Hartanto Wong

Daniel Eyers

An analytical framework for evaluating the value of enhanced customisation: An integrated operationsmarketing perspective

Keywords: Mass Customisation, Postponement, Integrated operationsmarketing problem Mass Customisation, Postponement, Integrated operations-marketing problem .manuscriptcentral.com/

An analytical framework for evaluating the value of enhanced customisation: An integrated operations-marketing perspective

Introduction

It can be argued that one of the most difficult problems faced by manufacturers nowadays is the need to present an ever more valuable service to customers whilst at the same time cutting delivery times and total operating costs. One attractive technique of increasing the value or utility of a manufactured product can be seen as product customisation, whereby products are tailored to the individual requirements of the customer. This has triggered the new manufacturing paradigm that is called mass customisation (MC). This new paradigm replaces mass production which is viewed as no longer suitable for today's competitive environment [START_REF] Pine | Mass Customisation: The New Frontier In Business Competition[END_REF]. The concept has already received considerable attention in the literature since its identification by [START_REF] Davis | Future Perfect[END_REF] and the influential book by [START_REF] Pine | Mass Customisation: The New Frontier In Business Competition[END_REF], however as yet failed to fully achieve the originally envisaged potential [START_REF] Piller | Mass Customisation: Reflections on the State of the Concept[END_REF].

MC combines the best of the craft era, where products were personalised but at high cost, with the best of Mass Production, where products were affordable but highly standardised [START_REF] Fralix | From mass production to mass customization[END_REF]. In an ideal world, MC will ultimately achieve a situation in which firms are able to provide customised products at a comparable price and speed of equivalent standardised offerings. However, empirical evidence suggests a more pragmatic view in that the customisation is not 'free' and need to be traded-off against lead time, cost, and other factors [START_REF] Mccutcheon | The customizationresponsiveness squeeze[END_REF][START_REF] Squire | The impact of mass customisation on manufacturing trade-offs[END_REF]. Hence, in deciding the right customisation level, firms would certainly need to consider these trade-offs, which essentially entail many aspects pertinent to the operations (production-inventory) as well as marketing functions.

Whilst it is evident that the current state of mass customisation is achievable through the adoption of innovative technologies and techniques such as flexible manufacturing systems, modularization, postponement and e-commerce, our literature review suggests that most of the extant academic literature tends to focus heavily on the evaluation of such technologies and techniques in the context of operations without adequate consideration being paid to the marketing factors. Postponement, for example, has been extensively studied in recent years and shown as an attractive means to accommodate MC. The main benefit of postponement is the possibility to lessen the total inventory cost. This is primarily achieved by the reduction of demand forecast errors and also by delaying expensive operations that enables companies to maintain the bulk of its inventories in the cheaper and/or pre-customized form [START_REF] Lee | Hewlett Packard gains control of inventory and service through design for localisation[END_REF][START_REF] Lee | Modelling the costs and benefits of delayed product differentiation[END_REF][START_REF] Swaminathan | Design for postponement[END_REF]. Typically, the value of postponement is evaluated on the basis that the demand rate from customers is assumed to be given (i.e. the consequences of factors such as price, lead time and product characteristics on the customer purchase choice are ignored).

We argue that such analysis focusing solely on the operations aspects would be deficient.

When firms move from mass production to mass customisation, the alignment of both the operations and marketing decisions is undeniably important. It would be legitimate to question whether, for example, there would be an effect of longer lead times on customer willingness to buy, which will consequently influence the total profitability. Similarly, firms' decision on product price cannot be ignored. The product price must be optimized by taking into account product variety, inventory cost reductions, and the possible dissatisfaction of customers due to longer lead times. Aware of the above discussed limitations, in this article we present a formal approach to evaluate the value of enhanced customisation by taking the operations-marketing interface into consideration. The model we developed captures the importance of operations and marketing decisions, which include the inventory level, number of product varieties, price, and delivery lead time. The rest of the paper is organised as follows. In the next section we present the literature review and highlight the main contributions we make to the existing body of knowledge.

Section 3 presents the model. We describe how the integrated model is built up from the marketing and production-inventory models. Section 4 presents and discusses our numerical findings. Finally, we summarise the results in Section 5 and conclude with some suggestions for further research.

Literature Review

Three streams of literature are relevant to our study. The first studies decisions made for manufacturing products, mostly concentrated on the choice between MTS or MTO strategies.

The second considers production-inventory systems that accommodate mass customisation, whilst the final stream analyses coordinated marketing and operations decisions. Our research serves to integrate and extend this literature.

Analytical models related to the decision of manufacturing products in a MTS or MTO fashion are presented by several authors including [START_REF] Federgruen | The impact of adding a make-to-order item to a make-tostock production system[END_REF], [START_REF] Arreola-Risa | Make-to-order versus make-to-stock in a productioninventory system with general production times[END_REF][START_REF] Arreola-Risa | Make-to-order versus make-to-stock in a productioninventory system with general production times[END_REF][START_REF] Rajagopalan | Make to order or make to stock: Model and application[END_REF]. [START_REF] Federgruen | The impact of adding a make-to-order item to a make-tostock production system[END_REF] consider systems where some products are made to stock while other product lines are made to order.

The primary focus of their paper is on the different strategies for deciding whether and when to "interrupt" the production of MTS with MTO items and providing related insights.

Arreola-Risa and DeCroix (1998) study the optimality of make-to-order (MTO) versus maketo-stock (MTS) policies for a company producing multiple heterogeneous products at a shared manufacturing facility. The authors also discussed to what extent reducing manufacturing lead time randomness helps a product to be produced for MTO. Similar work is presented in [START_REF] Rajagopalan | Make to order or make to stock: Model and application[END_REF] where the author considers a manufacturing setting faced with the decision about which items to make to stock and which ones to make to order.

There are numerous studies analyzing production-inventory systems that accommodate MC.

Relevant to our study are those particularly analysing the production and inventory systems employing postponement or delayed product differentiation. There is a large body of literature on postponement. We refer the reader to van Hoek (2001), [START_REF] Swaminathan | Design for postponement[END_REF], and Yang and Burns (2003) for a comprehensive review of research on postponement. Analytical models measuring the costs and benefits of postponement are presented by [START_REF] Lee | Modelling the costs and benefits of delayed product differentiation[END_REF], Garg and Tang (1997), [START_REF] Swaminathan | Managing broader product lines through form postponement using vanilla boxes[END_REF], and Aviv andFedergruen (2001a and2001b). However, these models ignore the effect of queuing at the production facility. [START_REF] Gupta | Make-to-order, make-to-stock, or delayed product differentiation? A common framework for modelling and analysis[END_REF] consider the capacitated production system and model the system employing form postponement as a two-stage system. Another study incorporating the queuing effect is by [START_REF] Su | Evaluation of postponement structures to accommodate mass customisation[END_REF]. In this paper, the authors compare two specific configurations. In the first configuration products are produced after orders arrive (MTO mode) and the second configuration represents the system employing form postponement.

More recently [START_REF] Wong | Analysis of form postponement based on optimal positioning of the differentiation point and stocking decisions[END_REF] examine different postponement configurations characterised based on the positioning of the differentiation point and the customer order decoupling point. All these studies are common in that their analysis is focused on the production-inventory system without considering any marketing factors. It is not surprising to observe that their results are based on an assumption that demand and number of product varieties are given, and that the evaluation is made based on a cost-minimisation strategy. In this paper we consider both production-inventory as well as marketing factors and hence a profit maximisation strategy is used instead of the cost-minimisation strategy.

The final stream of research identified in this review concerns both operations and marketing factors. For example, [START_REF] Li | The role of inventory in delivery-time competition[END_REF] considers a situation in which customer utility is sensitive to price, quality, and lead time with the supplier being able to control the production rate. The author first analyses the single-firm problem and derived simple 'newsboy'-like formulas to determine the optimal production/inventory policy and the optimal choice between make-toorder and make-to-stock operations. The model is then extended to address multiple suppliers who compete for demand based on delivery time. [START_REF] Palaka | Lead-time setting, capacity utilization, and pricing decisions under lead time dependent demand[END_REF] study how the interaction between lead time, capacity utilisation and price affect operational performance.

They model the firm's operations as an M/M/1 queue and treat demand as a linear function of price and quoted lead time. [START_REF] Webster | Dynamic pricing and lead time policies for make-to-order systems[END_REF] models a make-to-order system in which demand rate is a function of price and lead time. He models the system as a queuing system and allows the production rate to be changed dramatically. [START_REF] Yang | Inventory and lead time planning with lead-time-sensitive demand[END_REF] study a combined strategic and operational level planning model that determines the best positioning of a product with respect to price and promised lead time. They consider a continuous review inventory replenishment system, where two types of lead times, procurement and sales lead times influences both cycle stock and safety stock costs. Although they consider multiple factors affecting demand, it is obvious that their analysis treats each of these factors independently. This is different from our analysis in which we are interested in capturing the interplay of price, degree of customisation and quoted lead time.

From the literature assessment several papers were identified as studying the coordination of marketing and operations decisions similar to ours. De [START_REF] De Groote | Flexibility and marketing/manufacturing coordination[END_REF] analyses the joint problem of marketing/manufacturing coordination with the focus being on the exploration of cross-functional implications of the flexibility of manufacturing processes. In this work, two complementary problems were formulated: the marketing choice of the breadth of the product this work identified that the decentralised solution of the two problems typically yields a suboptimal solution. In a related study, [START_REF] Dobson | Product offering, pricing, and make-to-stock/make-to-order decisions with shared capacity[END_REF] assessed the situation faced by a manufactures which experienced demand that is not only influenced by price, but also lead time. In this scenario, the firm must decide which products to offer, how to price them, whether each should be made to stock or made to order, and how often to produce them. In the study, several assumptions are made. Firstly, the products are assumed to originate from a single manufacturing facility where setup times introduce diseconomies of scope and setup costs introduce economies of scale. Additionally, deterministic demand is assumed which is linearly decreasing in price and lead time. However, in contrast to both De Groote (1994) and ours, the models presented in [START_REF] Dobson | Product offering, pricing, and make-to-stock/make-to-order decisions with shared capacity[END_REF] fail to consider how the number of products offered influence customers' purchase decision. Furthermore, in comparison to the above mentioned two papers, the focus of our analysis in this paper is very different in that we are particularly keen to make comparisons between different manufacturing configurations in the context of Mass Customisation.

Mass Customisation has been a widely explored concept, for which this review serves only to identify the most pertinent discussions. One such study is that of [START_REF] Jiang | Satisfying customer preferences via mass customisation and mass production[END_REF], who compare two configurations: Mass Customisation and Mass Production. In their model, the Mass Customisation system consists of two stages: the initial build-to-stock phase and the final customise-to-order phase. By contrast, the Mass Production system has only a single stage that builds products with pre-determined specifications to stock. [START_REF] Jiang | Satisfying customer preferences via mass customisation and mass production[END_REF] characterise three possible benefits of Mass Customisation: (i) the gained surplus from offering each customer her ideal product; (ii) extra revenue from price discrimination; and

(iii) reduced costs due to risk pooling. Our analysis is different from theirs mainly in the following respects. Firstly, in addition to the make to stock and build to order systems that represent Mass Production and Mass Customisation, we also consider a make to order system accommodating the pure customisation strategy. Secondly, their model ignores the effect of queuing at the production facility while we explicitly model the queuing effect as a result of considering a capacitated production facility.

The model presented in this paper builds on earlier work [START_REF] Wong | Re-examining postponement benefits: An integrated productioninventory and marketing perspective[END_REF] in which an integrated operations-marketing model is used to re-examine the benefits of postponement.

The use of such an integrated model reveals a number of different aspects associated with postponement costs and benefits other than inventory costs typically considered when using the more traditional production-inventory model. In this paper the model is extended to particularly accommodate a wider range of customisation level. Finally, [START_REF] Alptekinoglu | Leadtime-variety trade-off in product differentiation[END_REF] analyse the trade-off between the enhanced ability to meet individual preferences and the longer lead time associated with customised products.

They develop a solution method to characterise the optimal product line design allowing a set of customised and standard products. While the modelling framework used in our paper is similar to theirs, our analysis is different in the following aspects. Firstly, while they consider two strategies, namely a MTS system producing standard products and a MTO system producing customised products, we consider three configurations that include the DD configuration employing postponement in addition to the MTS and MTO configurations. As postponement is a quite important strategy to accommodate Mass Customisation, we believe that the inclusion of the DD configuration will give more insights into our analysis. Secondly, while the main objective of their paper is to determine the optimal product line design strategy that allows a combination of the MTS and MTO products, our objective is to assess the relative merit of the three manufacturing configurations. We devise an optimisation procedure for each configuration so that comparisons of the three configurations can be made based on their respective best performances. Furthermore, though their market demand model assuming any continuous distribution is more general than our model based on a uniform distribution, their production-inventory model is more restricted as it is based on the assumption of zero product proliferation cost and identical manufacturing costs while we consider a product proliferation cost for the MTS and DD configurations and allow non identical manufacturing costs for the three configurations. Moreover, as most of the existing studies do, their model assumes the optimality of complete market coverage. Our model is more generic by virtue of its capability to accommodate partial market coverage.

The model

In this section, we provide an overview of the generic model framework that underlines our analysis. In Section 3.1 we formally present three different manufacturing configurations that will be compared. Section 3.2 presents the general market demand model. In Section 3.3 we outline the production-inventory models associated with the three manufacturing configurations. Section 3.4 presents an integrated framework in which the optimization problem is formulated as a joint marketing and production-inventory decision making problem. Further details on the operational description of the three configurations are as follows.

The description of manufacturing systems

Figure 1 should be placed around here

Configuration I: Make-to-stock system (MTS)

In the first configuration, a set of finished products are produced in a make-to-stock (MTS) mode, with items produced in advance of actual demand and resultantly held in stock. In these circumstances, demand will be satisfied from the stock (unless the stock is empty), and all shortages backlogged. This configuration is modelled as a one stage production-inventory system. In this configuration, the manufacturer offers N finished products (N is a decision variable), indexed by i = 1, 2, …, N. We denote Λ as the total demand rate. End customer demand of product i arrives in single units according to a Poisson process with rate i λ , and as we allow partial market coverage,

∑ = ≥ Λ N i i
1 λ . We assume that the processing times are i.i.d. random variables and exponentially distributed with rate µ 1 . For stability, we require

that 1 < = Λ ρ µ
. We assume that a base-stock policy is used for the inventory control. Let i S denote the base stock level for finished product i. Furthermore, changeover times between products are assumed to be negligible. occurs in a make-to-stock mode in Stage-1 and a make-to-order mode in Stage-2. It is notable to mention here that in both configurations, customers have the opportunity to choose their preferred product based on a set of product offerings pre-specified by the manufacturer. As producing to stock becomes costly when the number of products is large, one would reasonably expect that DD is capable to offer more product variety than MTS. But this does not include the cost associated to a longer waiting time experienced by customers, since DD does not hold an inventory of finished products.

We assume that the processing times for Stage 1 andStage 2 are i Again, we require that 1 < = Λ j j ρ µ for j=1 and 2, where j ρ is the j-stage utilisation rate.

The base stock level for generic components is denoted as 0 S , while the stock level for finished products is zero for all i = 1, 2, …, N. Here we also assume negligible changeover times.

Configuration III: Custom Manufacturing (CM)

Finally, the third configuration termed as Custom Manufacturing (CM) accommodates a full customisation strategy. The CM configuration is actually an MTO configuration in which customised finished products are manufactured through a single stage process. The main difference between CM and the other two configurations is that CM allows an individual customer to purchase a product based on her own specification. An example would be the customisation of a product to their own physical measurements (e.g. custom clothing, etc), rather than based on a pre-specified set of product offerings. Hence, the limit of the number of product variety could be as large as the population size of the market. The absence of tooling not only simplifies the manufacturing process, it also removes large fixed costs of production which inherently make traditional manufacturing processes such as injection moulding financially impractical for custom, low volume production. Already, these technologies are proving viable in many medical applications such as hearing aids, dental aligners, etc. The very promising development of these technologies seems to be an important catalyst for enhancing the viability of CM in the next few years [START_REF] Bulkeley | 3D printers reshape world of copying[END_REF][START_REF] Eyers | Rapid Manufacturing for Mass Customisation[END_REF][START_REF] Hopkinson | Rapid Manufacturing: An Industrial Revolution for the Digital Age[END_REF], Judah 2009).

In the CM configuration, we assume that the processing times are i.i.d. random variables and exponentially distributed with rate ' 1 µ , where µ µ ≥ ' . This reflects our optimistic view in that shorter manufacturing processing times (in comparison to MTS) are achievable through the advancement of new manufacturing technologies. For stability, we require that

1 ' < Λ µ . Let MTS c
, DD c and CM c denote the unit production cost for each of the manufacturing configurations respectively. To reflect the costs of adopting innovation, we assume that the direct cost of manufacturing is non-decreasing when we move along MTS, DD, and CM. This is due to the fact that employing systems with greater innovation would require new production processes to be setup and perfected. Formally,

CM DD MTS c c c ≤ ≤
. For each configuration, the unit production cost is assumed to be identical for all finished products. Let h denote the holding cost per unit per unit time for all finished products, and 0 h denote the holding cost per unit per unit time for the generic component. For the MTS and DD configurations there is a product proliferation cost K, incurred every time the manufacturer offers a new product variant. This cost could include redesign, tooling and setup costs. The linearity assumption of product proliferation cost in the number of products is in line with common observation in the operations literature [START_REF] Thonemann | The effect of product variety on supply-chain performance[END_REF]Benjaafar et al. 2004). To reflect the highly flexible feature such as offered by RM technologies, we assume that there is no proliferation cost incurred for the CM configuration.

For MTS, the manufacturer makes simultaneous decisions regarding the number of product varieties, their characteristics, base stock level of finished products, and price, maximising the expected profit. Note that the decision on the base stock level will also influence the promised lead time offered to customers. The DD manufacturer makes similar decisions as for the MTS manufacturer except for the fact that they must decide on the base stock level of generic components instead of finished products. For the CM manufacturer, the only relevant decision is price. All the notations used throughout the paper are presented in Table 1.

F

The market demand model

In this paper we base our marketing model on the locational model of customer choice. It is along the line of the spatial location model of [START_REF] Hotelling | Stability in competition[END_REF] and its extensions by [START_REF] Lancaster | The economics of product variety: A survey[END_REF], and well established in the marketing and economic literature. Specifically, we evaluate a single manufacturing firm monopolistically serving a market with heterogeneous consumers over a single time period. In this model customer tastes are uniformly distributed over the closed interval of product space [0, 1]. All products are horizontally differentiated, with each characterised by a single point in that interval (quantified by a real number between 0 and 1). This can represent, for example, the size or colour attribute of the product. As Mass Customisation applications are generally characterised by customer tastes rather than product qualities, models based on horizontal differentiation are deemed to be more appropriate in comparison to vertical differentiation [START_REF] Jiang | Satisfying customer preferences via mass customisation and mass production[END_REF]. Products are offered with price p, assumed to be identical for all products. The uniform pricing scheme is reasonable when the products are horizontally differentiated in which qualities of products are at the same level. It is also a common marketing practice to charge the same price for the customised products even if different customers choose different options while customising [START_REF] Syam | On customized goods, standard goods, and competition[END_REF]. Each customer buys one unit from the manufacturer and has her own ideal product represented by her location θ ∈ [0, 1]. We assume that demands arrive according to a Poisson process and the total potential demand rate in the market is given by Λ . As noted during the literature assessment, our demand model is different from some others in that it captures the situation in which demand is not only sensitive to price and product characteristics, but also to delivery lead time. This allows us to better consider the situation for Mass Customisation in which many characteristic are relevant in the selection of a product. In this model we assume that the manufacturer commits to satisfy a lead time guarantee w for all product lines and maintain a service level of 1-β (i.e. delivery occurs within w time units with 1-β probability). Customers pay a linear transportation cost x c per unit distance between their ideal product and the purchased product ( x c represents the intensity of customer preference). Furthermore, The utility of customer at θ derives from buying product i with characteristic x i , price p, and lead time guarantee w is given by

i x w i x c w c p r w p x U - - - - = θ θ ) , , , ( , (1)
where r is a reservation price (in this model all consumers are assumed to have a common reservation price r for their ideal product). In Equation ( 1) the customer's disutility of misfit relative to their ideal preference is expressed as

i x x c - θ
, and the disutility of waiting is represented by w c w . In each case, the consumer will select the product which maximises their utility. In the event that the utility is negative, the customer will not make a purchase.

Product i is said to be the first choice of a given customer if it gives a non-negative utility to that customer and its utility is the maximum among all products offered by the manufacturer.

Denote i π as the first choice probability of product i, the demand rate for product i can be defined as

Λ = i i π λ , i = 1, 2, …, N.
As stated earlier, it should be underlined here that our model is not based on the assumption that only complete market coverage is optimal, which is commonly adopted by most of the existing models.

To identify the optimal design of the product line we use the well known optimality condition for the Hotteling's location model as also identified in de Groote (1994). That is, for a given N, the optimal product line has a simple structure: the market should be partitioned in segments of equal lengths, the characteristics of the products should correspond to the taste of the customers located in the middle of the segments, and the manufacturer should set prices as to make the customers located at the extreme of the segments indifferent between buying and not buying. To put it more formally, given that N is fixed, the optimal product characteristics can be determined from:

N i x i 2 1 2 * - = , i = 1, 2, …, N (2)
For the case in which complete market coverage holds, given that N, w, w c , and x c are fixed, it is easy to show that the optimal price is equal to: (3)

But since we remove the complete market coverage restriction, the optimal price expression given in (3) is no longer applicable. Instead, we now have to consider a trade-off in maximising revenue either by maximising market coverage (and setting a lower price) or increasing price with some loss in market coverage. 4) is only valid for the MTS and DD configurations as N is a relevant decision variable. For the CM configuration, however, the optimal price can be determined using a different expression explained later in § 3.4. 2) and ( 4) new can now derive the first choice probability of product i:

Note that the expression in (

if 2 2 2 1 1 or , if 1 2          < - - + - ≥ - = . N c w c r c N w c c N r N N N c w c r N x w x w x x w i π (5)

The production-inventory model

In this section we present the evaluation model for each of the three configurations. The models are required to obtain relevant measures such as the expected inventory level and lead time that are dependent on the inventory decision.

For the MTS configuration:

In this paper we adopt the evaluation model of [START_REF] Buzacott | Stochastic Models of Manufacturing Systems[END_REF]. For a given base stock level, the expected inventory for finished product i is given by:

( ) i S i i i i i S S I ρ µ λ 1 ) ( -         Λ - - = , (6) where )
( ˆi i i - - = λ µ λ ρ and ∑ ≠ -= i j j i λ λ .
The probability that the order-fulfilment time will not exceed a quoted lead time w (w ≥ 0) is given by: [ ]

w S i i i e w S T i ) ( 1 ) ( Pr Λ - - ⋅ - = ≤ µ ρ (7)
The manufacturer sets a minimum service level 1-β, where 0 < β < 1 guaranteeing that the actual lead time will not exceed the promised lead time, i.e. [ ]

β - ≥ ≤ 1 ) ( Pr w S T i i
. It is very straightforward to find that, for a given base stock level S i , the manufacturer will be reasonably interested in setting the promised lead time such that the service constraint is binding. We can state: We use the evaluation models derived in [START_REF] Gupta | Make-to-order, make-to-stock, or delayed product differentiation? A common framework for modelling and analysis[END_REF]. Suppose b, the proportion of the total lead time used to manufacture the generic component, is known. For a given base stock level of generic component, the expected inventory level is given by:

        - Λ - = ) ln ln ( 1 0, max β ρ µ i i S w . ( 8
        - - - = 1 1 1 0 0 0 1 ) 1 ( ) , ( 0 ρ ρ ρ S S b S I , (9)
where

µ ρ / 1 Λ = b .
The probability that the order-fulfilment time exceeds a quoted lead time w (w ≥ 0) is given by We have a special case of the MTS configuration with zero base stock levels. For this special case, the expected inventory level is zero and the promised lead time is given by:

( )          - ⋅         - - + = = - + ≈ ≥ - - - - + - - - - otherwise ) 1 ( , if ) ) 1 ( 1 ( ) ) ( ( Pr ) 1 ( ) 1 ( 1 2 1 1 2 ) 1 ( 2
Λ - = µ β ) / 1 ( ln w . ( 11
)

The integrated Model

The relative merits of the three configurations will be compared based on the optimal profit within each configuration. The use of a profit rather than cost function is indeed an important differentiating factor between the proposed integrated approach and the traditional approach focusing on production-inventory systems. In the following discussion, we first present a vector of base stock levels. We formalise the manufacturer's optimisation problem as follows.

Problem P MTS Max N K S I h p S x c p p N Z i i N i i i i ⋅ - ⋅ - ⋅ - = ∑ = ) ( ) , , ( ) ( ) , , , ( 1 MTS λ S x (12)
Recall that the optimal product line has a structure in which the market should be partitioned in segments of equal lengths. This means for a given N, . As already discussed in § 3.2, for a given N we are able to determine the optimal x using (2) and this optimal x will not be affected by decisions made for the base stock level S and price p. We also know that when the base stock level is given, we are able to calculate the promised lead time which in turn allows us to determine the optimal price using (4). This leads us to developing a two-stage based solution procedure. In the first stage we fix N and optimize S, and in the second stage we optimize N.

N π π π = = = ...
From (7) it can be shown that the promised lead time w is linearly decreasing with S before reaching a zero level. It can also be proven that

) ( i i S I
is increasing and a convex function of i S . This means that the expected total profit Z is a concave function of S, which eases us to determine the optimal base stock level. We now are able to determine the optimal solution for a given N. The next step is to optimise N which can be done by gradually increasing N starting from N = 1. For each value of N we optimise x, p, and S. The search can be terminated when the following condition is met:

N K c r MTS ⋅ ≤ Λ -
) ( is met. The left term in this condition is a constant and represents the maximum profit which can be gained by setting the price equal to the reservation price. The right term represents the proliferation cost which is linearly increasing with N. So the condition ensures that no better improvement is possible by increasing N.

N i i i ⋅ - ⋅ - ⋅ - = ∑ = ] , [ ) ( ] , , [ ) ( ] , , , , [ 0 0 0 1 0 DD 0 λ x (11)
The optimal solution for the above defined problem can be obtained using a technique similar to the one used in solving the problem for MTS. For a given N we need to optimize S and b, and then we need to optimize N. Different from the problem P MTS , however, it is not easy to prove whether or not the profit function is concave in 0 S . Given that b is fixed, we know that ) ( 0 0 S I is increasing in 0 S and that when 0 S is relatively large we will reach a situation in which

) ( 0 S w ≈ ) 1 ( 0 + S w
. If we reach such a situation, no improvements can be made by increasing 0 S further. To optimize b, we use a simple search technique previously demonstrated in [START_REF] Wong | Analysis of form postponement based on optimal positioning of the differentiation point and stocking decisions[END_REF]. That is, we search over b values in the range 0<b<1 using a pre-specified incremental factor. For example, if the incremental factor used is .1 then we start with b=.1 and end with b=.9. Then the next step is to optimise N which can be done using the same technique as for solving the problem P MTS .

The CM configuration

As explained earlier, the manufacturer employing CM does not need to decide the number of products as they are capable to meet exactly the unique requirement of each individual customer. This means that N and x are not relevant decision variables. In addition, no decision needs to be made for the base stock level S since we have a MTO system i.e. S = 0. Hence, price is the only relevant decision variable. The optimization problem for CM can be formulated as:

Problem P CM : Max Λ ⋅ - = ) ( ] [ CM c p p Z (12)
Solving the problem P CM is very straightforward since we just need to find the maximum price value that does not give a negative utility for customers. From ( 3) and ( 11), the optimal price can be determined as follows:

Numerical Experiment

Parameter setting

In this section we present and discuss our numerical findings. Our main inquiry will focus on how different system parameters may influence the relative performance of each of the three configurations. Our experiment involves extensive data sets with a total of 5125 problem instances being tested. Table 2 presents all the parameter values used in the experiment. We fix the aggregate demand rate ( Λ = 5) in this experiment. The reservation price is also fixed at r = 500, which we consider large enough so that the net utility is always greater than zero, and so all customers will buy a product. Five different values of µ are used for the production rate. To study how the system's behaviour is affected by the sensitivity of customers to the delivery lead time and the deviation between their ideal preference and what are offered, different values of c w and c x are tested in this experiment. Further, five values are used as the product proliferation cost for the MTS and DD configurations. We fix the unit production cost for MTS and DD at c MTS = c DD = 100. We assume that these two costs are identical, so that at the very least this gives us an upper bound on the benefits of postponement. However, we test different values for the unit production cost of CM. Five values are used starting from c CM =100, the same value as for MTS and DD. By setting the same unit cost for the three systems, we obtain a more optimistic setting for CM and may be able to gain some insights on how the CM performs by excluding the cost factor, i.e. by putting more focus on the trade-off between the lead-time and product variety. However, the larger values are also used to capture the inevitable fact that the unit production cost of CM is indeed higher due to investment in the new technology and more expensive materials, etc.

The parameter values used in this experiment are selected such that we are able to obtain general insights from the experiment rather than to represent any specific industrial case. As the sensitivity of the system performance (profit function) to one input parameter can be different from other parameters, some preliminary experiments were conducted to find a more reasonable range of values for different parameters. Our primary consideration is to set the parameter values in such a way that we are able to observe the optimality of each configuration.

F

Numerical results

For each of the problem instances we apply the solution procedures presented in § 3 to determine the optimal decisions for the three configurations. This leads to the comparison of the three configurations being made on the basis of their maximum expected profits. A number of important findings are discussed in the following.

Comparing the overall performance The above observation, however, does not reveal if there are any circumstances where CM represents the best configuration. By examining more closely the individual data sets, we found some cases in which CM indeed gains the largest profits. The results are summarised in Figure 4. The figure shows that when the CM unit production cost is the same as the other two configurations, there are 405 problem instances (out of 2500) in which CM gives the largest profits. We still find 378 problem instances in which CM is the best configuration when its unit production cost is slightly higher (c CM =105). This observation suggests that the relatively high production cost associated to the new technology could be one of the main inhibitors for CM to become viable. Another interesting observation is shown in Figure 4a where we plot those 405+378 instances as a function of the waiting time cost. It is clearly shown that CM is only viable when the waiting cost is pretty low (c w =15), which is the minimum value used in the experiment. This means that the sensitivity of customers to the waiting time seems to be an important factor too. These observations are only visible when the proposed integrated approach is used. Traditional analyses focusing only on the production-inventory system would lead to different and partial results.

Figure 4 should be placed around here

Comparing the optimal number of product lines there are also applications in mass customisation e.g. customised shoes [START_REF] Berger | Mass customisation -an adidas perspective[END_REF] where we conjecture that these customised products serve only a niche market and the total market is still dominated by the mainstream products. It is not well understood whether the difference in the adoption level of the mass customisation concept is due to the difference in the transportation cost. Empirical research that attempts to assess and compare the transportation cost for different products would certainly be worthwhile.

Figure 5 should be placed around here

The effect of the production rate Figures 6 and 7 show how the average profits for the three configurations are affected by the production rate. In Figure 6 the average profits for CM are obtained by including all the CM production costs from 100 to 125, while in Figure 7 only instances with c CM =100 are included. Both figures indicate that increasing the production rate will improve the profitability of CM significantly. In Figure 6 we see that the average profit of CM is as high as the profit of MTS when the production rate is high and in Figure 7 is comparable to DD.

The increase in the production rate has a more profound impact for the CM profitability relative to the other two configurations. This confirms our optimistic view that the advent of advanced manufacturing technologies facilitating shorter design and manufacturing lead times would certainly enhance the viability of CM.

Conclusions and directions for further research

This paper is an attempt to extend the evaluation framework for assessing the value of enhanced customisation. In contrast to the vast majority of existing studies where the focus has been heavily on the production-inventory system, the model we developed tries to address the important alignment between the production-inventory and marketing functions. Under Our numerical study provides some insights on some important aspects that may inhibit as well as potentially facilitate the movement towards a highly customised manufacturing. The main inhibitors include the high unit production cost associated with the investment in new manufacturing technologies and the customers' sensitivity to the order waiting time. In the case of Rapid Manufacturing technologies, for example, the production cost remains as one of the major constraints due to the high machine as well as material prices. We may need to wait for a few years to reach a state where products would become more affordable, which will then able to grow a niche market into a more mass market of custom manufactured products. With regard to the second inhibitor, however, the developments have been more

promising. There are no doubts that those technologies are capable of reducing the total design plus manufacturing lead time considerably. Even though it is not possible to achieve As in all models, our model has limitations. First, our results rely on the assumption that customers are identical in terms of their reservation price, transportation cost, and waiting cost. In the situations where customer heterogeneity is more evident, some key insights may change. For example, if consumers are allowed to have uncommon reservation price for their ideal products, the full market coverage may no longer be optimal. To address this limitation, the market demand model can be extended by, for example, allowing consumers to have uncommon reservation price for their ideal products. One scenario that would be worthwhile to examine is to capture the possibility that customers are willing to pay more for a greater degree of customisation, and therefore have an impact on the assessment. The second limitation is due to the fact that the model ignores competition. Extending the model by incorporating competition where products manufactured by the three different configurations may co-exist in the market may prove to be useful. Such a study will complement the existing models analysing competition between firms adopting mass production and mass customisation strategies. Furthermore, empirical research to assess different parameters in real settings is a challenge. In particular, research to estimate the customers' disutility associated with lead time as well as to the deviation between their ideal taste and what is offered would be very valuable. This research will not only useful in placing the performance comparison in a more realistic scale, but also in acquiring enhanced explanation of why some mass customisation practices are successful while some others not.

  the manufacturing choice of the flexibility of the production process. Most notably,

  different manufacturing configurations, each having a different customisation level. A graphical depiction of the three configurations is shown in Figure1.

  Configuration II: Mass customisation with delayed differentiation (DD)The second configuration accommodates what so-called "delayed differentiation" (DD) or postponement.We model this configuration as a two stage production-inventory system, with Stage-1 producing a component that is common for all finished products and Stage-2 differentiating the finished products. This configuration maintains stocks of a generic component and differentiates the finished products only after demand is realised. Hence, manufacturing

b

  b (0<b<1) as the fraction of the mean total processing time consumed by the generic component. Thus, we may write b values represent early postponement while large b values represent late postponement.

  a linear delay cost w c per time unit of delivery lead time. Higher values of x c ( w c ) mean customers are more sensitive to the deviation from their ideal products (the delay incurred).

  Figure 2 can be used to explain such a trade-off. The figure illustrates an example of one product positioning. Following (1), the optimal product characteristic, x * , is located in the middle of the segment. The green line shown in the figure represents the disutility distribution of customers when the price p B is optimised under complete market coverage (π Β = 1). The other disutility function (shown in red) represents an alternative solution as a consequence of increasing the price to p A leading to reduced market coverage (π A < 1).

Figure 2

 2 Figure 2 should be placed around here

  the optimisation problem for each configuration. Subsequently, we present the solution procedures for determining the optimal solution for each configuration.

.

  Because of this symmetry it is reasonable to have identical optimal base stock levels for all products i.e.

Figure 3

 3 Figure 3 shows the overall average profit for each of the three configurations as a function of CM c , the Custom Manufacturing unit production cost. As there is no effect of CM c for MTS and DD, the average profits for these two configurations are constant. From the figure we can see that the overall performance of DD outperforms both MTS and CM and moreover, MTS outperforms CM. This observation represents the advantage of employing delayed product differentiation in compromising what can be offered by the other two configurations. MTSdoes not offer too many product variants but offers relatively short lead times while, in contrast, CM offers unlimited product variants but with the cost of longer lead times.

Figure

  Figure 3 should be placed around here

Figure 5

 5 Figure5shows the average of the optimal number of product lines for the different values of the transportation cost for both the MTS and DD configurations. Recall that the number of product lines is not relevant for CM and that the transportation cost represents customers' dissatisfaction in not getting their ideal preferences. It is clear that increasing the transportation cost would lead to more product lines. The figure also shows how the DD configuration employing postponement has the advantage over the MTS configuration in terms of number of product lines. This is inline with the well-known result of most studies suggesting that postponement is an effective means in dealing with increasing product proliferation. By holding the common intermediate good and executing the final

FigureFigure 8

 8 Figure 6 should be placed around here

Figure 8

 8 Figure 8 should be placed around here

  , we are able to get a more complete view on how factors including inventory, lead time, price, and product variation are all important and hence, must be taken into account when analysing customisation strategies.In this paper we compare three manufacturing configurations, each with a different customisation level. The first configuration represents a traditional mass production setting characterised by a make-to-stock mode. The second configuration represents a mass customisation setting exploiting the benefit of postponement. And the final configuration represents a pure customisation setting characterised by a make-to-order mode and facilitated by advanced manufacturing technologies. The three configurations analysed correspond to the movement that attempts to bring the Mass Customisation concept towards a state with a greater degree of personalised offerings. We develop a stylised model that captures a number of aspects pertinent in Mass Customisation, which can be associated to the productioninventory as well as marketing decisions. For each of the three configurations we formulate an integrated optimisation problem and devise a solution procedure to determine the optimal set of decisions. This enables us to evaluate the relative merits of all the manufacturing configurations based on their respective best performances. The results of our numerical experiment show how different system parameters may have an impact on the preference of a certain manufacturing configuration. While our results are in favour of most studies suggesting postponement as an effective means to accommodate mass customisation, the proposed integrated approach allows us to examine the value of postponement beyond the traditional inventory cost savings. The use of a profit instead of cost function offers a more complete and holistic understanding of postponement benefits as the model captures the postponement capability in compromising product variety and delivery lead time on top of cost savings gained from reduced inventories.

  waiting time as in the mass production environment supported by finished goods inventory, this capability would certainly enhance the viability of Custom Manufacturing particularly in markets where customers' order waiting time should not be prohibitively long.

Figure 4 .-Figure 5 .Figure 7 .Figureµµhc

 457 Figure 1. Description of the three configurations

  The main concept behind RM is that any 3D shape can be fabricated as an ordered set of 2D layers with a discrete thickness, with a key advantage being the direct production of goods without any tooling (such as moulds or dies).

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To be competitive, this configuration would definitely require the support of advanced manufacturing technologies that are able to address the responsiveness and flexibility issues prevalent in the traditional MTO environment. The promising development of new techniques of manufacturing, such as found in Rapid Manufacturing, should be seen as a potential enabler of CM. Rapid Manufacturing (RM) is a term used to name a group of additive fabrication technologies that have evolved from Rapid Prototyping (RP).

Table 1 should be placed around here

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Table 2 should be placed around here

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http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research

Appendix

Recall that the optimal price that covering a complete market is equal to

Increasing the price will obviously result in reduced market coverage. It is easy to see that a price increase of p ∆ ( p ∆ ≤ 0

) will reduce the market coverage by

x c p ∆ . The revenue function as a result of a price increase of p ∆ can be represented as:

Differentiating R with respect to p ∆ , the first order condition for maximising this function is

Solving for p ∆ we obtain the optimal price increase:

The second-order condition is given by 0 4


Simona Rada
email: simona.rada@phys.utcluj.ro

Adriana Dehelean

Eugen Culea

FTIR, Raman, UV-VIS spectroscopy and DFT investigations on the structure of the iron-lead-tellurate glasses

Keywords:

In this paper, we have analyzed the effects of iron ions intercalations on lead-tellurate glasses by investigations of FTIR, Raman and UV-VIS spectroscopy. The homogeneous glass system has compositions xFe 2 O 3 •(100-x)[4TeO 2 •PbO 2 ] where x = 0-60 mol%. The presented observations in these mechanisms show that the lead ions have an affinity pronounced towards [TeO 3 ] structural units yielding the deformation of the Te-O-Te linkages and pursuant to the intercalation of [PbO n ] (n=3, 4) and [FeO n ] (n=4, 6) entities in the [TeO 4 ] chain network. The formation of [FeO 4 ] -1 structural units with negative charge implies the attraction of Pb +2 ions for compensation of electrical charge. By increasing of the Fe 2 O 3 DFT calculations show that the addition of Fe 2 O 3 content to lead-tellurate glasses seems to break the axial Te-O bonds and the [TeO 4 ] structural units are transformed little by little into [TeO 3+1 ] and [TeO 3 ] type polyhedra. The analysis of these data further indicates a gradual adaptation of lead ions from covalent to ionic environment. Then, there is a change transfer between the tellurium atoms tri-and tetra-coordinated due to the flexibility of the leadtellurate network to form the appropriate coordination environments with structural units of opposite charge such as iron ions, [FeO 4 ] -1 .

content up to 60mol%, the accommodation of the network with excess of oxygen can be supported by the formation of [FeO 6 ] structural units and the conversion of [TeO 4 ] into [TeO 3 ] structural units.

For higher Fe 2 O 3 content, the Raman spectra revealed a greater degree of depolymerization of vitreous network than do the FTIR spectra. The bands due to the Pb-O bond vibrations are very strongly polarized and the [TeO 4 ] structural units convert into [TeO 3 ] units via an intermediate coordination labeled as [TeO 3+1 ] structural units.

Our UV-VIS spectroscopic data show two mechanisms: i) the conversion of the Fe +3 to Fe +2 species in same time with the oxidation of Pb +2 to Pb +4 ions for sample with smaller Fe 2 O 3 content; ii) when the Fe 2 O 3 content is higher (x ≥ 50 mol%), the Fe +2 ions capture positive holes and are transferred to Fe +3 ions through photochemical reaction while the Pb +2 ions are formed by reduction of the Pb +4 ions.

Introduction

Oxide glasses including transition metal ions were extensively studied due to their semiconducting properties [1][2][3][4][5][6]. The conduction in ternary iron oxide glasses was confirmed to be due to hopping conduction of polaron [7].

The structural role of lead oxide in many oxide glasses is unique since lead oxide is known to play a dual role both as a network modifier and former [1,8,9]. This role depends on the type of bond between lead and oxide. These studies proposed that at high content of PbO [7,8], it would become difficult to form a network structure of binary glasses.

The structure and the properties of the oxide glasses are dependent strongly on the nature and the concentration of the constituent oxides. In normal glass system, the modifier atoms cause the network to break. In tellurate glasses, the modifier atoms cause the modification of the basic structural units such as [TeO 4 ] trigonal bipyramid and [TeO 3 ] trigonal pyramid with one of the equatorial position occupied by a lone pair of electrons [9].

The objective of this work is to analyze the structural and spectroscopic properties iron-leadtellurate glasses by investigations of FTIR, Raman, UV-VIS spectroscopy and DFT calculations. Particular attention is devoted to understand the role played by lead and iron ions in the determining the structural properties of the glasses.

Experimental

Glasses were prepared by mixing and melting of appropriate amounts of lead (IV) oxide, tellurium oxide (IV) and iron (III) oxide of high purity (99,99 %, Aldrich Chemical Co.).

Reagents were melted at 1000 °C at 15 minutes and quenched.

The samples were analyzed by means of X-ray diffraction using a XRD-6000 Shimadzu Diffractometer, with a monochromator of graphite for Cu-Kα radiation (λ = 1.54 Å) at room temperature. The X-ray diffraction patterns did not reveal the crystalline phase in the sample with x ≥ 60 mol% Fe 2 O 3 .

The FT-IR absorption spectra of the glasses in the 370-1200 cm -1 spectral range were obtained with a JASCO FTIR 6200 spectrometer using the standard KBr pellet disc technique.

The spectra were carried out with a standard resolution of 2 cm -1 .

UV-Visible absorption spectra of the powdered glass samples were recorded at room temperature in the range 250-800 cm -1 using a Perkin-Elmer Lambda 45 UV/VIS spectrometer equipped with an integrating sphere. These measurements were made on glass powder dispersed in KBr pellets.

The Raman spectra have been recorded for bulk glasses using an integrated FRA 106 Raman module in a 180° scattering geometry, at room temperature. The spectral resolution was 1cm - 1 .

The geometry optimization of the proposed structural model was carried out using the density function theory (DFT). The DFT computations were performed with B3PW91/CEP-4G/ECP method using the Gaussian'03 program package [START_REF] Frisch | Gaussian 03, Revision A1. Gaussian Inc[END_REF]. i) The larger band centered at ~625 cm -1 is assigned to the stretching mode of the [TeO 4 ] trigonal bipyramidal with bridging oxygens. The shoulder located at about 750 cm -1 indicates the presence of [TeO 3 ] structural units, Table 1 [START_REF] Frisch | Gaussian 03, Revision A1. Gaussian Inc[END_REF][11][12][13][14][15]. For all glasses, the general trend is shift towards higher wavenumber (668 cm -1 ). This suggests the conversion some [TeO 4 ] to [TeO 3 ] structural units because the lead ions have a strong affinity towards these groups containing non-bridging oxygens, which are negative-charged.

Results and discussion

FTIR spectroscopy

ii) The broader band centered at about 670 cm -1 can be attributed to Pb-O bonds vibrations from [PbO 3 ] and [PbO 4 ] structural units [16][17][18][19]. With increasing Fe 2 O 3 content up to 15 mol%, the formation of larger numbers of non-bridging oxygen's yields the apparition of Accordingly, the excess of non-bridging oxygen ions will coordinated with iron ions only after the tellurium and lead cations attain the maximum of the number of coordination (tellurium atoms -4 and lead atoms -4), in agreement with our FTIR data.

iii) For sample with x = 20 mol% Fe 2 O 3 , the participation of the lead ions than network former yields drastically modifications in the IR spectrum and the change from the leadtellurate network to the continuous iron-lead-tellurate network with interconnected through Pb-O-Te, Pb-O-Fe and Te-O-Fe bridges. This compositional evolution of the structure could be explained by considering that the excess of oxygen may be accommodated by the conversion of some [FeO 4 ] to [FeO 6 ] structural units. A new band appears at 470 cm -1 corresponding to the Fe-O vibrations from [FeO 6 ] structural units [19]. iv) For sample with x ≥ 30 mol% Fe 2 O 3 , the increasing trend towards higher wavenumbers of the bands located in the region between 550 and 850 cm -1 can be due to the conversion of

UV-VIS spectroscopy

The iron is present in glasses as Fe +2 and Fe +3 ions, both of which can exist in tetrahedral and octahedral sites [20][21][22][23][24][25]. Each redox and coordination state produces its own set of characteristic optical absorption bands. The majority of Fe +3 ions are believed to occupy tetrahedral network-forming sites in glasses, although this has been disputed [20][21][22][23].

Conversely, the majority of Fe +2 ions are through to occupy octahedral network modifying sites [21,24,25].

Fe +2 produce an oxygen-iron charge transfer band centered in the ultraviolet [26]. Spinforbidden bands are also expected in the 450-550 nm, but have been ignored in most studies of iron absorption in glasses. Then, Fe +2 ions yield two main spin allowed d-d absorption bands located at about 1100 nm and has been attributed to a range of distorted octahedral sites. Accordingly, the energy diagram of the 3d 6 configuration (Fe +2 ) indicates that its spectrum will consist essentially of a single band in the infrared region as well as a number of very weak spin-forbidden bands in the visible and ultraviolet regions.

The Fe +3 ions produce a more complicated set of absorptions than Fe +2 . Since the Fe +3 ion has a d 5 configuration, all d-d transitions are forbidden by spin-selection rules [START_REF] Burns | Mineralogical Applications of Crystal Field Theory[END_REF]. This means they are approximately 10-100 times less intense than spin-allowed transitions. The majority of Fe +3 d-d bands are observed at wavelength in the 325-450 nm region, although some Fe +3 bands are observed at wavelength as low as 700 nm.

The UV-VIS absorption spectra of xFe 2 O 3 •(100-x)[4TeO 2 •PbO 2 ] glasses with x = 0-60 mol% are shown in Fig. 2. The examinations of these spectra show that the characteristic UV-VIS bands are modified namely: i) For all glasses, the UV absorption bands begin at 250 nm by an ascending lobe. These UV absorption bands are assumed to originate lead tellurate host matrix. The stronger transitions in the UV-VIS spectrum can be due to the presence of the Te=O bonds from [TeO 3 ] structural units and Pb=O bonds from [PbO 3 ] structural units which allow n-π * transitions. Ions Pb +2 with s 2 configuration absorb strongly in the ultraviolet and yield broad emission bands in the ultraviolet and blue spectral area. The intense band obtained centered at about 310 nm corresponds to the Pb +2 ions [START_REF] Ehrt | [END_REF].

ii) By introduction of low Fe 2 O 3 content (x ≤ 5 mol%) in the host matrix, the formation of new absorption UV bands is dominant. These bands located in the 320-450 nm region are due to the presence of the Fe +3 ions. Then, the intensity of absorption band located at about 250 nm increases and the iron in some cases is reduced to Fe +2 by trapping electrons [START_REF] Friebele | Optical Properties of Glass[END_REF]. Some weak bands appear in the 450-550 nm region. These bands show that some Fe +3 were converted to Fe +2 ions.

Such tendency can be interpreted by the conversion of the Fe +3 to Fe +2 species and the same time of the present Pb +2 ions are oxidized to Pb +4 ions. Based on these experimental results, we propose the following possible redox reactions:

2 Fe +3 + 2e -↔ 2 Fe +2 Pb +2 ↔ Pb +4 + 2e -
The increase of intensity of the band situated near 300 nm can be attributed the formation of new Pb=O bonds from [PbO 3 ] structural units.

iii) The addition of Fe 2 O 3 content until 15 mol% causes a decrease in the intensity of the UV absorption bands situated in the 320-450 nm domain. This noticeable decrease can be due the iron ions can participate as former network. The sharp of the increase trend of the IR bands located at about 600 cm -1 shows the vibrations of the Fe-O bond from [FeO 4 ] tetrahedral structural units (Fig. 1). iv) Further by increasing of Fe shows the vibrations of the Fe +2 -O-Fe +3 linkages [19]. On the other hand, these intense transitions can be due to formation of [TeO 3 ] structural units from [TeO 3+1 ] structural units, in agreement with Raman spectra. vii) For sample with x = 60 mol% Fe 2 O 3 , the UV absorption bands situated in the 250-290 nm disappear and new bands appear at 320 nm. These bands show the presence of new Fe +3 ions.

Then, the kink located at about 430 nm is characteristic of Fe +3 ions in octahedral symmetry. Also, it is suggested that some of the Fe +2 ions present capture positive holes and are converted to Fe +3 according to the following photochemical reactions:

Fe +2 + positive holes → Fe +3 Pb +4 + 2e -→ Pb +2
It seems that some of the Fe +2 ions capture positive holes and are transferred to Fe +3 ions through photochemical reaction. This mechanism explains the observed increase in the UV region.

The observed continuous increase of the UV band intensity with adding of the Fe 2 O 3 content can be related to the progressive growth of induced color centers. This color center is obviously correlated with the transformation of Fe +2 to Fe +3 ions by capturing positive holes.

In brief, UV-VIS spectroscopic data show two mechanisms: i) the conversion of the Fe +3 to Fe +2 species in same time with the oxidation of Pb +2 to Pb +4 ions for sample with smaller Fe 2 O 3 content; ii) when the Fe 2 O 3 content is higher (x ≥ 50mol%), the Fe +2 ions capture positive holes and are transferred to Fe +3 ions through photochemical reaction while the Pb +2 ions are formed by reduction of the Pb +4 ions.

The conduction in ternary iron oxide glasses was confirmed to be due to hopping conduction of polaron [1,[4][5][6][7]. In the conduction of these glasses, a valence change, Fe +2 → Fe +3 + e - takes place between two iron ions in the glass. The Fe +3 ions in excess are sixfold coordinated and the remaining Fe +3 ions are in fourfold coordinated. The redox can also control the tetrahedral to octahedral Fe +3 ratio: an increase of Fe +3 leads to an increase of octahedral Fe +3 .

DFT calculations

In the quantum chemical calculations we will use the IR and UV-VIS data in order understand of the local structure 50Fe 2 O 3 •50[4TeO 2 •PbO 2 ]. Similar methodology has previously been reported to study other glasses [START_REF] Rada | [END_REF][31][32][33][34]. The study on structural modifications of the vitreous network and the equilibrium geometry were found by optimization (Fig. 3).

There are some sites in our model (Fig. 3), namely: v) Iron site is coordinated to four oxygens atoms. The three bonds have shorter Fe-O interatomic distances (1.79-1.87 Å) and one has longer interatomic distance (1.93 Å). The EXAFS analysis [35] reveals that in the iron glasses, the Fe-O bond length is equal to 1.86-1.88 Å in the [FeO 4 ] tetrahedral structural units. The distance of 1.93 Å is intermediate between that corresponding to tetrahedral (1.88 Å) and octahedral (2.00 Å) coordinated iron [36]. Therefore, it is expected that in this sample, the iron atoms occupy both tetrahedral and octahedral sites. The majority of Fe +3 ions are believed to occupy tetrahedral network-forming sites in glasses while the majority of Fe +2 ions are through to occupy octahedral network modifying sites. Then, the reduction of Fe +3 to Fe +2 always acts a network modifier, forms [FeO 6 ] structural units during glass melting is possible.

Additionally, the EXAFS analysis [35] disclosed that the coordination number of iron depends on the Fe 2 O 3 concentration. Accordingly, the number of the oxygen atoms attached in the [FeO 4 ] structural units decreases when the Fe 2 O 3 concentration increases suggest that the tetrahedral coordination of iron into the glass is destroyed.

The distribution of the electronic states of the HOMO and LUMO can be seen in Fig. 4. An interesting finding in these systems is that:

i) The HOMO gives character of electron donor for the [TeO 4 ] structural units.

ii) The LUMO gives the character of electron acceptor for the [TeO 3 ] structural units of the network.

iii) The HOMO -1 gives character of electron donor for the [TeO 4 ], [TeO 3 ] structural units and Fe +2 ions.

iv) The LUMO +1 gives the character of electron acceptor for the [TeO 3 ] and [TeO 4 ] structural units of the network.

There is a change transfer between the tellurium atoms tri-and tetra-coordinated. This can be explained considering that the lead-tellurate network is flexible to form the appropriate coordination environments with structural units of opposite charge such as iron ions, [FeO 4 ] -1 .

Accordingly, the addition of Fe

Raman spectroscopy

Fig. 5 shows the Raman spectra of the xFe 2 O 3 •(100-x)[4TeO 2 •PbO 2 ] glasses with x=0-60mol%. The shape of the Raman spectra is influenced by the presence of iron oxide in the studied glasses. The bands centered at around 465cm -1 are assigned to the stretching vibrations of Te-O-Te linkages [37]. The bands centered at around 652cm -1 are originated from vibration of the continuous networks composed of [TeO 4 ] tetragonal bipyramids and the bands centered at around 710cm -1 are contributed to [TeO 3+1 ] and [TeO 3 ] structural units [38].

It is found that the maximum phonon energy of doped glasses increased from 710 to 745 cm -1 gradually. With the increase of Fe 2 O 3 content up to 60moli%, the number of [TeO 3+1 ] coordinated polyhedral and [TeO 3 ] trigonal pyramidal structural units increase in the network structure.

The [TeO 3+1 ] unit can be thought of as distorted trigonal bipyramidal [TeO 4 ] units, with one oxygen further away from the central tellurium than the remaining three oxygen. This increase in lower coordination at the expense of higher coordination units is indicative of depolymerization of the lead-tellurite glass network.

The Raman band centered at about 270 cm -1 may be associated with Pb-O stretching and O-Pb-O bending vibrations. The strong bands situated near 120 and 135 cm -1 in the Raman spectra of iron-lead-tellurate glasses is almost certainly due to Pb-O symmetric stretching vibration [39,40]. One evidence in support is that the relative intensity of this band increases with the increasing of Fe 2 O 3 content of the glasses from x = 1 to 40 mol% Fe 2 O 3 , after that its intensity decreases evidently. This shows that the high doped with Fe 2 O 3 content can cause the broken of Pb-O bond in iron-lead-tellurate glasses. On the other hand, this is need because the content of [TeO 3 ] structural units increases. For samples with x ≥ 50 mol%Fe 2 O 3 , the increases in intensity of the UV-VIS bands located at about 310nm check up this hypothesis.

The fact that this band is very strongly polarized also indicates a high degree of symmetry of the nearest neighbors of lead atoms [39]. Except the drop of the intensity of 135 cm -1 , we find no new bands appear in the Raman spectra. By increasing of the higher Fe 2 O 3 content, the 135 cm -1 band would then be the Pb-O symmetric stretch of [PbO 4 ] pyramidal units. We think that the higher doped can cause the broken of Pb-O bonds and make the [PbO 4 ] structural units change to [PbO 3 ] chains [41]. For sample with x = 60 mol%, supplementary, well-defined Raman band appears around 415 cm -1 . This band is due to the covalent Pb-O bond vibrations [42,43].

For higher Fe 2 O 3 content, the Raman spectra revealed a greater degree of depolymerization of the vitreous network than do the FTIR spectra. It seems that the Raman spectroscopy is a more sensitive technique to the changes that appear in the short-range order of our glass structure at Fe 2 O 3 addition.

Conclusions

We were analyzed the effects of iron ions on structure of the lead-tellurate glasses by

Figure captions

Fig. 1

 1 Fig. 1 show the FTIR spectra of the Fe 2 O 3 doped lead-tellurate glasses. The examination of the FTIR spectra of the xFe 2 O 3 •(100-x)[4TeO 2 •PbO 2 ] glasses shows that the Fe 2 O 3 content modifies the characteristic IR bands as follows:

[

  PbO n ] structural units (n = 3, 4) in the vicinity of the [TeO 3 ] structural units. The increase in the intensity of the band located at about 600 cm -1 shows that the formation of the [FeO 4 ] structural units. It seems that the formation of [TeO 4 ] structural units is reduced because the modified [TeO 3 ] units containing one or more Te-O-Pb bonds are unable to accept a fourth oxygen atom. With the adding of Fe 2 O 3 in the host matrix which tend to coordinate with Fe +3 , will contribute to coordinate with glass former cation ions. According to the electronegativity theory, the covalency of the bond will become stronger with the decrease of the difference of electronegativity between cation and anion ions. Since the values of electronegativity, for Te, Fe, Pb and O elements are 2.1, 1.83, 2.33 and 3.5, respectively, the covalency of Pb-O are stronger than Te-O and Fe-O, respectively. As a result, the covalency of Te-O and Pb-O bonds is stronger than this of the Fe-O bond.

[

  TeO 4 ] into [TeO 3 ] structural units. A noticeable change appears in content of [TeO 3 ] structural units. Iron in the oxidation state +3 is reported to occur predominantly in fourfold coordinations, as [FeO 4 ] -1 . These tetrahedral geometries have a negative charge and hence need cations, in the case of the glasses studied, Pb +2 for charge compensation. Accordingly, it is possible a better stabilization of Fe +3 from [FeO 4 ] -1 tetrahedral geometry through compensation with Pb +2 ions. The presented observations in these mechanisms show that the lead ions have an affinity pronounced towards [TeO 3 ] structural units yielding the deformation of the Te-O-Te linkages and pursuant to the intercalation of [PbO n ] (n=3, 4) and [FeO n ] (n=4, 6) entities in the [TeO 4 ] chain network. The formation of [FeO 4 ] -1 structural units with negative charge implies the attraction of Pb +2 ions for charge compensation.

  2 O 3 content up to 20 mol%, the observed shift of the UV band from 250 to 260 nm and the apparition of new band located at about 285 nm is correlated to the possible distortion of the iron species symmetry. The new IR band situated at about 470 cm -1 can be attributed to the [FeO 6 ] octahedral units. The evolution of the structure can be explained considering the accommodation of the network with excess of oxygen by the conversion of some [FeO 4 ] to [FeO 6 ] structural units. v) For sample with x=30mol% Fe 2 O 3 , a new band appears at about 267 nm. This tendency can be explain again to the distortions of the iron species. It is possible a conversion of the [FeO 6 ] to [FeO 4 ] structural units. The intensity of the band centered at about 600 cm -1 increase in the FTIR spectrum. These inter-conversions of geometry decrease by increasing of Fe 2 O 3 content up to 40 mol%. vi) The very intense transitions appear in the sample with x = 50 mol% Fe 2 O 3. New band of larger intensity situated at about 305 nm are due to the presence of Pb +2 ions. The bands located in the 250-277 nm region are due to a strong oxygen-iron charge transfer derived to the Fe +2 and Fe +3 ions. The increase in the intensity of the IR band located at about 689 cm -1

  i) The basic coordination polyhedrons are [TeO 4 ] structural units which can be found in the glass in four states: tetrahedral, square pyramids, trigonal bipyramids, and trigonal bipyramids with three strong bonds and one elongated axial bond. The Te-O bonds from the square pyramids have shorter interatomic distances (2x1.74 and 2x1.85 Å) than the covalent Te-O bond length (2.15 Å). The Te-O bonds from tetrahedral geometry have one bond with shorter interatomic distances (1.78 Å) and three bonds with longer interatomic distances (1.87 Å). The Te-O bonds of the irregular polyhedrons are subdivided into two groups: (1) three bonds have shorter interatomic distances (1.74-1.82Å) and one has intermediate interatomic distance (1.92-2.02 Å); (2) three bonds have intermediate interatomic distances (1.95-2.05 Å) and one has longer interatomic distances (3.05 Å) but significantly shorter than the sum of the van der Waals radii (3.58 Å). These irregular polyhedrons are situated in the vicinity of the [PbO n ] and [FeO n ] structural units. Accordingly, the [TeO 4 ] structural units have a marked tendency towards deformation and lability of one of the axial bonds. This lability is sharply increased in the liquid state, where due to kinetic factors the axial bonds easily undergo a dynamic elongation over 2.15 Å. The coordination number of the tellurium atom changes from 4 to 3+1 and marked tendency towards elongation of the Te-O distances over 2.15 Å is observed. In the last states, as a consequence, a 3+1 coordination of the tellurium atom is required. The extent of bond deformation, besides the kinetic factors, is also influenced by the composition, temperature and viscosity of the melt, by the nature of the modifier, as well as by some thermodynamic factors. ii) The presence of [TeO 3 ] polyhedra in the glass is also possible and depends strongly on the modifier concentration. The Te-O distances are divided into three sets: a set of three shorter distances range from 1.79 to 1.85 Å, three have intermediate bonds range from 1.93 to 2.06 Å and one has longer interatomic distance (3.39 Å). iii) In this structure, four-coordinated lead atoms occupy two different sites. The first are coordinated with four oxygen atoms forming distorted tetrahedral octahedral geometries, the four Pb-O bonds have short interatomic distances (1.98-2.13 Å). The second lead atom has ionic character. One Pb-O bond have shorter interatomic distances (2.11 Å), one has longer Pb-O bond distances (2.83 Å) than the Pb-O covalent bond (2.22 Å) but significantly shorter than the sum of the van der Waals radii (3.54 Å) and two oxygen atoms remain relatively far away from lead cation (4.12-4.75 Å). These bonds are too long to be accepted as a chemical bond in the usual sense. iv) The three-coordinated lead atoms are in two diverse sites. In the first site, three bonds have shorter interatomic distances (1.90-2.06 Å). Another site has two shorter interatomic distances (2.19-2.21Å) and one Pb-O bond has longer interatomic distance (2.96 Å) than the Pb-O covalent bond.

  2 O 3 content to lead-tellurate glasses seems to break the axial Te-O bonds because of the strong polarizability of the tellurium lone pair electrons and leads to the formation of glass structure. As a result more non-bridging Te-O bonds are formed and the [TeO 4 ] structural units are transformed little by little into [TeO 3+1 ] and [TeO 3 ] type polyhedra when the metal oxides are added more and more. The analysis of these data further indicates with an increase in the concentration of Fe 2 O 3 , a gradual adaptation of lead ions from covalent to ionic environment.

  investigations of FTIR, Raman and UV-VIS spectroscopy. Based our results, we conclude that the accommodation of the networks with the excess of oxygen it is possible by the deformation of Te-O-Te linkages, the participation of lead and iron atoms as former network and the intercalation of [FeO 6 ] entities in the [TeO 4 ] chain network. Our UV-VIS spectroscopic data show the existence of the reversible redox process in the matrix host by increasing of the Fe 2 O 3 content. For smaller Fe 2 O 3 content the mechanism implies the conversion of the Fe +3 to Fe +2 species in same time with the oxidation of Pb +2 to Pb +4 ions. Inversion redox processes take place for higher Fe 2 O 3 content. DFT calculations show that the [TeO 4 ] structural units have a marked tendency towards deformation and lability of one of the axial bonds. This can be explained considering that the lead-tellurate network is flexible to form the appropriate coordination environments with structural units of opposite charge such as iron ions, [FeO 4 ] -1 . The Raman spectra show that a very strong depolymerization appears in studied iron-leadtellurate glasses with the Fe 2 O 3 addition. The bands due to the Pb-O bond vibrations are very strongly polarized indicating a high degree of symmetry of the nearest neighbors of lead atoms. The intensity of band around 720 cm -1 increases relative to the band at 660cm -1 with increase in Fe 2 O 3 content indicating that the [TeO 4 ] structural units convert into [TeO 3 ] units via an intermediate coordination labeled as [TeO 3+1 ] structural units.

Fig. 1 FTIRFig. 3 Fig. 4 1 ,Fig. 5

 13415 Fig. 1 FTIR spectra of xFe 2 O 3 •(100-x)[4TeO 2 •PbO] glasses with 0 ≤ x ≤ 60 mol%

Acknowledgments

The financial support of the Ministry of Education and Research of Romania-National University Research Council (CNCSIS, PN II-IDEI 183/2008, contract number 476/2009) is gratefully acknowledged by the authors.

Tables

 Table 1 Assignments