1. Introduction
Balance of supply and demand has been one of the most important issues in manufacturing companies in recent decades. Manufacturing companies look for an inventory and supply management approach which can obtain the most benefit out of the investment in raw materials, work in process, and finished products inventories ( ^{Donath, 2002} ). As discussed by ^{Wu & Olson (2008)} and ^{Wang (2009)} , holding finished products, delayed orders, shortages, and disposing outmoded and expired products are the most common inventory costs in a manufacturing system.
Many of the above mentioned inventory costs are related to using MTS strategy, where the company produces finished products based on its market demand forecast. The most important feature in MTS strategy is to obtain higher order satisfaction rates in comparison to the other strategy, MaketoOrder (MTO). MTS strategy offers a lower possibility of customization, but less expensive products compared to MTO strategy. On the other hand, issues such as higher average order delay, higher average response time and due date setting are considered as concerns of MTO production systems. These systems offer more expensive products due to higher variety of customer customization ( ^{Soman et al., 2004} ).
The system under study tries to mix the MakeToStock (MTS) and MakeToOrder (MTO) strategies to benefit from the both manufacturing systems. This idea is developed by applying the Order Penetration Point (OPP) in production lines. The main idea of using such a point in manufacturing systems mostly addressed in research articles in the field of supply chain management. This point is defined as a point of a supply chain where each product is dedicated to a specific order of a known customer ( ^{Olhager, 2003} ). In order to emphasize that this point is directly related to the customer order, some researchers considered that as Customer Order Decoupling Point (CODP). The usage of OPP in production lines is depicted in Figure 1 .
The positioning of OPP is widely studied as a challenging issue in supply chain management in recent decades. Nonetheless, considering this concept in manufacturing systems to compare different production strategies (MTS/MTO) has not been widely studied yet. In this regard, by doing a search in “scholar.google.com” to find an article with the words “Manufacturing” and “Order Penetration Point” in the title, we can’t find even one article. According to the best knowledge of authors (doing research in this area about 10 years), the most related study is a book chapter by ^{Süer & Lobo (2011)} , where they considered the hybrid strategy in cellular systems. Their study compared the connected and disconnected cellular systems in a case study of a medical device manufacturing company and simulated different scenarios to compare two cellular manufacturing companies.
The motivation of this paper is to show how manufacturing companies can apply the OPP to obtain benefits from both MTS and MTO strategies according to various cost parameters of the production lines. Moreover, using queuing theory concepts to model the problem under study helps to consider the external factors such as impatient customers and demand arrival uncertainty that can affect the performance measures of the system besides the internal factors such as production rate and inventory related costs. In real production environments, it is possible that a company wants to expand the production line after a specific station and have more customization lines to improve customer satisfaction. This multiple customization line idea is studied in this study as well.
The rest of the paper is organized as follows. The related literature of different applications of OPP in both academia and industry is reviewed in Section 2. Section 3 is dedicated to describe the focus of this study and define the notation to model the problem. Section 4 formulates the problem and presents the solution method. A numerical example with a vast sensitivity analysis is presented in Section 5, and Section 6 concludes the study and discusses the future study paths.
2. Literature review
In the past two decades, developing new production strategies such as MTS/MTO manufacturing gained a high attention from the researchers to work out the lack of compliance between real market demand and demand forecasts. The differentiation point between MTO and MTS strategies is known as Order Penetration Point (OPP) ( ^{Olhager, 2003} ) in the literature and determining the OPP has become an important strategic decision in supply chains and production systems according to its capabilities to reduce the inventory management costs. The terminology of Decoupling Point (DP) ( ^{Sharman, 1984} ) and Customer Order Decoupling Point (CODP) ( ^{Hoekstra & Romme, 1992} ) is noted in the literature for the same concept.
According to ^{Herer et al. (2002)} , the OPP distinguishes the customer response part of a manufacturing system from the forward strategic planning part. From the strategic viewpoint, there are two encouraging factors to place the OPP in the final processes of a production line: decreasing the lead time and improving the production efficiency. Table 1 presents the advantages and disadvantages of shifting the OPP toward the end of the production line:
Competitive advantage addressed  Reasons for forward shifting  Negative effects 

Delivery speed  Reduce the customer lead time  Rely more on forecasts (risk of obsolescence) 
Delivery reliability  Process optimization (improved manufacturing efficiency)  Reduce product customization (to maintain work in process and inventories levels) 
Price  Increase workinprocess (due to more items being forecastdriven) 
On the other hand, the main reason to moving OPP toward the upperhand processes of a production line is to gain more knowledge about the customer order specifications in manufacturing period, which enhance the possibility of customization and reducing the amount of workinprocess. Table 2 presents the advantages and disadvantages of shifting the OPP toward the first machines of a production line.
Competitive advantage addressed  Reasons for backward shifting  Negative effects 

Product range  Increasing the degree of product customization  Longer delivery lead times and reduced delivery reliability (if production lead times are not reduced) 
Product mix flexibility  Reduce the reliance on forecasts  Reduced manufacturing efficiency (due to reduced possibilities to process optimization) 
Quality  Reduce or eliminate WIP buffers  
Reduce the risk of obsolescence of inventories 
The concept of using hybrid manufacturing beside pure MTO in a scheduling problem is developed by ^{Wu et al. (2008)} to maintain high utilization of machines. Their research proposed a scheduling method for a hybrid manufacturing system with the characteristics of machinededication. The goal of the presented model is to achieve a high throughput for MTS products and high ontime delivery rate for MTO products.
A recent study by ^{Olhager & Prajogo (2012)} compared MakeToOrder and MakeToStock firms by examining the data from 216 Australian manufacturing firms. It is shown that MTO systems exhibits a specified impact for integration of suppliers on improving the performance of business, but this is not the case for supplier rationalization and lean practices.
Queuing theory concepts are applied to find the OPP in a study by ^{Teimoury et al. (2012)} . They considered a multiproduct MTS/MTO manufacturing system which has probabilistic distribution for both customer arrival and manufacturing semifinished products. ^{Zhang et al. (2013)} used queuing theory for dynamic pooling of the MTS and MTO operations. In their model, a subset of machines is dynamically switched between two strategies. They quantified the performance measures of the system by developing analytical formula. This approach minimizes the total costs of the system with customer satisfaction constraints.
The performance analysis issue in MTS/MTO manufacturing systems is studied by ^{Almehdawe & Jewkes (2013)} . This study is more dedicated to inventory costs including replenishment and batch ordering policies.
Table 3 shows a brief introduction of recent studies of OPP in different aspects of production and service systems:
Authors  Problem  Objective Function  Case Study  Environment  DemandProduct Structure  OPP  Modelling/ Solution Approach 

Sun et al. (2008)  Positioning multiple decoupling points in a supply network  Min. setup cost, inventory holding cost, stockout cost and asset specificity cost  No  MTS/MTO  Stochastic demand, multiple parts of a product  Decision variable  Mathematical modeling/Optimization 
Rafiei & Rabbani (2011)  Order partitioning and locating OPP  Comparing various performance measures  Yes  MTS, MTO, MTS/MTO  Exact demand, Product families  Decision variable  Fuzzy analytic network process 
Kalantari et al. (2011)  Order acceptance or rejection  Min. production cost, outsourcing cost and lateness/earliness penalty  No  MTS/MTO  Fuzzy demand, Multiproduct  Located at the middle of production line  Fuzzy TOPSIS, Mixed integer mathematical programming 
Sharda & Akiya (2012)  Selecting the inventory management policy  Max. on time fulfillment, Min. production and inventory cost  Yes  Combined MTS/ Postponement 
Stochastic demand, Multiproduct  Decision variable  Discrete event simulation 
Zhang et al. (2013)  Finding the optimal plan of switching servers between MTS and MTO  Min. total cost of system, satisfying service constraints  No  MTS, MTO  Stochastic demand, Single product  Non applicable  Queueing theory/Direct search procedure 
Almehdawe & Jewkes (2013)  Applying batch ordering policy to optimize a MTS/MTO manufacturing system  Min. holding cost, batch ordering cost and penalty cost of fulfillment delay  No  MTS/MTO  Stochastic demand, Single product  Located at the middle of production line  Matrixanalytic method, optimization model/Enumeration 
Shidpour et al. (2014)  Comparing single and multiple customer order decoupling point  Max. sold product income and Min. holding cost, production cost and back order cost  Yes  MTS/MTO  Stochastic demand, Multiproduct  Located at the middle of production line  Multiobjective mathematical programming 
Liu et al. (2014)  Time scheduling of logistics service  Min. operation cost, tardiness and Max. service providers satisfaction  No  MTS/MTO  Deterministic demand, Stochastic multiprocess time  Decision variable  Multiobjective Programming/Genetic Algorithm 
Ghalehkhondabi et al. (2016)  Multiple OPPs in a supply chain with uncertain demands in two consecutive echelons  Min. manufacturing cost, holding cost, and waiting cost.  No  MTS/MTO  Stochastic demand, Multiproduct  Decision variable  Mathematical modeling/Optimization 
The viewpoint of current study is similar to ^{Teimoury et al. (2012)} , where the authors used queuing Matrix Geometric Method (MGM) to find the OPP in a twostage supply chain. The mathematical models in the literature of MTS/MTO manufacturing commonly try to find an optimal balance between the customer satisfaction levels and inventory costs, but to the best knowledge of authors, system idleness and multiple customization lines have not been studied in the literature yet.
3. Problem description
The following notations are used for problem description and mathematical modeling:
Decision Variables:
Parameters:
We consider a production line with m stations, where customer orders arrive to the line following a Poisson distribution with rate
According to above explanations, the time needed to complete a semifinished product based on a specific demand follows an exponential distribution with mean
It is notable that the customization of semifinished products can be done by T number of production lines after OPP. More explicitly, in order to increase the rate of service in completing semifinished products and decreasing the waiting time, the manufacturing plant can resume the production after OPP with more than one production line, which is a decision variable in the current study. The cost of constructing a new line is a decreasing function of
The customers of this production line have the characteristics of impatient customers including balking and reneging. A customer on arrival to the line may find n customers already in the line (including the one currently being served). Arriving customer may decide to enter the line with probability
The customers who are in the queue may get impatient and run out of the line without being served (which is known as reneging in Queuing Theory). This waiting time follows an exponential distribution with mean
The object is to achieve the following goals under two scenarios: 1 Obtaining the best place for semifinished products buffer (OPP). 2 Comparing the cost of MTS/MTO manufacturing and MTS/MTO manufacturing plus MTS when there is no specific order in the system. 3 Finding the optimal number of customization lines after the place of OPP.
3.1. Scenario 1
In the first scenario, semifinished products are produced by the first g machines (g<m) and stored in a buffer after machine g. The percentage of completion can be considered by
3.2. Scenario 2
In the second scenario, we use both MTS and MTO for completing the semifinished products. When there is no customer in the system, semifinished products are completed based on the MTS strategy and finished products are sent to a warehouse. But, when an order comes in for customization, a semifinished product get assigned to that order and after finishing the current MTS job on each machine, this MTO job starts to complete the semifinished product. The second scenario manufacturing system can be shown as Figure 3 .
There is a major difference between the two scenarios, where semifinished products are present in the system but there is no customer to get service. Here, the conflict between the idle cost and inventory cost should be balanced by choosing one of the above mentioned scenarios. In Section 4, main parts of problem formulation and solution approach are presented only for first scenario to avoid the extra writing. Some of important issues of second scenario are explained as well.
4. Problem formulation and system performance measures
In order to obtain the cost of performing under each scenario, there is a need to find the steady state measures of the system. As the arrival orders and producing semifinished products have a probabilistic nature, bidimensional queue is used to model the system.
4.1. State transition diagrams and balance equations
The system consists of probabilistic arrival of customers and semifinished products, so each of these arrivals can create a queue in the production line. Such a system can be modeled by a quasi birth and death Markov process with the states of
In order to model the long term costs of current production line, it is necessary to obtain the probabilities of steady states
In this matrix
Each steadystate probability vector
Where a is the rate at which semifinished products are converted to finished products and equals to
By all of the previous information, the second scenario steady state diagram is depicted in Figure 5 .
Where a is the rate at which semifinished products are converted to finished products and equals to
By solving the queuing balance equations, we can find the probability of system idleness and also the probability of states that customers are waiting in the system but no semifinished product exists in the buffer. By these probabilities, we can define a costbased objective function which includes cost of idle machines, holding inventory and order fulfillment delay.
4.2. Performance evaluation measures
In order to construct optimization models for two scenarios under study, we need to derive some performance measures of the production line considering the steady state probabilities. Table 4 shows the applied performance measures in the optimization model.
Performance measure  Formula  Identifier 

The expected number of semifinished products in the buffer 

(15) 
The expected time at which the machines after semifinished products buffer are idle 

(16) 
The mean number of products which are produced based on pure MTS when there is no specific order in the system 

(17) 
The mean number of customers in the system when there is no semifinished product available to satisfy their order 

(18) 
The expected number of orders in the line 

(19) 
The mean value of waiting time 

(20) 
The mean value of balking customers 

(21) 
The mean value of reneging customers 

(22) 
The expected number of lost customers 

(23) 
It is notable, when there is no customer in the system in the second scenario, one of the semifinished products goes to the line to be completed based on MTS and after producing this product, if a customer with a specific order had come into the system, the line starts to produce on MTO. So, in calculating E(H), steady state probabilities are multiplied by k=1.
4.3. Model of the first Scenario
In order to construct the mathematical models in this study, the approach of ^{Jewkes & Alfa (2009)} and ^{Teimoury et al. (2012)} is applied. The objective function is based on the defined costs of the system. The total cost of the system should be minimized considering the operational constraints of the system. The mathematical formulation of Scenario 1 is as follows:
subject to:
Objective function 24 minimizes the total cost of holding semifinished products in the buffer, cost of lost customers, cost of delay in fulfilling customer orders, cost of idleness for T lines, backorder cost and the cost of establishing T customization production lines. Constraint 25 denotes the service level of the product, where the expected customization time
4.4. Model of the second Scenario
The mathematical formulation of Scenario 2 is as follows:
subject to:
Objective function 28 minimizes the total cost of holding semifinished products in the buffer, cost of lost customers, cost of delay in fulfilling customer orders, cost of holding completed products by MTS, backorder cost and the cost of establishing T customization production lines. Constraint 29 denotes the service level of the product where the expected customization time
In Section 5, a numerical example is presented to depict the applicability of presented models and a vast sensitivity analysis is performed to understand how the system behaves versus various parameter values.
5. Numerical example
In order to represent the applicability of the presented model and the solution method, a numerical example with parameter analysis is presented in this section. We consider a production line with
The line manager wants to choose a strategy between Full MTO, Full MTS and MTS/MTO manufacturing according to the presented scenarios in Section 4. According to system cost parameters, it is desired to find a place for the semifinished products buffer (finding
There is a setup time for each machine if it wants to customize a product due to a specific order, which follows an exponential distribution with the parameter of
As discussed in the model presentation, there are some specific costs for each scenario. The cost of idleness for each machine in scenario 1 is
As a logical assumption, the holding cost of semifinished products is related to the completion percentage of the product ( ^{Jewkes & Alfa, 2009} ), so the product value follows the equation
The results of solving this numerical example by MATLAB 7 are presented in Table 5 . As it is seen in Table 5 , presented model works well for the considered production line. In this example we also want to consider Full MTO and Full MTS options besides the MTS/MTO manufacturing strategy, which is equal to

first Scenario  second Scenario  



Total Cost 


Total Cost  
Full MTO  MTS/MTO Manufacturing  Full MTS  Full MTO  MTS/MTO Manufacturing  Full MTS  
1  80%  4  6.79  4.58  10.34  60%  3  6.05  4.72  10.52 
2  60%  3  6.39  4.56  10.87  60%  3  4.40  3.91  11.06 
3  80%  4  7.37  5.13  NS  40%  2  4.01  3.85  NS 
4  80%  4  8.88  5.62  NS  40%  2  4.09  4.07  NS 
5  80%  4  10.63  6.15  NS  20%  1  4.38  4.46  NS 
Each T value has an optimal total cost which is shown by italic underlined font, and the best answer of each scenario is shown by bold font in Table 5 . For example in second Scenario, manufacturing based on the MTS/MTO strategy for
Table 5 shows the optimum completion percentage of each semifinished product with the number of product completion lines after OPP. As it is seen in the first scenario, two product completion lines is the best option based on cost function value. If we consider two completion lines after OPP, the best percentage of product completion before OPP is 60%, which means to place OPP after the third station. Following the above mentioned condition, adopting the MTS/MTO manufacturing strategy with two completion lines and producing 60% completed products has a cost of 4.56 monetary unit in steady state, which is lower than Full MTO and Full MTS strategies due to customer and market characteristics.
In the first scenario, the total cost and completion percentage are both convex in
It is notable that even in this case, service level decrease costs by improving the customization speed, but establishing a new completion line has its own cost, which was represented by a decreasing formula of
The behavior of
But, with faster lines the customers will get faster service and the idle time of the system increases in the line. This is the reason that the total cost increases when
As shown in Figure 6 , the minimum cost of second scenario is related to a production line with three completion lines after OPP and producing 40% semifinished products. More explicitly, the OPP place in the second scenario is after the second station and the remaining process is done in three lines, each has three stations. According to customer and market characteristics, the cost of optimal answer in the second scenario is 3.85 in steady state. Comparing costs of two offered scenarios for this production line, it is shown that the second scenario has a lower cost and its better for the system to produce completed MTS products when there is no customer in the system, and bear the holding cost of finished products instead of bearing the cost of idle machines.
In the second scenario, the behavior of total cost against increasing
In this section, some other system behaviors are analyzed by various values of system parameters to better show the applicability of model and clarify the concept. Moreover, the logical behavior of system performance measures can be considered as the validity of the presented calculations and the proposed model.
5.1. Total cost variations against
It is a basic rule in queuing theory to consider the rate of customer arrivals less than the service rate of the system to make the system stable; otherwise the queue will be long and longer to infinity. In current study, there is no need to consider such a rule due to the fact that our system has a finite queue and also the service rate of the system is more than
According to the convergence of the total cost of the system by increasing
As it is seen in Figure 7 , for
Another important trend is the higher total costs of lower
5.2. System performance measures versus
As the customer arrival rate has specific effects on the system cost and its performance, changing production rate can affect the system performance, too. Here, the production rate
Figure 8 a represents the increasing trend of semifinished products versus increasing
Changes of expected time for fulfilling orders and customer loss rate are shown in Figures 8 8d. When the production rate increases, the customer orders are satisfied faster and the queue length gets shorter, which leads to lower waiting and order fulfillment time. The queue length is directly used in the formulas of calculating customer loss rate. As a result, decrease of customer loss rate versus increased
5.3. Affect of different numbers of customization lines T on system performance measures
As the production rate and customer arrival rate affected the system performance, number of production lines after OPP can affect the system performance by changing important characteristics of the system, as well. Variations of system performance measures versus the number of product customization lines are depicted in Figures 9 9d.
The analysis of system performance measures versus
This system behavior versus increasing
6. Conclusions
In this article a model is developed to show the application of Make to Stock (MTS)/Make to Order (MTO) manufacturing in a production line to derive the benefits of both MTS and MTO strategies. The model is capable to find the Order Penetration Point (OPP) in the production line, which is the buffer of semifinished products in the production system. Such as many real production systems, the production processes and customer arrivals have stochastic nature and customers have the possibility of not entering the system due to the long queue or departing the system due to long waiting time.
A twodimensional queueing model is developed to obtain the performance measures under two different scenarios. The main difference between two scenarios is the utilization of the customization stations, where the system can only customize semifinished products based on the specific customer orders or customize semifinished products based on both customer orders and forecast. The objective function is costbased and lets the production line manager to find the optimal place of OPP, optimal number of customization lines after the OPP and the best scenario to customize the semifinished products.
The applicability of presented model and scenarios is shown by a numerical example and the observations show the convexity of total cost in terms of product completion percentage and number of customization lines after the OPP. Also, it is shown that increasing the production rate leads to higher expected number of semifinished products in the buffer, less expected number of backorders, less expected order fulfillment time and less customer loss rate. Observing the system behavior by increasing the number of customization lines after the OPP shows the reduction of expected number of semifinished products in the buffer, increase of expected number of backorders, reduction of expected order fulfillment time and customer loss rate.
The current study considers the exponential time between the arrivals of customers and semifinished products. As a possibility of future research, other applicable distributions can be considered to model this problem. Applying Fuzzy theory is another interesting way of studying the uncertain behavior of customers and production line in the studied system. Moreover, the effect of some other market characteristics such as competing companies or substitute products on OPP or the required production rate can be studied in future research.