Grzegorz Bocewicz
email: bocewicz@ie.tu.koszalin.pl

Peter Nielsen

Zbigniew A Banaszak
email: z.banaszak@wz.pw.edu.pl

Vinh Quang Dang

Cyclic Steady State Refinement: Multimodal Processes Perspective

Keywords: cyclic processes, multimodal process, state space, periodicity, dispatching rules

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Operations in cyclic processes are executed along sequences that repeat an indefinite number of times. In everyday practice they arise in different application domains such as manufacturing as well as service domains (covering such areas as workforce scheduling, timetabling, and reservations [START_REF] Fournier | Cyclic scheduling following the social behavior of ant colonies[END_REF], [START_REF] Liebchen | A case study in periodic timetabling[END_REF], [START_REF] Song | Petri net modeling and scheduling for cyclic job shops with blocking[END_REF]). Such systems belong to a class of systems of concurrently flowing cyclic processes (SCCP) [START_REF] Alpan | Dynamic analysis of timed Petri nets: a case of two processes and a shared resource[END_REF], [START_REF] Bocewicz | Design of admissible schedules for AGV systems with constraints: a logic-algebraic approach[END_REF], [START_REF] Polak | The performance evaluation tool for automated prototyping of concurrent cyclic processes[END_REF], and relevant cyclic scheduling problems belong to a class of NP-hard ones [START_REF] Levner | Complexity of cyclic scheduling problems: A state-of-the-art survey[END_REF]. Subway or train traffic can be considered as an example of such kind of systems. Subway trains following particular metro lines can be treated as cyclic processes passing, the sequence of stations, allows one to state a question concerning a minimization of the total passenger travel time. So, if passengers travel between two distinguished locations in the transportation network for which no direct connection exists, i.e., transfers become inevitable, the relevant scheduling problem can be stated in the following way. Given is a set of metro lines, i.e. the set of trains' routings. Some lines may share common stations. Given is also a headway time, i.e., the fixed interval between the trips of a line sometimes called the period time. The question considered is: Which transportation route between two designated terminal stations in the transportation network provides the shortest travel time subject to assumed constraints? So, the best transportation route of the multimodal process, i.e. sharing different lines, is sought. This type of system finds many analogies in manufacturing, in the form of routing between fixed manufacturing lines, e.g. routing and scheduling of AGVs within an Automated Storage and Retrieval System environment.

Many models and methods have been proposed to solve the cyclic scheduling problem. Among them, the mathematical programming approach (usually IP and MIP), max-plus algebra [START_REF] Polak | The performance evaluation tool for automated prototyping of concurrent cyclic processes[END_REF], constraint logic programming [START_REF] Bocewicz | Design of admissible schedules for AGV systems with constraints: a logic-algebraic approach[END_REF], [START_REF] Bocewicz | Cyclic Steady State Refinement[END_REF], [START_REF] Wójcik | Constraint programming approach to designing conflict-free schedules for repetitive manufacturing processes. Digital enterprise technology[END_REF] evolutionary algorithms and Petri nets [START_REF] Alpan | Dynamic analysis of timed Petri nets: a case of two processes and a shared resource[END_REF], [START_REF] Song | Petri net modeling and scheduling for cyclic job shops with blocking[END_REF] frameworks belong to the more frequently used. Most of these methods are oriented towards finding a minimal cycle or maximal throughput while assuming deadlock-free process flow. Approaches trying to estimate the SCCP cycle time from local cyclic processes structure and the synchronization mechanism used (i.e. rendezvous or mutual exclusion instances) are quite unique [START_REF] Alpan | Dynamic analysis of timed Petri nets: a case of two processes and a shared resource[END_REF].

In that context our main contribution is to propose a new modeling framework enabling to evaluate the cyclic steady state of a given SCCP on the base of the assumed processes topology, dispatching rules employed, and an initial state. So, the objective of the presented research is to provide the observations useful in the course of multimodal processes routing and scheduling in systems composed of concurrently flowing cyclic processes interacting between oneself through mutual exclusion protocol. The goal is to provide the conditions useful for routing and scheduling of SCCP so as to be effective in the course of multimodal processes control.

In order to achieve it, the paper presents an introduction to the SCCP, and then to the concept of state space of considered systems. Consequently, the terms of a cyclic steady state and the corresponding space of cyclic steady states are introduced as well as conditions linking them with multimodal processes scheduling are presented.

Concept of Multimodal Processes System

Systems of Concurrent Cyclic Processes

Consider the digraph shown in Fig. 1. The distinguished are three cycles specifying routes of cyclic processes , and respectively. Each process route, specified by the sequence of resources passed on among its execution, can interact with other processes through so-called system common resources. So, the process routes are specified as follows:

, , , where the resources , , , are shared resources, since each one is used by at least two processes, and the resources , , , are non-shared because each one is exclusively used by only one process. Processes sharing common resources interact with each other on the base of a mutual exclusion protocol. Possible resources conflicts are resolved with the help of assumed priority rules determining the order in which processes make their access to common shared resources (for instance, in case of resource , the priority dispatching rule determines the order in which processes can access to the shared resource , i.e. at first to the process , then to the process , next to and once again to , and so on).

Fig. 1. Process routes structure of SCCP owning three processes

In general case, each process (where: ,a number of processes) executes periodically a sequence of operations performed on resources creating the given process route , , where a length of cyclic process route, --the number of resources, and . The time , of operation executed on along , is defined in the domain of uniform time units ( set of natural numbers). So, the sequence describes the operation times required by . To each common shared resource the priority dispatching rule , , is assigned, where , is a number of processes dispatched by . In that context a can be defined as follows [START_REF] Bocewicz | Cyclic Steady State Refinement[END_REF]:

, ( 1
)
where:

the set of resources, the set of local processes, the set of local process routes, the set of local process routes operations times, the set of dispatching priority rules. Let us assume the all operation times are equal to a unit operation time (noted as: u.o.t.) , , , . In the case of the SCCP considered the following constraints imposed on processes interaction are assumed:

 The new process operation may begin only if current operation has been completed and the resource designed to this operation is not occupied.  The new process operation can be suspended only if designed resource is occupied.  Processes suspended cannot be released and processes are non-preempted.

The main question concerns of a SCCP cyclic steady state behavior and a way this state depends on direction of local process routes as well as on priority rules, and an initial state, i.e. initial process allocation to the system resources. Assuming such a steady there exists the next question regarding of travel time along assumed multimodal process route linking distinguished resources plays a primary role.

-the resource occupied by the process -the resource occupied by the process and controlled by the priority dispatching rule -the unoccupied resource Legend:

the multimodal process mP1 the multimodal process mP2

States Space

Consider the -th state

(2) composed of the sequence of processes allocation , the sequence of semaphores (encompassing the rights guaranteeing processes' access to a resource)

, and the sequence of semaphore indices : ,

where: the processes allocation (a number of CCPS resources), (a set of processes:

) means the process is allotted to the -th resource in the -th state, means, the -th resource is occupied by the process , and -the -th resource is unoccupied.

the sequence of semaphores corresponding to the -th state, where means the name of the process (specified in the -th dispatching rule , allocated to the -th resource) allowed to occupy the -th resource . the sequence of semaphore indices corresponding to the -th state, where means the position of the semaphore in the priority dispatching rule :

, ( , for .

The state is feasible only if for any of its co-ordinate in , the following conditions hold: i) ,

if the values of the semaphore and the sequence of semaphore indices result from allocation (3), (4) (i.e., semaphores determining busy resources show the processes allotted to them, while indexes show semaphore values).

The set of all feasible states is called a state space . The states and can be linked determining transitions among states, e.g. means the state follows the state . In general case, the states can be linked via other states, e.g. , what leads to the following sequence of transitions: , in short, where: -means the number of states , linking , , e.g., in case consider , and . a transition , can be represented as the following function:

, ( 5
)
where:is a transition function [START_REF] Bocewicz | Cyclic Steady State Refinement[END_REF].

The deadlock state

(denoted in the rest of the paper by ) is defined as the state such that does not exist any feasible state , following the transition . So, the deadlock state means the all processes in the CCPS are suspended. In a state space following from a given SCCP model [START_REF] Alpan | Dynamic analysis of timed Petri nets: a case of two processes and a shared resource[END_REF], and the next state function (5) one can easily distinguish two kinds of reachability digraphs (see Fig. 2a). The properties specifying particular kinds of possible behaviors are as follows: Fig. 2. Illustration of the state space structure a), the string-like digraph ending with a deadlock state b), and the string-like digraph ending with a state belonging to a cyclic steady state c)

Property 1

Consider the SCCP model ( 2) and an initial state . The reachability digraph, generated from an initial state , is either a string-like digraph ending with a deadlock state, i.e. (Fig. 2b): , , or a string-like digraph ending with a state belonging to the cyclic steady state (Fig. 2c): , , where a number of states creating the cycle.

Property 2

Consider the sets of initial states ending with the same the -th deadlock state , and initial states ending with states belonging to the -th cyclic steady state , respectively. Assume a state space generated by the SCCP model ( 1) and the next-state function [START_REF] Levner | Complexity of cyclic scheduling problems: A state-of-the-art survey[END_REF]. The following conditions hold: i)

, where -the set of deadlock states, ii)

, where: -the set of cyclic steady states.

That means the following questions can be considered:

 What are the sufficient conditions guaranteeing the state space is free of deadlock states and states leading to the deadlocks?  What are the conditions guaranteeing transitions among assumed cyclic steady states?  What is the period of the cyclic state of multimodal processes performed in the SCCP executed in a given cyclic steady state?

The multimodal processes

Let | } be the set of cyclic processes determined by the set of process routes | }. Consider the set of multimodal processes , where -is a number of multimodal processes. Due to our in-Legend: formal definition, each multimodal process is specified by the transportation route which is a sequence of sections of local cyclic process routes: , ). In that context a can be defined as a pair [START_REF] Bocewicz | Cyclic Steady State Refinement[END_REF]:

, ( 6
)
where:

is specified by the (1), characterizes the SCCP behavior, i.e.

the set of multimodal process, the set of multimodal process routes, the set of multimodal process routes operations times. Since, the multimodal processes execution depends on a steady state of the SCCP considered their periodicity depends on the current of (see Fig. 3). In turn that means that initial states and sets of dispatching rules can be seen as control variables allowing one to "adjust" multimodal processes schedule.

Illustrative example

The approach proposed is based on the system of concurrently flowing cyclic processes concept assuming its cyclic steady state behavior guaranteed by the given sets of dispatching rules and initial states. So, the multimodal processes scheduling, that can be seen as processes composed of parts of local cyclic processes, lead to the Legend:

-the k-th local state -the transition -the k-th multimodal state -the transition -the local cyclic steady state -the multimodal cyclic steady state , = 28, under assumption two fundamental questions. Does there exist a control procedure (i.e. a set of dispatching rules and an initial state) guaranteeing an assumed steady cyclic state subject to SCCP's structure constraints? Does there exist a SCCP's structure such that an assumed steady cyclic state (e.g. following requirements caused by multimodal processes at hand) can be achieved? In other words, an approach provides a framework enabling to take into account both the forward and backward way of cyclic scheduling problem formulation. Moreover, the question regarding possible switching among both the local and multimodal steady state states can be considered. The illustration of the local and multimodal cyclic state spaces prototyping is shown in the Table 1. Because of the discrete structure of SCCP topology and dispatching rules as well as the discrete event nature of processes execution the considered problems of and scheduling (including switching among cyclic steady states) can be modeled in terms of Constraint Satisfaction Problem (CSP) [START_REF] Bocewicz | Design of admissible schedules for AGV systems with constraints: a logic-algebraic approach[END_REF], [START_REF] Bocewicz | Cyclic Steady State Refinement[END_REF], and consequently implemented in declarative languages environment -OzMozart system. The illustration of pos-

4

Concluding remarks

In contradiction to the traditionally offered solutions the approach presented allows one to take into account such behavioral features as transient periods and deadlock occurrence. So, the novelty of the modeling framework offered lies in the declarative approach to reachability problems enabling multimodal cyclic process evaluation as well as in CSP-based evaluation of possible switching among cyclic steady states from both the local and multimodal cyclic state spaces. The approach presented leads to solutions allowing the designer to compose elementary systems in such a way as to obtain the final SCCPSs' scheduling system with required quantitative and qualitative behavioral features while employing the sufficient conditions provided. So, we are looking for a method allowing one to replace the exhaustive search for the admissible control by a step-by-step structural design guaranteeing the required system behavior.

  is the length of the -th multimodal route

Fig. 3 .

 3 Fig. 3. Graphical illustration of the relationship between the cyclic steady state of SCCP and the multimodal cyclic steady state

Fig. 4 .

 4 Fig. 4. Illustration of cyclic steady state spaces ( and ) for SCCP from Fig. 1

  time [u.t.]Switching among cyclic steady states sible cyclic schedules taking into account possible switching among cyclic steady states is shown in Fig.4.

Table 1 .

 1 The local and multimodal cyclic state spaces prototyping for SCCP from Fig.1.

	Structure	Cyclic	Period of the	Period of the	Cyclic	Period of the	Period of the
		Steady	Cyclic Steady	multimodal	Steady	Cyclic Steady	multimodal
		State	State [u.o.t]	process [u.o.t]	State	State [u.o.t]	process [u.o.t]
		Sc1	14	28	Sc6	14	28
		Sc2	14	28	Sc7	12	24
	SCCP (Fig. 1)	Sc3	14	28	Sc8	12	24
		Sc4	14	28	Sc9	12	24
		Sc5	12	24	Sc10	12	24


Nariaki Nishino
email: nishino@tmi.t.u-tokyo.ac.jp

Satoshi Kawabe

Game Theoretic Analysis of Production Structures in the Japanese Animation Industry: Comparison of Conventional and Production Committee Systems

Keywords: Japanese animation industry, Game theory, Decision-making, Production committee system

This paper presents a game theoretic analysis of production structures including several stakeholders in the Japanese animation market and its related goods markets. We construct a decision-making model of the industry including players of four kinds: an animation studio, a broadcasting company, a related products manufacturer, and consumers. Additionally, we model two production structures: the conventional system and the production committee system. By analyzing the equilibrium states of this model, we conclude theoretically that the animation studio raises the effort level with decreasing marginal costs of related products and/or with increasing network externality effect and increasing royalties the studio receives. For the total profit and the effort level, we found that the production committee system is better than the conventional system.

Introduction

In Japan, the content industry market size, including that for Animation, is estimated at more than 100 billion dollars. Particularly, Japanese animation is so popular throughout the world that the role of the Japanese animation industry is expected to become increasingly important in the future [START_REF]Current Status and Issues Facing Japanese Industries[END_REF]. Furthermore, although the animation industry is a service industry, it is closely related to tangible manufacturing products because related goods such as DVDs, character figures, and TV games are produced and provided in parallel.

According to a report released by the Digital Content Association of Japan [START_REF]Digital Content Association of Japan: Digital Content White Paper[END_REF], however, some problems exist in the content industry. Although the content industry in America, exemplified by that in Hollywood, earns profits worldwide, the Japanese content industry cannot make big gains abroad in spite of its popularity. Some reasons underlie the current situation. One problem is piracy, which is an important issue in the content industry [START_REF]Current Status and Issues Facing Japanese Industries[END_REF] [START_REF]Digital Content Association of Japan: Digital Content White Paper[END_REF]. Many researchers have conducted studies of piracy. Tanaka [START_REF] Tanaka | Does file sharing reduce music CD sales?: The case of Japan[END_REF] studied the effect of file-sharing software on music CD sales in Japan. Smith et al. [START_REF] Smith | Piracy or promotion? The impact of broadband Internet penetration on DVD sales[END_REF] pointed out that increased broadband internet penetration has led to a significant increase in DVD sales in the US.

Another problem is the "production structure" of the Japanese animation industry. This industry has many stakeholders: for example, animation companies to which animation creators belong, broadcasting companies, manufacturers of DVDs and other anime-related goods, advertising agencies, trading companies, consumers, and so on. The most important issue in this structure is that animation studios, most of which are small, cannot obtain sufficient profits to maintain the quality of their content because large companies such as broadcasting companies dominate negotiations. Animation studios will be disadvantaged if these circumstances continue. Concern persists about the decline of this industry in the future. Nevertheless, few studies have used a mathematical analysis approach to examine these problems related to the Japanese animation industry.

This study examines production structures of the Japanese animation industry, especially addressing two kinds of production structures: the conventional and the production committee systems. Based on a game theoretic approach, we formulate stakeholders' decision-making and production structures. Then, we analyze them theoretically and compare the two structures.

Modeling of Animation Production Structures in Japan

Formulating Each Player

We construct a game theoretic model of Japanese animation industry composed of players of four kinds: an animation studio, a broadcasting company, a related products manufacturer, and consumers.

Animation Studio. The animation studio receives a budget from the broadcasting company. Then the studio makes a decision about the effort level, which dictates the amount of its production expenditure. In addition, the studio receives as royalties some revenues from sales of the products that the related product manufacturer produces. The profit function is therefore defined as Π s = B -F (x) + α ∑ s k=1 p k q k , where B signifies the budget from the broadcasting company, p k and q k respectively denote the price and the sales quantity of product k, α is the rate of royalties which the studio receives, s is the number of types of anime-related goods that the manufacturer produces, x stands for the effort level of the studio, and F (x) is the cost of producing the anime, which is the function of the effort level x. The studio decides the effort level x to maximize its profit.

Broadcasting Company. The broadcasting company pays some revenues from sponsors to the animation studio for its production. The company also receives a part of the sales of anime-related products as royalties. The profit is

Π b = A -B + β ∑ s k=1 p k q k + L,
where A signifies the budget from sponsors, β denotes the rate of royalties which the company receives, and L is defined as the license fee from a related products manufacturer. Herein, A, β, and L are exogenous variables. Then the company decides how much of budget B is paid to the studio.

Manufacturer. The related products manufacturer produces anime-related goods and pays a part of its sales to the studio and company as royalties. The profit is described as

Π m = (1 -α -β) ∑ s k=1 p k q k - ∑ s k=1 (c k (q k ) + f k ) -L, where c k (q k )
and f k respectively stand for the variable cost and fixed cost of production for product k.

Consumers. The utility function of consumer

i who purchases product k is U i,k = v i,k + a k (m) -p k .
In that equation, v i,k denotes consumer i's own utility of product k. In addition, a k (m) signifies the increment of utility by increasing m. Here, m is defined as the number of consumers who have watched the anime. Consequently, a k (m) denotes the effect of indirect network externalities.

Production Structures

Conventional Production System. A conventional production system can be depicted as Figure 1. There are interdependent relationships among the players. Their decisions are fundamentally made with the sequence of a broadcasting company, an animation studio, and related products manufacturers. Therefore, the game structure in our model can be described simply as a sequential game with perfect information: first, the company chooses budget B; then the studio makes a decision about the effort level x; finally, the manufacturer decides the price p k of product k.

Production Committee System. This type of system has been emerging recently in anime production in Japan. In the production committee system, stakeholders form a committee by agreeing to finance the project. Therein, a chain of decision process from animation production to selling related products is conducted collaboratively. Thereby, their decisions are made by working together. The structure is depicted in Figure 2. It can be represented by replacing each profit with the total profit that is the sum of each player's profit. The decision sequence is the same as the previous one.

Theoretical Analysis

Condition setup

For simplicity, we assume that the related products manufacturer produces only one type of product. Accordingly, we can omit k from the formulas. The variable cost and indirect network externalities are defined as c(q) = cq and a(m) = a(m(x)) = rx, respectively. Herein, c stands for the marginal cost. a(m) is assumed as a linear function of m and m as a linear function of x; r is a constant and signifies the effect of indirect network externalities related to the anime. Moreover, we simplify the anime production cost as F (x) = x 2 + d, where d is the fixed cost to produce the anime. By such an arrangement, consumer i's utility function can be represented as U i = v i + rx -p. Then, we assume that the value of v i is distributed with uniformity from 0 to 1 and that consumers purchase the product only if consumer i's utility U i is positive. Consequently, the sales quality q is calculated as

q = ∫ Ui≥0 dv = ∫ 1 p-a(m) dv = rx -p + 1
, which signifies the demand function. Constraint rx ≤ p ≤ rx + 1 can be derived by the assumption of a uniform distribution of v i in [0, 1].

Deriving Equilibrium

Subgame perfect Nash equilibrium in the conventional production system can be derived using backward induction. First, we calculate the price p for which the manufacturer makes a decision to maximize the profit Π m . The price p * in equilibrium is calculated as p * = argmax p Π m . Second, we derive the effort level x of the animation studio. The studio makes a decision in anticipation of the manufacturer's decision. Therefore x is calculated as

x * = argmax x Π s s.t. p = p * .
If the studio's profit Π s is a negative value, we assume that the studio produces no cartoon film and that each decision-maker's profits are zero. Finally, we calculate budget B. The broadcasting company makes a decision in anticipation of the decision of the animation studio. Here, B is calculated as

B * = argmax B Π b s.t. x = x * and p = p * .
In the production committee system the decisions can be made cooperatively. They make decisions to maximize the total profits of Π total = Π s + Π b + Π m . Subgame perfect Nash equilibrium is similarly derived as follows: first, p * is calculated using p * = argmax p Π total and then x * is determined by x * = argmax x Π total under the condition of p = p * . Here, B * cannot be determined because variable B disappears from the formula of Π total .

Subgame Perfect Nash Equilibrium in The Two Structures

Equilibrium states are presented in Tables 123. Tables 1 and2 present the theoretical equilibrium in case of the conventional production systems. The equilibrium values of p * and x * are classified according to the values of α, r, and c. The company decides budget B * on the condition that the value of studio's profit Π s is positive. Therefore B * depends on x * as well as some exogenous variables such as d, A, and L. Therein, l is defined as l = 1 -α -β.

Table 3 presents the theoretical equilibrium for the production committee system. As in the previous case, the equilibrium values of x * and p * are classified according to the values of r and c.

Discussion

Implications from Theoretical Analysis

We discuss the structures of the animation industry. Figure 3 As shown in 3-(c), the effort level, x * = ar 4-ar 2 , brings about the largest studio's profit and the manufacturer's best response p * is determined by selecting the corresponding point from the reaction function in 3-(a). In this case, the studio's effort level x * is positive, derived as an inner point. In addition, the value of x * = ar 4-ar 2 at equilibrium means that the studio's effort level is increasing by a large α or r, implying that the increment of royalties to the studio or large effect of network externalities makes the studio's effort level enlarge. For example, to increase r, social networking services might be useful to promote communication among anime fans, thereby producing word-of-mouth effects [START_REF] Duan | The dynamics of online word-of-mouth and product sales -An empirical investigation of the movie industry[END_REF] [START_REF] Reynolds | Customer Benefits and Company Consequences of Customer-Salesperson Relationships in Retailing[END_REF].

Meantime, in case of c

≥ 2l √ 4-αr 2 (3-(b), 3-(d)
), the effort level at equilibrium is x * = 0. Therefore, as the manufacturer's marginal cost c increases, it decreases the studio's effort level. Therefore, for high-quality anime, it is necessary to reduce the marginal cost of the related products manufacturer. For instance, it can be considered that the manufacturer should provide an online distribution service instead of DVD packages because the marginal cost to copy digital data is almost zero.

The same effects are basically present in cases of the production committee system as well. Such indirect effects imply that the relationship among stakeholders is intricately interwined, demanding careful strategies to foster high-quality anime production.

Problems in Conventional Production Structure

Table 2 presents many cases in which the animation studio's profit Π s is zero even if the production is conducted and makes other players profitable because the broadcasting company provides a very small budget to the studio, meaning the decision is best for the company at theoretical equilibrium. The situation indicates that the studio cannot obtain profits because the broadcasting company has a clear advantage over the animation studio in the production structure. The studio will suffer financially and creators associated with the studio will be Table 1. Theoretical equilibrium in conventional production: x * and p * .

Condition of α and r Condition of marginal cost

x

* p * 0 < αr 2 < 2 0 < c < 2l √ 4-αr 2 αr 4-αr 2 1 2 ( αr 2 4-αr 2 + c l + 1) c ≥ 2l √ 4-αr 2 0 1 2 ≤ αr 2 ≤ 3 0 < c < (αr 2 -2)l 2 αr 2 αr 2 2 1 2 (αr 2 -2)l ≤ c < 2(αr 2 -2)l 4-αr 2 l+c rl l+c l 2(αr 2 -2)l 4-αr 2 ≤ c < 2l √ 4-αr 2 αr 4-αr 2 1 2 ( αr 2 4-αr 2 + c l + 1) c ≥ 2l √ 4-αr 2 0 1 αr 2 > 3 0 < c < (αr 2 -2)l 2 αr 2 αr 2 2 1 2 (αr 2 -2)l ≤ c < (αr 2 -1)l l+c rl l+c l c ≥ (αr 2 -1)l 0 1
Table 2. Equilibrium in conventional production: B * and profits.

x * Condition B * Π * b Π * s Π * g αr 2 d < α 2 r 2 4 0 A + β αr 2 2 + L -d + α 2 r 2 4 lαr 2 2 -c -f -L α 2 r 2 4 ≤ d < A + L +β αr 2 2 + α 2 r 2 4 d -α 2 r 2 4 A -d + L + α+2β 4 αr 2 0 lαr 2 2 -c -f -L d ≥ A + L +β αr 2 2 + α 2 r 2 4 0 0 0 0 l+c rl d < α l+c l -( l+c l ) 2 0 A + β l+c l + L -d + α l+c l -( l+c l ) 2 l -f -L α l+c l -( l+c l ) 2 ≤ d < A + L +(α + β) l+c l -( l+c l ) 2 d -α l+c l +( l+c l ) 2 A -d + L +(α + β) l+c l -( l+c l ) 2 0 l -f -L d ≥ A + L + (α + β) l+c l -( l+c l ) 2 0 0 0 0 αr 4-αr 2 d < α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) 0 A + β 4l 2 {( 4l 4-αr 2 2 ) -c 2 } + L α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) -d 1 4 ( αr 2 4-αr 2 + c l + 1) 2 -4c 4-αr 2 -f -L α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) ≤ d < α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) + A + L + β 4l 2 {( 4l 4-αr 2 2 ) -c 2 } d -α 4l (l 2 -c 2 ) -α 2 r 2 4(4-αr 2 ) A -d + α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) + β 4l 2 {( 4l 4-αr 2
2 ) -c 2 } + L 0 forced to work in harsh conditions at low pay. If such a situation were to continue, talented creators in the next generation would decrease and they would shun the industry. Eventually, the Japanese animation industry might lose competitiveness in international markets, as reported by the Digital Content Association of Japan [START_REF]Digital Content Association of Japan: Digital Content White Paper[END_REF].

1 4 ( αr 2 4-αr 2 + c l + 1) 2 -4c 4-αr 2 -f -L d ≥ α 4l (l 2 -c 2 ) + α 2 r 2 4(4-αr 2 ) + A + L + β 4l 2 {( 4l 4-αr 2 2 ) -c 2 } 0 0 0 0 0 d < A + L d A -d + L 0 -f -L d ≥ A + L 0 0 0 0 Table 3. Equilibrium in production committee system. Condition of r Condition of c x * p * Π * total 0 < r 2 < 2 0 < c ≤ 1 (1 -c)r 4 -r 2 -r 2 c + 2c + 2 4 -r 2 A -f -d + (1 -c) 2 4 -r 2 c > 1 0 1 A -f -d 2 ≤ r 2 < 4 0 < c ≤ 1 2 (r 2 -2) r 2 r 2 2 A -f -d + r 2 4 -c 1 2 (r 2 -2) < c ≤ 1 (1 -c)r 4 -r 2 -r 2 c + 2c + 2 4 -r 2 A -f -d + (1 -c) 2 4 -r 2 c > 1 0 1 A -f -d r 2 ≥ 4 0 < c ≤ r 2 4 r 2 r 2 2 A -f -d + r 2 4 -c c > r 2 4 0 1 A -f -d

Comparison of Two Production Structures

In terms of profits and the effort level, we the structures. Because there are many theoretical states combination of some parameters, it is difficult to compare the two analytically. We therefore compare them with numerical calculations as follows:

r is set, varying in [0.1, 3.0] with an increment of 0.1 c is set, varying in [0.1, 2.0] with an increment of 0.1 α and β are set, respectively varying in [0.01, 1.00] with an increment of 0.01 to satisfy the condition of 0 < α + β < 1

Accordingly, combinations of values of those parameters are 3,090,600. Figure 4 presents the comparison of the two production systems with numerical calculation. The circle graphs represent the ratio, counting the frequency of outputs of the numerical comparison with respect to the total profit and the effort level. Herein, the total profit stands for the sum of the studio's profit, the broadcasting company's profit and the manufacturer's profit. The result means that the total profit of the production committee system is greater than or equal to that of the conventional system in all parameter combinations. Regarding the effort level, the cases that the conventional system is greater are very few. Therefore, the production committee system can be regarded as a good structure in anime production.

Concluding Remarks

In Japan, the animation industry will become increasingly important in the future. However, it confronts severe problems in its production structure. To elucidate the mechanism, we constructed and analyzed a game theoretic model comprised of decision-makers of four kinds. Results show that the studio reduces the effort level with increasing marginal cost of related products. For example, an online distribution service might be a more valid method than DVD packages to increase the studio's effort level. In addition, the effort level of the studio becomes high with increasing royalties from the manufacturer and with the effect of externalities. Comparison between two production structures shows that the production committee system is better than the conventional one in terms of the total profit and the effort level. Approaches like those in our study are important to assess the future development of competitiveness in this industry.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Conventional production.

  depicts the reaction function of the manufacturer (3-(a), 3-(b)) and the profit function of the studio (3-(c), 3-(d)) in the conventional production, which are derived as an theoretical output especially in case of 0 < αr 2 < 2. First, see 3-(a) and 3-(c) in Figure 3.

Fig. 3 .

 3 Fig. 3. Manufacturer's reaction and studio's profit functions in case of 0 < αr 2 < 2.

Fig. 4 .

 4 Fig. 4. Comparison between the conventional and the production committee systems.


Josefa Mula
email: fmula@cigip.upv.es

Manuel Díaz-Madroñero

David Peidro

A Conceptual Model for Integrating Transport Planning: MRP IV

Keywords: MRP, integration, production planning, transport planning

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Nowadays, the MRP (Material Requirement Planning) system, developed by Orlicky [START_REF] Orlicky | Material Requirements Planning[END_REF], continues to be the most widely used production planning system, despite the deficiencies identified in it. The evolutions of the MRP were reflected in the MRP II (Manufacturing Resource Planning) [START_REF] White | MRP II-Unlocking America's Productivity Potential[END_REF] system, which considers productive capacity constraints, MRP III (Money Resource Planning) [START_REF] Schollaert | Money resource planning, MRP-III: the ultimate marriage between business logistics and financial management information systems[END_REF], which introduces the financial function; and the MRP commercial evolution into the ERP (Enterprise Resource Planning) [START_REF] Wylie | ERP: A vision of the next-generation MRP II[END_REF], which incorporates all the company functions into a unique decision system through modules whose central nucleus is the MRP. Later ERP systems developments have incorporated new information and communication technologies. Moreover, these have been adapted to the current economic context characterized by business globalization and the offshoring of suppliers by developing other functions such as supply chain management or transport, among others [START_REF] Stadtler | Supply chain management and advanced planning: concepts, models, software and case studies[END_REF]. Original MRP systems were designed in the 70s as push systems in an environment where demand was greater than supply. Subsequently, and to adapt to new manufacturing environments where the supply was greater than demand pull systems appeared such as lean manufacturing and drum-buffer-rope. However, the inadequacy of push-based philosophy to today's environment characterized by high volatility and low demand, and the limited set of tools for materials planning and inventory control in pull systems, has led to the emergence of a new MRP, called Demand-Driven MRP (DDMRP) [START_REF] Ptak | Orlicky's Material Requirements Planning 3/E[END_REF].

Many works exist in the academic literature that have attempted to overcome some of the deficiencies of traditional MRP such as results optimization, considering uncertainty in certain parameters, inflated lead times, etc. However in both the commercial and academic environments, the MRP and its variants focus on material requirements and on production capacity planning, which are the main disadvantages in supply chains where there is considerable offshoring of raw materials and parts suppliers. In these contexts, transport planning plays a leading role since high costs and logistical constraints usually make the proposed production plans suboptimal, and even infeasible, and manual replanning is a common practice in companies. This work aims to develop a new conceptual model, the MRP IV, which integrates the material, production resource capacities and transport planning (type of transport, form of collection, etc.) decisions in the supply chain to avoid the suboptimization of these plans which, nowadays, are usually generated sequentially and independently.

The rest of the paper is arranged as follows: Section 2 offers a literature review about MRP and production planning problems. Section 3 presents the MRP IV conceptual model. Finally, the last section provides conclusions and directions for further research.

2

Literature review

In today's competitive environment, organizations need MRP systems to optimize their production planning decisions. Thus according to Yenisey [START_REF] Ptak | Orlicky's Material Requirements Planning 3/E[END_REF], although the earlier MRP formulations were not associated with any form of optimization, aspects such as profit maximization and constraints related to supply, demand or available resources were gradually incorporated to optimize MRP problems. In this sense, the seminal works of Karni [START_REF] Karni | Integer linear programming formulation of the material requirements planning problem[END_REF] and Billington et al. [START_REF] Billington | Mathematical programming approaches to capacity-constrained MRP systems: review, formulation and problem reduction[END_REF] who model MRP problems with mixed integer linear programming can be highlighted. Later, Yenisey [START_REF] Yenisey | A flow-network approach for equilibrium of material requirements planning[END_REF] presents a flow network with a side constraints approach to optimize material flows in MRP problems. Noori et al. [START_REF] Noori | Optimization of material requirement planning by fuzzy multi-objective linear programming[END_REF] develop a fuzzy multi-objective linear programming model to extend the work proposed by Yenisey [START_REF] Yenisey | A flow-network approach for equilibrium of material requirements planning[END_REF] which considers the minimization of total costs and time. However, the premise of a completely deterministic scenario does not match the reality of a manufacturing environment. The literature reports different approaches to consider uncertainty in MRP systems, such as simulation [START_REF] Tavakoli-Moghaddam | Application of fuzzy lead time to a material requirement planning system[END_REF], [START_REF] Sun | Simulation analysis of a multi-item MRP system based on factorial design[END_REF], stochastic inventory control [START_REF] Inderfurth | How to protect against demand and yield risks in MRP systems[END_REF], fuzzy logic [START_REF] Barba-Gutiérrez | Reverse MRP under uncertain and imprecise demand[END_REF], fuzzy mathematical programming [START_REF] Mula | MRP with flexible constraints: A fuzzy mathematical programming approach[END_REF][START_REF] Mula | Material Requirement Planning with fuzzy constraints and fuzzy coefficients[END_REF][START_REF] Mula | Capacity and material requirement planning modelling by comparing deterministic and fuzzy models[END_REF][START_REF] Mula | Fuzzy Material Requirement Planning[END_REF], fuzzy programming with resources based on the credibility theory [START_REF] Li | Application of Fuzzy Programming with Recourse in Material Requirement Planning Problem[END_REF] and MRP parameterization [START_REF] Hnaien | Planned lead time optimization in material requirement planning environment for multilevel production systems[END_REF][START_REF] Louly | Optimal supply planning in MRP environments for assembly systems with random component procurement times[END_REF][START_REF] Louly | Optimal time phasing and periodicity for MRP with POQ policy[END_REF], among others. Other approaches to consider uncertainty in MRP systems can be found in several reviews [START_REF] Mula | Models for production planning under uncertainty: A review[END_REF][START_REF] Dolgui | Supply planning under uncertainties in MRP environments: A state of the art[END_REF][START_REF] Wazed | A review of manufacturing resources planning models under different uncertainties: state-of-the-art and future directions[END_REF].

On the other hand, the importance of the bill of materials (BOM) in MRP systems is reflected in several works that redefine the traditional BOM concept to adapt MRP systems to new manufacturing environments. Chen et al. [START_REF] Chen | Adjusting MRP for dynamic differentiation of identical items for process customisation[END_REF] adjust the traditional MRP approach for the make-to-order environment to consider customization features by generating a BOM for each customized product. Ram et al. [START_REF] Ram | Material requirements planning with flexible bills-of-material[END_REF] propose a flexible BOM to deal with possible shortages when using MRP to plan the requirements of dependent demand items. The requirements stated in the MPS (Master Production Schedule) are met in a timely manner by substituting items for one another should shortages arise. A linear programming model is used to minimize deviation from the default BOM when shortage occurs. Lin et al. [START_REF] Lin | Critical material planning for TFT-LCD production industry[END_REF] develop a single-period, multiperiod mathematical programming model to optimize the purchase quantity from suppliers, while they satisfy demand using specific characteristics from the TFT-LCD industry. These specific issues are based on the alternative bill of materials (ABOM), customer preference for ABOM and the purchase quantity ratio.

Standard MRP calculations are based on the dynamic multi-level capacitated lotsizing problem (MLCLSP). Capacitated lot-sizing problems have attracted the scientific community's attention in recent decades and several literature reviews like [START_REF] Karimi | The capacitated lot sizing problem: a review of models and algorithms[END_REF][START_REF] Jans | Modeling industrial lot sizing problems: a review[END_REF][START_REF] Quadt | Capacitated lot-sizing with extensions: a review[END_REF], among others, have been published. Moreover, Buschkühl et al. [START_REF] Buschkühl | Dynamic capacitated lot-sizing problems: a classification and review of solution approaches[END_REF] discuss both different modeling approaches to the optimization of MLCLSP problems and different algorithmic solution approaches by classifying them into five groups: mathematical programming-based, Lagrangian heuristics, decomposition and aggregation approaches, metaheuristics and problem-specific greedy heuristics. Armentano et al. [START_REF] Armentano | A network flow model for the capacitated lot-sizing problem[END_REF] use a branch-and-bound procedure, with a linear programming relaxation based on a network flow formulation. The efficiency of the branch-and-bound method can be increased by reformulating the mathematical model, and by redefining the corresponding decision variables [START_REF] Tempelmeier | A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures[END_REF][START_REF] Stadtler | Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing[END_REF][START_REF] Stadtler | Reformulations of the shortest route model for dynamic multi-item multilevel capacitated lotsizing[END_REF][START_REF] Denizel | Equivalence of the LP relaxations of two strong formulations for the capacitated lot-sizing problem with setup times[END_REF] and/or by introducing valid inequalities [START_REF] Belvaux | Modelling practical lot-sizing problems as mixed-integer programs[END_REF][START_REF] Suerie | Modeling of period overlapping setup times[END_REF][START_REF] Absi | The multi-item capacitated lot-sizing problem with setup times and shortage costs[END_REF]. Other solution approaches can be found in the literature such as fix-and-relax heuristics [START_REF] Suerie | The capacitated lot-sizing problem with linked lot sizes[END_REF], [START_REF] Federgruen | Progressive interval heuristics for multi-item capacitated lot sizing problems[END_REF], rounding heuristics [START_REF] Akartunalı | A heuristic approach for big bucket multi-level production planning problems[END_REF], column generation [START_REF] Degraeve | A new Dantzig-Wolfe reformulation and branch-and-price algorithm for the capacitated lot-sizing problem with setup times[END_REF] and Lagrangian relaxation [START_REF] Chen | A Lagrangian relaxation approach for supply chain planning with order/setup costs and capacity constraints[END_REF], among others. On the other hand, according to Jans and Degraeve [START_REF] Jans | Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches[END_REF], several metaheuristics have been developed for extensions of the standard lot sizing problems for which no good special purpose algorithm exists and which are too difficult to solve with commercial integer optimization. Metaheuristic algorithms range from simple local search procedures to complex learning processes which can handle large and complex problems. Chen and Chu [START_REF] Chen | A Lagrangian relaxation approach for supply chain planning with order/setup costs and capacity constraints[END_REF] develop a heuristic method based on the combination of Lagragian relaxation and local search. At each iteration, a feasible solution of the original problem is constructed from the solution of the relaxed problem. This feasible solution is further improved by a local search that changes the values of two setup variables at each time. Barbarosoglu and Özdamar [START_REF] Barbarosoglu | Analysis of solution space-dependent performance of simulated annealing: the case of the multi-level capacitated lot sizing problem[END_REF] analyze the performance of a general purpose simulated annealing procedure in solving the dynamic MLCLSP with general product structures. The proposed neighbourhood transition schemes are based on relaxing different types of constraints, each of which defines a different solution space. Moreover, Özdamar and Barbarosoglu [START_REF] Özdamar | An integrated Lagrangean relaxation-simulated annealing approach to the multi-level multi-item capacitated lot sizing problem[END_REF] propose a solution method by combining the capability of the Lagrangean relaxation to decompose the hard-to-solve problems into smaller subproblems and the intensive search capability of the simulated annealing. Berretta et al. [START_REF] Berretta | Metaheuristic approaches for the multilevel resource-constrained lot-sizing problem with setup and lead times[END_REF] develop a heuristic which integrates simulated annealing components and tabu search for solving MLCLSP with general product structures, setup costs, setup times, and lead times. Karimi et al. [START_REF] Karimi | A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over[END_REF] propose a tabu search heuristic which starts from an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing variable costs, by solving a minimun-cost network flow problem. Besides, Hung and Chien [START_REF] Hung | A multi-class multi-level capacitated lot sizing model[END_REF] compare the performance of the tabu search, simulated annealing and genetic algorithms to solve MLCLSP. Xie and Dong [START_REF] Xie | Heuristic genetic algorithms for general capacitated lot-sizing problems[END_REF] propose a heuristic genetic algorithm for these problems in which the presentation technique encodes only the binary variables for the setup patterns but derives other decision variables by making use of the problem-specific knowledge. Moreover, Jung et al. [START_REF] Jung | Genetic algorithm-based integrated production planning considering manufacturing partners[END_REF] present a genetic algorithm for the integrated production planning problem considering manufacturing partners (suppliers). The proposed genetic algorithm with a unique chromosome structure, chromosome generation method and genetic operators, generates quite good solutions when compared to commercial solvers.

However, despite the development of sophisticated solution methods, according to Lee et al. [START_REF] Lee | A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem[END_REF], the majority of lot-sizing models have not considered any productioninventory problem with incorporated transportation activities. Nowadays, the issue of transportation scheduling for shipping products (or delivering orders) by proper shipping modes at the right time becomes significantly important in production (or distribution) management, or for import and export activities. Thus, Lee et al. [START_REF] Lee | A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem[END_REF] analyze a dynamic lot-sizing problem which contemplates the order size of multiple products and a single container type simultaneously. The objective of this study is to determine the production lot sizes and the transportation policy that minimize total costs by means of a heuristic algorithm. Garcia-Sabater et al. [START_REF] Garcia-Sabater | A capacitated material requirements planning model considering delivery constraints: A case study from the automotive industry[END_REF] present an MRP model that successfully integrates delivery and production processes in an automotive supply chain with a just-in-time environment. Moreover, Hwang [START_REF] Hwang | Economic lot-sizing for integrated production and transportation[END_REF] provides efficient solution procedures to solve lot-sizing problems with integrated production and transportation operations. Concave production costs and stepwise transportation costs are assumed to model the economies of scale in production with the effect of shipment consolidation on transportation. In relation to inbound logistics, Ertogral [START_REF]Multi-item single source ordering problem with transportation cost: A Lagrangian decomposition approach[END_REF] incorporates transportation costs into a multi-item, lot-sizing problem as a piecewise linear function of the amount transported. A Lagrangean decomposition-based solution procedure is suggested to compare the proposed model in different scenarios. Sancak and Salman [START_REF] Sancak | Multi-item dynamic lot-sizing with delayed transportation policy[END_REF] propose a multi-item, lot-sizing, mixed-integer mathematical programming approach to determine the number of items to order and how many trucks to use in a stochastic environment for the purpose of minimizing total inventory holding and transportation costs. However, neither case contemplates production planning.

MRP IV: a conceptual model

Today there is a large number of firms with offshore suppliers. The production planning systems they use do not simultaneously consider aspects relating to the transport of parts and raw materials to their installations. The most habitual procedure is MPS calculation and MRP, used to determine the quantities of each finished good to be produced in a given planning horizon, as well as the requirements of the associated parts and raw materials. Corresponding orders are firmly placed if the quantities to be ordered to suppliers can be transported via an existing transport network. Should the results obtained with MRP be infeasible as regards the transport network, the results obtained with MRP need to be manually amended until they are feasible, or it is necessary to increase the existing transport capacity and to rerun MRP. In this case, transport decisions are based on the commitment between covering demand, available occupation and the inventories of parts and raw materials. Generally in this context, transport planning is done manually with the help of spreadsheets, and is based on planners' experience and personal judgments; this situation generally implies obtaining suboptimum results. This article proposes a conceptual model, called MRP IV, for production planning which integrates those aspects relating to provisioning transport. For this purpose, MRP IV contemplates various inputs (which could be considered in generic MRP and provisioning transport planning models) that generate different outputs to achieve one objective or several objectives. Figure 1 illustrates the proposed model. The left-hand side of Figure 1 includes the input parameters associated with production planning systems or MRP, while the right-hand side shows those relating to transport decisionmaking processes. Those parameters which can be used simultaneously for aspects relating to both production and transport planning are presented as elongated rectangles overlapping both areas. The MRP IV inputs, outputs, modelling and solution approaches are described below:

INPUTS:

1. Planning horizon with an equivalent extension to the suppliers' maximum lead time. The planning horizon is divided into equal periods, for instance, of a daily duration 2. Customer demand of the finished goods to be produced 3. BOM 4. Initial inventory and initial delayed demand of finished goods, parts and raw materials 5. Safety stocks of each finished good, part and raw material 6. The supply lead time of each part and raw material as it is considered null for finished goods. The lead time for parts and raw materials comprises the supplier production time, the transport time and the safety time. 7. Programmed receptions for each part and raw materials 8. Production system function costs. These are variable production costs, inventory holding costs, delayed demand costs, undertime hour costs of productive resources, overtime hour costs of productive resources and subcontracting costs 9. Production capacity of available productive resources 10. Production time. This is the time required to produce each product with the available productive resources 11. Setup time. It represents the capacity lost due to cleaning, machine adjustments, calibration, inspection, change in tooling, etc., when production for a new product starts 12. Production batch size 13. Parts and raw materials dimensions 14. Order lot size of each part and raw material. The quantities to order are multiple integers of this lot size. It may, or may not, coincide with the production lot size because, occasionally, the supplier can arbitrarily fix an order lot size in accordance with its preferences 15. Transport suppliers function costs. These are costs that are fixed per vehicle employed, variable costs according to occupied volume, discounts, costs for using extra transport capacity, costs incurred by urgent deliveries, waiting truck costs, etc. 16. Transport capacity. This corresponds to the capacity of the transport network between the suppliers of parts and raw materials and the manufacturer of finished goods. This transport network is generally stable and is regulated by contracts drawn up between the manufacturer receiving parts and raw materials and the logistics or transport suppliers 17. Shipment modes. Different shipment modes can be considered depending on the order size of parts and raw materials and the suppliers' geographic location. For instance, full-truckload (FTL) for those suppliers with whom large-sized orders are placed; less-than-truckload (LTL) for those suppliers with whom smallersized orders are placed; milk-run for those suppliers close by to whom smallsized orders are sent, which are delivered on a vehicle occupied by orders frequently received from several similar suppliers. Shipment modes can also be regulated by means of contracts drawn by with transport suppliers 18. Shipment frequency. This consists in the frequency of parts and raw materials arriving from different suppliers. Frequency of arrival can also be fixed by drawing contracts between the manufacturer of finished goods and its transport suppliers 19. Shipping units. They are required for transporting parts and raw materials; for example, special containers, racks, pallets, etc.

MODELLING APPROACH:

Different modelling approaches, such as linear programming, (mixed) integer programming, multiobjective programming, fuzzy programming, stochastic programming or simulation/hybrid models can be considered to develop an analytical model which would represent MRP IV. This model will be composed of several constraints and one or several objectives such as minimizing total production, inventory, delayed demand, overtime, undertime, subcontracting and transport costs.

SOLUTION APPROACH:

Buschkühl et al. [START_REF] Buschkühl | Dynamic capacitated lot-sizing problems: a classification and review of solution approaches[END_REF] identify five groups of solution approaches to solve lot sizing problems:

1. Mathematical programming 2. Lagrangian heuristics 3. Decomposition and aggregation heuristics 4. Metaheuristics 5. Problem-specific greedy heuristics

OUTPUTS:

1. MPS, which specifies the quantity to produce of each finished good 2. Overtime and undertime hours of productive resources and subcontracting hours 3. Planned ordering of raw materials and parts, which specifies the quantities to order of each part or raw material to each supplier 4. Number of vehicles and routes and number of shipping units per vehicle. The number of vehicles employed is obtained for each shipping mode, as is the number of shipping units that each vehicle transports. Likewise for the milk-run shipping mode, the route to be followed by each vehicle to reach the manufacturer of finished goods is also determined 5. Inventory at the end of each planning period 6. Delayed demand at the end of each planning period After obtaining the outputs for the MRP IV model, their feasibility has to be evaluated. If outputs are infeasible, this may be due to causes relating to the production or transport system design. Therefore when outputs are infeasible, it is necessary to especially examine production and transport capacities, and to adjust them suitably before rerunning the MRP IV. Moreover, if outputs are feasible, it is necessary to economically evaluate the solution obtained by bearing in mind the different costs associated with the model. Although this situation can lead to obtaining a feasible solution for the MRP IV model, truck occupation may diminish and some vehicles have available space, which might involve an inappropriate cost. Therefore, it is necessary to reach a compromise solution that enables better truck occupation and maintains acceptable inventory levels. Similarly, the MRP IV model should include a period that reviews the transport network and the production system so that it can adapt to the various changes taking place in the environment.

Conclusions

This paper has reviewed the main advances and deficiencies of MRP systems, one of which is sequential provisioning transport and production planning decision-making processes. In order to address this, we propose a conceptual model, the MRP IV, which acts as a reference to develop a new production technology which integrates transport planning and MRP systems in the same decision-making system. The main inputs, objectives and outputs of the MRP IV model have been identified. A forthcoming work is related to the modeling and solution approaches for the proposed conceptual model, MRP IV.

Fig. 1 .

 1 Fig. 1. MRP IV inputs, outputs, objectives, m modeling and s solution appro oaches

Acknowledgment.

This work has been funded by the Spanish Ministry of Science and Innovation project: 'Production technology based on the feedback from production, transport and unload planning and the redesign of warehouses decisions in the supply chain' (REVOLUTION) (Ref. DPI2010-19977).


Hirpa G Lemu
email: hirpa.g.lemu@uis.no

Jan Frick

Tadeusz Uhl

Wojciech Lisowski

Piotr Piwowarczyk

Study on Need Assessment of Mechatronics Education in Norway and Poland

Keywords: Mechatronics, mechatronics curriculum, multidisciplinary field

This article presents a summary result of the survey on the need for mechatronics education. The study was conducted as a cooperation project between two teams established at two universities: AGH-UST from Poland and University of Stavanger (UiS) from Norway. Both companies and High School Pupils are surveyed in this project, but only feedbacks from the former are analyzed in this article. As a result of the declining interest for engineering and science education in general and mechatronics education in particular, the project is intended to work out an International Curriculum for mechatronics education that can stimulate pupils for science and technology fields as well as to encourage students in engineering education. The field of mechantronics has been focused because this field, as a new and multidisciplinary area, has a high potential to integrate topics that are necessary for modern engineering industries and can provide graduates in a multi-skill and knowledge.

Introduction

Complex mechanical systems of today like airplanes, cars, industrial process machines and spaceships have many embedded mechanical and electronic systems that monitor and control the behavior to avoid catastrophic failure and improve the performance. With its origin in Japan in late 1960s [START_REF] Buur | Mechatronics Design in Japan[END_REF] the term mechatronics was in principle coined to define such control and operation systems. The concept has since spread all over the world and a significant international growth has been observed within the last three decades. According to technology review of MIT press [2], mechatronics is identified as one of the top 10 technologies that will change the future world. The field is in general viewed as the vehicle by which students are introduced to and made to comprehend the diverse disciplines (Fig. 1) such as computer science, electrical and mechanical engineering areas concurrently. By combining diverse fields, mechatronics curriculum provides sufficient background, knowledge, depth and breadth enabling the graduates to tackle complex engineering problems.

Fig. 1. Illustration of the diverse fields and concepts making up mechatronics

Understanding the fact that mechatronics is a newly emerging branch of study, that can interlink engineering, science and technology (Fig. 1(b)), many universities [START_REF] Lyshevski | Mechatronic curriculum -restrospect and prospect[END_REF][START_REF] Meek | Mechatronics education in the Department of Mechanical Engineering at University of Utah[END_REF][START_REF] Akpinar | Mechatronics education in Turkey[END_REF] have examined the curriculum in order to, among others, improve the structure and content of the program, increase the recruitment of students and improve effectiveness of teaching.

A number of these recent studies have attempted to investigate the organization of universities and how teaching of this discipline can be conducted. Some of the previous studies focused on the issue from the view of education philosophy of engineering [START_REF] Parasuraman | Philosophy and objectives of mechatronics education[END_REF] while others worked on the programs of curriculum [START_REF] Kayis | Trends in undergraduate mechanical, manufacturing, aerospace and mechatronics programs Wordwide: In-depth Study of 55 Universities' Programs[END_REF] as well as the evolutionary development of the field as an engineering branch and the possible standardization of the education on nearly universal base [START_REF] Grimheden | Mechatronics -the evolution of an academic discipline in engineering education[END_REF]. The reported surveys, mainly in universities, have both national and regional characteristics [START_REF] Acar | Mechatronics: the basis for new industrial development[END_REF].

Other studies [START_REF] Grimheden | What is Mechatronics? Proposing a Didactical Approach to Mechatronics[END_REF] have attempted to define the identity and legitimacy of mechatronics as well as the implications on the selectivity and communication of the subject. This identity definition considers mechatronics as the "synergistic combination of precision mechanical engineering, electronic control and systems thinking in the design of products and manufacturing processes" rather than the descriptions of the discipline solely as an interdisciplinary subject, as the union between mechanical and electrical engineering, control theory and computer science or other combinations of traditional disciplines within an engineering sphere. It is also important to recognize that mechatronics is not only a combination of engineering subjects, but it, as a multidisciplinary field of study, integrates science and technology with engineering (Fig. 1(b)).

The focus on formulation of mechatronics curriculum and defining its identity is, in a way, well motivated because comprehending a multidisciplinary field is challenging unless a suitable curriculum that motivates the students is outlined. At the same time it is essential that the formulated curriculum fulfils the expectations of the job market. A recent review by Alvarez Cabrera, et. al. [START_REF] Alvarez Cabrera | Towards automation of control software: A review of challenges in mechatronic design[END_REF] highlights the list of some of the existing challenges in design of mechatronics curriculum and systems for both the academia and industrial sector.

Based on the declining trend of interest for mechatronics study at well established universities like AGH-UST of Kraków, Poland, assessment of the need for this study has been initiated. The purpose of this study partially reported in this article is primarily to formulate a fundamentally new curriculum that enables a greater degree of self-direction in designing and developing mechatronics systems. To make the survey more comprehensive the expectations of students concerning the mechatronics study were also taken into account during the assessment. This article attempts to present a brief summary of the results of this cooperative research.

The rest of the article is organized as follows: Some highlight of the assessment approach used in the study and analysis of the company feedbacks are given Section 2 and 3 respectively. Section 4 discusses the practical implications of the feedbacks and Section 5 presents briefly students' expectations to mechatronics study. Finally, conclusion is given in Section 6.

Assessment Approach

This study is a result of a collaboration project between two teams: one team from AGH-UST of Kraków, Poland, and the second team from University of Stavanger (UiS), Norway. During formulation of the project objectives the team understood the mission of universities in formulating the curriculum as twofold:

1. Supporting professional success of their graduates on the labor market, and 2. Providing the candidates that suit the needs of the job market.

To achieve both objectives, questionnaires were prepared and concurrently distributed among companies and high schools in Norway and Poland. The study in this article presents the analysis results of company feedbacks in which 25 companies from Krakow area, and 12 companies from Stavanger area, are involved. In line with the stated project objectives, the questionnaires focus on two main parts.

1) Collecting information on the companies: this involves, among others, company size, profile, business life and the legal form of the company, and the role of mechantronics as a multidisciplinary area of knowledge as well as the extent of research oriented activity in the company and cooperation with universities.

2) Assessing the companies' expectations: this focuses on what the companies expect from a university graduate (possible recruit) related to the knowledge and predispositions. This includes what guides the company's recruitment policy and the basic knowledge, competence and skill the company expects from a graduate. In order to collect sufficient information for this part of the questionnaire, the survey has attempted to address the following three issues:

i. personal traits of the graduates, ii. the theoretical knowledge base of the graduates and iii. the necessary practical engineering skills.

Analysis of Company Feedbacks

Characteristics of the Surveyed Companies

Company Size, Profile and Legal Form: As depicted in Fig. 2(a), some specific features are observed regarding the results of the survey. The survey from Stavanger area covers mostly SME companies that were founded recently. This has a clear historical reason related with the recent development of oil industries in the region. Quite a large number of these companies have operated as individual business companies. The survey indicates also that about a half of them are involved in R&D activity and knowledge-based products and/or services do not constitute the critical part of their output.

The Polish partners, on the other hand, conducted the survey mainly at large companies, where a considerable amount of them have been operated quite long and currently most of them are international firms (with partial ownership). Majority of the companies conduct their own research at their R&D units. Most of the products and/or services offered by these companies are knowledge-based ones. The majority of the companies in both areas are involved in production and services (Fig. 2(b)). Further, the legal form of the companies involved in this study, in both areas, is limited liability ones that are usually the most innovative part of the technical service as well as manufacturing market.

A good communication between industries and the academia can be considered as a key to correlate the needs of the job market and the content and depth of teaching as well as the conducted research at universities. The diagrams in Fig. 3 show the results of two of the questions forwarded to the companies in order to get some indication on the level of R&D activities in the companies and the degree of cooperation with universities. The survey shows that many of the companies in both areas have their own R&D department and they do cooperate with universities. The usual forms of the cooperation are R&D projects and support of teaching by arranging visits and internships for students. The companies in Stavanger area do have high level of cooperation with universities, particularly in research consulting. On the contrary, the important area of cooperation between companies and universities in Kraków area is support of testing by universities. Further, the role of mechatronics field of study will depend on how the identity of the field is defined and recognized both at universities and on the job market. A challenge to universities in stimulating interest in this discipline is to find the right identity in terms of coining courses from computer, electrical and mechanical engineering fields and clear professional definition of the graduates so that the job market understands the skill and knowledge gained by a graduate. Clear definition of the identity will have high implications on, for example, the design methodology, the modeling approach, the manufacturing processes and the material selection of mechanical products, components and systems.

Contrary to the suspicion of the project team, the feedbacks in general show that the companies use mechatronics as the methodology of solving problems in their everyday activity (Fig. 4 (top)). Among the areas listed in the questionnaire, the feedbacks indicate that mechanical engineering and automation are mostly used (Fig. 4 (bottom)). Quite strikingly, the distribution profile of the used technology in both surveyed regions is similar.

Most preferred plan of teaching for mechantronics:

Expectation of Companies from Mechatronics Education

Apart from few exceptions, the feedbacks from both regions have similar characteristics in terms of expectations and preference to mechatronics education and its curriculum. Most of the companies consider professional knowledge to be the most important skill of a candidate to be recruited. In order to contribute to this expectation, they stressed that practical application of knowledge through internships or trainings should be focused as part of education in engineering, compared with laboratory works and lectures (Fig. 5). Though the general preference tendency is similar in both regions, companies in Poland indicate a significant interest in lectures and laboratory work based teaching.

Fig. 5. Preferred teaching plan of study in mechatronics curriculum

With respect to preference of personalities of a graduate, the feedbacks (Fig. 6) indicate that the following are most appreciated by the employers: ability to work in team, creativity, independence, responsibility and loyalty with integrity.

In addition, companies in Poland stressed ability to seek self-knowledge through patents and standards, while Norwegian companies indicated importance of the communication skills and ability to cope with stress as their best preference. One main objective of the project is to formulate a new mechatronics curriculum that reflects the needs and expectations of the modern industry. The assessment (as depicted in Fig. 7) indicates that companies from both countries have high preference for

• ability to integrate knowledge from different fields, • ability to analyze structural behavior and functionality of products in their environment,

• knowledge of computer-aided engineering systems, • knowledge of mechanical systems and • knowledge of construction and operation of machines.

The companies from Poland highly prefer practical knowledge of a foreign language as a language of professional communication, while the response of companies from Norway indicates very low preference for this skill.

The last question in the questionnaire focuses on assessment of expectations with respect to specific skills that are important for the company in the future. The preference of the companies in those specific skills (Fig. 8) is no exceptional. Most preferred skills include knowledge of use of computer-aided design (CAD) systems, knowledge of manufacturing technologies and selection of the engineering materials. Though only few companies are assessed in this study, the feedback gives some indications to be taken care of in formulating a new curriculum for mechatronics education. The majority of the companies are willing to cooperate with universities in order to improve teaching methodology in the filed. Unless this is materialized, it is difficult to include practical trainings and internships in the study program. This study has also brought some obstacles to our attention. Introducing internships in both countries bears difficulties and risk of making the study program longer. Though a successful internship may require only 2 -3 months, it is impractical to be completed parallel with the studies in accordance with the current academic plan.

The companies, in general, seem to underestimate theoretical knowledge and give less emphasis on skills in application of mathematical tools and laws of physics, while concurrently they demand the innovative approach and skills that need training. To train these skills a project based teaching and problem solving in a team with clear distribution of tasks and responsibility is suggested by the project team.

Students' expectations

The goal of any student to attend a given field of study is gaining knowledge and skills that provides him/her with well earned job. In addition, there are certain other factors that drive to enroll into a study program and strive to complete it. This involves primarily the correlation between interest and capability. One important challenge for mechatronics curriculum is thus its multidisciplinary character. The curriculum can be viewed as the means of introducing the subject matter in those diverse areas such as mathematics, electronics, mechanical and computer engineering fields. Lack of interest or fundamental understanding in one or several of these elements possibly leads to lack of interest in mechatronics study.

The other issue is making the teaching process interesting. This can be enhanced by introducing a practical oriented teaching process as discussed in the previous section. Experience shows that students, particularly engineering students, prefer hands-on learning than theory based ones. This demands resources in terms of cooperation with industries and qualified teaching staff.

The field of mechatronics is relatively new and not well known in the ordinary people's life. In a survey carried out as part of this project in Stavanger area, about 44% of the responded High School pupils do not know/understand what the word "mechatronics" means. Some work is needed to make the field well known to the potential candidates of the university enrollment.

Conclusions

The survey reported in this article was initiated due to an existing problem in recruiting students to mechatronics study program. As stated earlier in this article, few articles have appeared in the literature addressing this issue with a target of formulating an effective curriculum for mechatronics education. As it stands now, the solution to the problem has more of regional or local characteristic than universal. Among others, the knowledge and skill needed by the locally operating companies influence the content, depth and method of teaching. The feedbacks from this assessment have provided key indications in the extent to which mechatronics is known and implemented in companies and enabled us to identify their preferences. This will for sure help us to formulate an effective and attractive curriculum of the future. Further, it is highly expected that the obtained responses in the assessment will provide a good basis for discussions among members of the project team on the study curriculum, methodology of education, and contents of the didactic materials.

Fig. 2 .

 2 Fig. 2. (a) Size and (b) profile of surveyed companies

Fig. 3 .Fig. 4 .

 34 Fig. 3. (a) Availability of R&D department at the company and (b) degree of cooperation with universities

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig. 6. Feedbacks on required personalities of a graduate in engineering

Acknowledgement: The authors gratefully acknowledge the financial support provided by Island, Liechtenstein and Norway by means of co-financing by European Economic Area and Norwegian Financial Mechanism under the Scholarship and Training Fund, project number FSS/2008/X/D5/W/0045.