x_{h_2, z}^{m,k,n,t+\Delta(h_1, h_2)+\theta, p} \quad \forall k \in K_p, \forall t \in T, \forall h_2 \in H \quad (15) $$

$$ \sum_{m \in M, h \in H} x_{h,d}^{m,k,t} = D_z^{k,t} \times y_{h,d}^m \quad \forall k \in K_p, \forall t \in T, \forall d \in D \quad (16) $$

$$ NV_{o,d}^{m,k,t} \geq \sum_{k \in K_p} \frac{x_{o,d}^{m,k,t}}{CT_m \times f^n} \quad \forall t \in T \land o \in O \land d \in D \land m \in M \land n \in N \quad (17) $$

Constraints (2, 3, 4) express the single allocation of nodes to hubs. Constraints (5, 6, 7, 8) control the allocation mode to physical links. Outgoing hub flows exist only if the hub is active (9, 10, 11) and require that this modal link should be already activated (12, 13). Constraints (14, 15) ensure flow conservation at each period of time where $\Delta$ (o, h) + $\theta$ is the sum of the transports to h and transit time within h. Outgoing flows toward distribution centers must be equal to their respective demand (16). Equation (17) computes the number of modal vehicles within the network where $CT_m$ is the capacity of a vehicle.

### 3.3. Second Sub-problem: postponement location problem

Given a set of located hubs $H_l \{h \in H/\tilde{z}h=1\} \cup D_z$ and a set of active links $L=\{(o, d, m); o \in O, d \in D, m \in M/ \hat{y}_{o,d}^m=1\}$, we have to select the suitable location of postponement units in the designed distribution network. Location can be either on regional hubs, sub-regional ones or on local distribution centers, in order to minimize the total logistic costs (Equation 18) where $b_h^e$ is a binary variable equal to 1 if the postponement unit is located on hub h at echelon e, while $Bin(H, e)$ is a Boolean value equal to 1 if hub h is located at level e.

$$ \text{Min}(\text{Cost\_postp}) = \sum_{h \in H_l, e \in E} co_h \times Am \times b_h^e + \quad (18) $$

$$ [ \sum_{m \in M, t \in T, o \in O, d \in D} (ct_m^1 + cd_{o,d}^m + cm_m^1) \times NBV_{o,d}^{m,t} + \sum_{m \in M, t \in T, k \in K_p, o \in O, d \in D} cm_m^1 \times \text{int} \times x_{o,d}^{m,k,t} ] + $$

$$ [ \sum_{m \in M, t \in T, o \in O, d \in D} (ct_m^2 + cd_{o,d}^m + cm_m^2) \times NCV_{o,d}^{m,t} + \sum_{m \in M, t \in T, k \in K_p, o \in O, d \in D, p \in P_k} cm_m^2 \times \text{int} \times \bar{x}_{p,o,d}^{m,k,n,t} ] $$

Subject to:

$$ \sum_{e \in E} b_h^e = \bar{z}_h \quad \forall h \in H \land Bin(H, e) = 1 \quad (19) $$

$$ \sum_{m \in M, p \in P_k} x_{h_1, h_3}^{m,k,t} \leq \text{BigM} \times \bar{y}_{h_1, h_2}^m \times b_{h_3}^3 \quad \forall t \in T \land k \in K_p \land h_1, h_3 \in H_l \quad (20) $$

$$ \sum_{m \in M, p \in P_k} x_{h_1, h_2}^{m,k,t} \leq \text{BigM} \times \bar{y}_{h_1, h_2}^m \times (b_{h_2}^2 + b_{h_3}^3) \quad \forall t \in T \land k \in K_p \land h_1, h_2, h_3 \in H_l \quad (21) $$
$$ \sum_{m \in M} x_{h_2, z}^{m,k,t} = \sum_{m \in M, k' \in K_c, p \in P_k} \hat{y}_{h_2, z}^{m} \times \bar{x}_{p, h_2, z}^{m, n, k, t + \Delta(h_2, z) + \theta} \times \mathrm{Conv}(n) \times \mathrm{Cs}(k, k') \times b_z^3 \quad (22) $$

$$ \forall t \in T, h_2 \in Hl, z \in Dz, k \in K_b $$

$$ \sum_{m \in M} x_{h_1, h_2}^{m,k,t} = \sum_{\substack{m, m' \in M, \\ k' \in K_c, \\ p \in P_k, z \in Dz}} \hat{y}_{h_1, h_2}^{m} \times \hat{y}_{h_2, z}^{m'} \times \bar{x}_{p, h_2, z}^{m', n, k', t + \Delta(h_1, h_2) + \theta} \times \mathrm{Conv}(n) \times \mathrm{Cs}(k, k') \times (1 - b_{h_1}^1) \quad (23) $$

$$ \forall t \in T, h_1, h_2 \in Hl, k \in K_b $$

$$ \sum_{m \in M} x_{h_1, z}^{m,k,t} = \sum_{\substack{m \in M, k' \in K_c, \\ p \in P_k, z \in Dz}} \hat{y}_{h_1, z}^{m} \times \bar{x}_{p, h_1, z}^{m, n, k, t + \Delta(h_1, h_2) + \theta} \times \mathrm{Conv}(n) \times \mathrm{Cs}(k, k') \times (1 - b_{h_1}^1) \quad (24) $$

$$ \forall t \in T, h_1, h_2 \in Hl, k \in K_b $$

$$ NBV_{o,d}^{m,t} \geq \sum_{k \in K_b, p \in P_k} \frac{x_{p,o,d}^{m,k,t}}{CT_m^1} \times NV_m ; \forall t \in T \wedge m \in M \wedge h \in Hl \wedge h_3 \in Dz \quad (25) $$

$$ NCV_{h_1, h_3}^{m,t} \geq \sum_{e \in E} b_h^e \times \left[ \sum_{k \in K_c, p \in P_k, n \in N} \frac{\bar{x}_{p, h_1, h_3}^{m, k, n, t}}{CT_m^2 \times f^n} \right] ; \forall t \in T \wedge m \in M \wedge h \in Hl \wedge h_3 \in Dz \quad (26) $$

$$ NCV_{h_2, h_3}^{m,t} \geq (b_{h_1}^1 + b_{h_2}^2) \times \left[ \sum_{\substack{k \in K_c, \\ p \in P_k, n \in P_g}} \frac{\bar{x}_{p, h_2, h_3}^{m, n, k, t}}{CT_m^2 \times f^n} \right] ; \forall t \in T \wedge m \in M \wedge h_1, h_2 \in Hl \wedge h_3 \in Dz \quad (27) $$

Constraint (19) translates that a postponement activity can only be located on activated hubs, at only one level. “Continuous flows” $x^{m,k,t}_{o,h}$ exist only if postponement units are located before that hub if a modal link is activated (20, 21). (22, 23, 24) express a flow balance at each period and on each hub and computes the ingoing discrete flows to each hub depending on location of postponement units. Conv(n) is the conversion ratio from unit of packaging product under n commodity to a continuous unit (tons for example) and Cs(k, k') is the amount of component k needed to produce a unit of product k'. (25, 26, 27) assess the number of bulk and container vehicles within the network.

## 4. Illustrative study

This case study aims to illustrate the application of the proposed models. It concerns the location of blending units within East Africa for specific industries involving hybrid (discrete-continuous) flows, like the fertilizer industry. Three production zones located in Morocco, Ethiopia and Nigeria and considered. Five Regional hubs are defined: Kenya-Angola-Tanzania-Djibouti, so that ten sub-regional hubs: Nairobi-Kisumu-Dodoma-Arusha-Tabora-Kuito-Tete-Lichinga-Kigali. The considered data are summarized in Tables 1 and 2. The demand (aggregated on one year) varies for each zone. We assume that shipment is done every month and that all the market zones require the same service level. Distances and traveling times are extracted from Google Maps. The problem was solved using the Xpress-IVE solver tools. The results of models 1 and 2 are summarized in Tables 3 and 4.
<table><caption>**Table 1.** List of transport cost parameter</caption><thead><tr><th>Parameter</th><th>Discrete flow</th><th>Continuous flow</th></tr></thead><tbody><tr><td>Transport capacity-sea</td><td>50 palette</td><td>30000 Tons</td></tr><tr><td>Transport capacity-rail</td><td>40 palette</td><td>25000 Tons</td></tr><tr><td>Transport capacity-road</td><td>40 palette</td><td>25000 Tons</td></tr><tr><td>Rail unit transport cost</td><td>0.06/train/km</td><td>0.04/Train/km</td></tr><tr><td>Road unit transport cost</td><td>3.75$/truck/km</td><td>2$/truck/km</td></tr></tbody></table>

<table><caption>**Table 2.** List of other cost parameters</caption><thead><tr><th>Cost</th><th>Regional hub</th><th>Sub-regional hub</th></tr></thead><tbody><tr><td>Hub Location cost ($/year)</td><td>5760000</td><td>2880000</td></tr><tr><td>Blending location</td><td>30000</td><td>30000</td></tr><tr><td>Intern handling (bulk)</td><td>15$/Tons</td><td>35$/Tons</td></tr><tr><td>Extern handling (rail)</td><td>100 $/train</td><td>120 $/train</td></tr><tr><td>Intern handling (discrete)</td><td>5 $/palette</td><td>10 $/palette</td></tr><tr><td>Extern handling (rail) (discrete)</td><td>40 $/train</td><td>50 $/train</td></tr></tbody></table>

<table><caption>**Table 3.** Results of sub-model 1</caption><thead><tr><th>Located hub</th><th>Plant</th><th>Sub-hub</th><th>% DC</th></tr></thead><tbody><tr><td>Kenya</td><td>Morocco<br>Ethiopia</td><td>Kisumu-<br>Lichingua</td><td>25%</td></tr><tr><td>Mozambique</td><td>Morocco</td><td>Tete</td><td>10%</td></tr><tr><td>Angola</td><td>Nigeria</td><td>Luau</td><td>10%</td></tr><tr><td>Tanzania</td><td>Morocco<br>Ethiopia</td><td>Kuito-Kigali</td><td>10%</td></tr></tbody></table>

<table><caption>**Table 4.** Results of sub-model 2</caption><tr><td>Total logistic cost</td><td>216 M$</td></tr><tr><td>Sea Transport</td><td>9.52 M$</td></tr><tr><td>Rail Transport</td><td>8.75 M$</td></tr><tr><td>Road Transport</td><td>21.97 M$</td></tr><tr><td>Intern handling</td><td>109.45 M$</td></tr><tr><td>Extern handling</td><td>26890.5 $</td></tr><tr><td>Location</td><td>66.3 M$</td></tr></table>

<table><tr><td>Blending location</td><td>Kenya-Mozambique-Angola-Tanzania</td></tr><tr><td>Level</td><td>1</td></tr></table>

<table><tr><td>Total logistic cost</td><td>157 M$</td></tr><tr><td>Total bulk costs</td><td>47.1 M$</td></tr><tr><td>Total discrete costs</td><td>109.9 M$</td></tr></table>

The location of the blending within the distribution network is the result of a comparison between investments and operational costs linked to postponement and to the transportation of bulk and packed materials. Especially, it requires to compare the profit generated by several small blending units, close to the final customers, and the one of larger units, located earlier in the network but requiring more time to adapt their production to the final demand. In real cases, good sense is not sufficient to figure out this decision problem. Our model helps the decision maker to assess quantitatively each possible solution.

## 5. Conclusion et research perspectives

In the context of mass customization, postponement activities may provide an answer to fulfill customized orders, increase customer responsiveness and increase service level. However, the literature combining design of logistic hub networks and implementation of postponement facilities is scarce and usually assumes that the location of the distribution centers is already known. In order to address the problem, we have developed and tested a two-phase deterministic mathematical programming model where, as a first step, we design incapacitated discrete logistic hub, then allocate postponement services on some hubs. In our future work, this model will be coupled with a discrete event simulation model in order to take into consideration uncertainties on the demand and on the availability of the resources. Simulation will
also allow to assess postponement capacities and to refine logistic costs, these results
being re-injected in the mathematical model as new constraints.

References

1. S. Alumur and B. Y. Kara, Network hub location problems: The state of the art, European Journal of Operational Research, 190(1), pp. 1–21, 2008.

2. H.-W. Wang, R.-Q. Chena, and Y. Li, Case study on the application of postponement strategy and managerial insights, Asia Pacific Man. Review, 11(3), pp. 141–153, 2006.

3. M. Lambert and M. C. Cooper, "Issues in supply chain management," Industrial marketing management, vol. 29, no. 1, pp. 65–83, 2000.

4. S. A. Alumur, H. Yaman, and B. Y. Kara, Hierarchical multimodal hub location problem with time-definite deliveries, Transportation Research Part E: Logistics and Transportation Review, 48(6), pp. 1107–1120, 2012.

5. S. Gelareh, R. Neamatian Monemi, and S. Nickel, Multi-period hub location problems in transportation, Transportation Research Part E, 75, pp. 67–94, 2015.

6. H. Sohrabi, B., Montreuil, and W. Klibi, On Comparing Dedicated and Hyperconnected Distribution Systems: An Optimization-Based Approach. ILS 2016, 1-4 June, Bordeaux, France, 2016.

7. M. T. Melo, S. Nickel, and F. S. Da Gama, Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning, Computers & Operations Research, 33(1), pp. 181–208, 2006.

8. S. A. Alumur, B. Y. Kara, and O. E. Karasan, Multimodal hub location and hub network design, Omega, 40(6), pp. 927–939, 2012.

9. V. Rodriguez, M. J. Alvarez, and L. Barcos, Hub location under capacity constraints, Transportation Research Part E: Log. and Transp. Review, 43(5), pp. 495–505, 2007.

10. M. Albareda-Sambola, E. Fernandez, and S. Nickel, Multiperiod Location-Routing with Decoupled Time Scales, European Journ. of Op. Research, 217(2), pp. 248–258, 2012.

11. B. Yang and N. Burns, Implications of postponement for the supply chain, International Journal of Production Research, 41(9), pp. 2075–2090, 2003.

12. R. I. Van Hoek, The rediscovery of postponement a literature review and directions for research, Journal of operations management, 19(2), pp. 161–184, 2001.

13. J. Hsuan Mikkola and T. Skjøtt-Larsen, Supply-chain integration: implications for mass customization, modularization and postponement strategies, Production Planning & Control, 15(4), pp. 352–361, 2004.

14. F. Schwartz, S. Voss, and J. A. Ceroni, Designing distribution networks taking into account aspects of postponement, in The Development of Collaborative Production and Service Systems in Emergent Economies, Proceedings of the 19th International Conference on Production Research, 2007.

15. L. Schulze and L. Li, Location-allocation model for logistics networks with implementing commonality and postponement strategies, in Proceedings of the International Multi Conference of Engineers and Computer Scientists, 2, pp. 1615–1620, 2009.

16. I. Contreras, J.-F. Cordeau, and G. Laporte, Stochastic uncapacitated hub location, European Journal of Operational Research, 212(3), pp. 518–528, 2011.

17. J. Rieck, C. Ehrenberg, and J. Zimmermann, Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery, European Journal of Operational Research, 236(3), pp. 863–878, 2014.

18. A. Alibeyg, I. Contreras, and E. Fernandez, Hub Network Design Problems with Profits, Transportation Research Part E: Logistics and Transportation Review, 96, pp. 40-59, 2015.

19. S. Gelareh, S. Nickel, and D. Pisinger, Liner shipping hub network design in a competitive environment, Transportation Research Part E: Logistics and Transportation Review, 46(6), pp. 991-1004, 2010.