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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.2 pp.335-346
DOI : https://doi.org/10.7232/iems.2020.19.2.335

# A Routing Problem in Global Production Planning

Qian Huang*, Jiahua Weng, Shunichi Ohmori, Kazuho Yoshimoto
Waseda Research Institute for Science and Engineering, Waseda University, Japan
Department of Industrial Engineering and Management, Kanagawa University, Japan
Department of Business Design and Management, Waseda University, Japan
Department of Industrial and Management Systems Engineering, Waseda University, Japan
*Corresponding Author, E-mail: huangqian365@gmail.com
June 21, 2019 September 29, 2019 December 17, 2019

## ABSTRACT

The paper proposes an integrated approach for global production planning of production, transportation, and sales problems wherein transportation routing must be optimized simultaneously. Multi-market, multi-product, multi-plant, and multi-path frameworks comprise the research contexts. The objective of this study is to determine how to maximize total profit with path-selection of marine transportation. Products are transported from plants to markets by marine shippers that are business partners of the manufacturer. Unit production costs from each plant to each market are not constant in this study, changing according to transportation path, and discount policy on each liner. Since the proposed model is a nonlinear problem with a nonconvex objective function and has nonlinear constraints, the model was linearized into a mixed-integer linear problem so that it could be solved with an optimization solver. moreover, computational experiments were conducted. the findings show that, because of transportation routing influences production allocation and sales operations, the proposed integrated approach is proven to be effective at increasing total profit and can be used as a decision support tool to aid global manufacturers to contract with transportation booking companies.

## 1. INTRODUCTION

Globalization has a fundamental link with transportation, even if the significance of transportation has been overlooked in globalization studies (Kherbash and Mocan, 2015). This fact may especially be seen in global production planning, where transportation planning always pertains to sub-planning which is decided after production allocation.

Production decentralization occurs obviously in the global economy, which has been becoming the main method for global manufacturing. Production decentralization means that a manufacturing firm split its production activities into various process or regions. In this paper, it is referred to a same final product can be assembled in not one but multiple plants. Thus, which product type of mar- ket demand would be supplied by which plant is a significant problem which is also called production allocation problem in global production planning.

The transportation process is a link between demanders and suppliers becoming more complex because demand and production environment are in flux. Transportation infrastructure covering is the depot or port to use, the route or path to travel has been increasing. Therefore, the rationalization and efficiency improvement of cargo transportation is required in international transportation. Also, what is the relationship between the transportation process and production process, meanwhile, what is the influence bringing from transportation complication on global production planning should be considered.

International transportation is essential for global manufacturing firms to deliver products from local plants to overseas retailers. Marine transportation is the main mode and remains popular, based on its cost-effectiveness and ability to transport a wide range of products. There are three main modes of marine transportation: industrial, tramp, and liner. In industrial shipping, the cargo owner controls the vessels and the routing. In tramp shipping, the cargo owner rent vessels for a trip or time, and controls the routing. In liner shipping, the cargo owner can control the transportation routing but not vessel routing, which is operated according to a published itinerary and schedule by the shipping lines. More manufacturing firms are changing from industrial and tramp shipping to liner shipping, due to the risk of fixed assent in the other methods and better utilization of resources (Fagerholt, 2004;Tran and Haasis, 2015). Moreover, consolidation of part of the liners has been a recent development of international marine transportation, which would result in lowering transportation costs for manufacturers and raising utilization for transporters.

However, in many production-distribution system types of research, transportation cost is calculated by the unit-cost times distribution volume. In other words, the unit-price of distribution cost is constant whenever the volume is high or low. The simplified expression is insufficient in the transportation process and is not adaptive nowadays. It should encompass more changes such as concave cost function of transportation process.

Another important issue is that when liner shipping is used, the route is predetermined, and the planner needs to select the path from origin to a destination out of a given route set. Therefore, the interplay of the economy of scale and routing problem should be simultaneously considered in production-distribution problem. Further, from shipper’s point of view, they can choose the routing which effect production allocation. The routing problem of transportation should be decided simultaneously with production allocation problem, not after production allocation. To our best knowledge, there is no research has examined this issue yet.

This study develops a global production planning model that integrates sales, production, and transportation planning while considering product routing problem (path selection) as decision variables and discount policy in transportation process to optimize global production planning. The remainder of this paper is organized as follows: Section 2 includes a review of the relevant literature regarding production-transportation problems, Section 3 describes the research problem and presents the model. Section 4 discusses the model’s reformulation, and the results of the numerical experiments are presented in Section 5. Finally, Section 6 summarizes the conclusions.

## 2. LITERATURE REVIEW

### 2.1 Transportation Problems in Integrated Production Planning

Previous papers on transportation problems in production planning have been examined. From the viewpoint of the role of the transportation process for a manufacturer, we classify the previous papers into three aspects as production-transportation with vehicle, productiontransportation with vehicle-hire, and production-transportation with booking.

Most of the contribution to routing problems in the literature pertains to production-transportation with vehicle problem since this type of manufacturer has transportation resources like trucks. Therefore, how to operate the resources of both the production and transportation processes is obviously important. Kuhn and Liske (2011) combined a lot-sizing problem and the routing problem into a simultaneous problem-solving approach. The number of trips described in their paper amounts to one per vehicle during each period, which is same as Boudia et al. (2008), Adulyasak et al. (2012), and Amorim et al. (2013). Based on those studies, some papers consider reutilizing vehicles that have returned to a depot during the same period. The number of trips in their papers is a multiple of the per vehicle figure during each period. Çetinkaya et al. (2009) developed an integrated lot-sizing and vehiclerouting model with multi-trip, multiproduct considering. Adulyasak et al. (2014) introduced multi-vehicle production routing problem formulations to resolve multi-trip routing problems under replenishment policies. Moreover, split deliveries also have been considered in other papers. Shiguemoto and Armentano (2010) consider splitting anticipated customer demand to coordinate with production planning, with the objective of minimizing the sum of production and inventory costs.

Some works have been done on the productiontransportation with vehicle-hire problem. This issue is similar to the production-transportation with vehicle problem in its cost construction. Both of the two face a fixed transportation process cost. Tang et al. (2007) transfer the transportation mode to vehicle-hire because of the high investment costs for vehicles and maintenance. They formulate the production vehicle-hire planning into mixedinteger programming. However, they focus on calculating the optimum number of vehicles to hire and only consider direct shipping strategy. Sakawa et al. (2001) and Aydinel et al. (2008) also propose an integrated model of production- transportation problems. In their distribution processes, the number of trucks was decided to calculate vehicle rental costs.

Type three is the production-transportation with booking problem. How to book appropriate transportation capacity with transporters on different routes is important. The majority of the previous production-transportation with booking models have considered transportation factors as single-path and unit transportation cost as being constant parameters (Fahimnia et al., 2013). The total unit cost of each product was calculated by the unit production cost plus the unit transportation cost, both of which were given in advance. Fahimnia et al. (2013) reviewed the integrated production-transportation planning models. They emphasized that the multi-product, multi-plant, multi-market, multi-transport route, multi-period problem is the most complex but comes closest to the real world for integrated production-transportation planning. Gunnarsson et al. (2007) considered integrated planning of transportation of raw materials, production, and distribution of products in a supply chain. Distribution is carried out by three different transportation modes: vessels, trains, and trucks in their study. Transportation costs change according to mode; however, unit transportation costs are constant under each one in their multi-path productiontransportation model. The same situation is also in papers by Ferrio and Wassick (2008) and Kim et al. (2008).

However, in practice, when conducting production planning for the following year, neither an accurate unit production cost nor a unit transportation cost was constant. More specifically, the unit production cost constantly changes with the production quantity of each product type in each plant, setup frequency and operational rate of each plant. Meanwhile, the unit transportation cost also changes according to certain factors such as contract patterns as vehicle-hire or booking: varying on whether the transportation method is direct or go around, a single product or a mixed one, the visitation sequence in depots or ports, quantity or distance discounts applied, etc.

Our paper, plan and optimize routing from the shipper’s point of view under given possible transportation routes with a different cost function. Our model includes both the production and routing decision, and thus, there is flexibility as production allocation can be adjusted by routing decision. Different routing pattern brings different production pattern, as we can see more opportunity from consolidating the shipment. None of the research considers this issue.

### 2.2 Mathematical Programming Models

A multi-path with unit transportation cost varying with product volume is considered in this study. A production- transportation-sales model with consideration of transportation booking is proposed while including routing selection and discount policy. Global factors such as tariff rates, labor costs among different regions and discount policy among different liners, etc. are also included in the proposed model.

However, the problem is NP-hard and difficult to solve, as was experienced in previous studies. Hou and Chang (2002) discussed that non-polynomial time must be spent to solve production allocation problem. The production allocation itself is a combinatorial optimization problem and an NP problem, which has been proved by Ibaraki and Katoh in 1988. Furthermore, Hakimi and Kuo (1991) considered a network location-productionallocation problem with concave cost functions and revenue functions. The problem is broken down into four subproblems to find an easier way to solve it. One of the subproblems, the production-transportation problem, had been proven to be an NP-hard problem. Meanwhile, Chang and Hou (2008) discussed that the production allocation problem is a constrained optimization problem that could be recognized as an NP-hard problem that was later proven by Garavelli in 1996. Also, solving such problem within polynomial time using general algorithms is impossible. Lately, Ekşioğlu et al. (2006), Fahimnia et al. (2013), and Abraham et al. (2015) argued that integrated production-distribution problems have been reported in the literature as NP-hard problems.

Because of this, in order to solve the integrated production- distribution problems within proper time, a variety of meta-heuristics methods have been suggested: genetic algorithm, tabu search, simulated annealing, and ant colony optimization. However, solving mathematical programming and constraint programming models using solvers have been reporting as effective way for reducing costs and increasing profitability in recent years, some solvers accept general LPs, MILPs as input as GUROBI, CPLEX which has been widely used in production allocation problems. Miller and de Matta (2008), de Matta and Miller (2015) used LP solvers in integration production networks with transfer pricing models, Rizk et al. (2008), Meisel et al. (2013) considered production-distribution networks models to find the minimum cost solutions using MILP solvers. Furthermore, Jahani et al. (2017), Xu et al. (2017), Liu and Papageorgiou (2018) applied decision optimization technology of CPLEX on a strategic level to an operational level of supply chain management problems. Especially, Hammam and Frein (2014) considered removing non-linearities constraints for a nonlinear global integration model by adding new variables and a set of linear constraints, then linearized the model and solved it with CPLEX.

In this study, the model is also a nonlinear problem, such that an integrated solution approach is developed to linearize the nonlinear problem to a mixed-integer linear programming (MILP) model.

## 3. MATHEMATICAL FORMULATION

The purpose of this proposed approach is to maximize the profits of sales, production, and transportation for manufacturers while using routing selection and discount policy in the transportation booking process. In this global production network, there are markets, plants, and a transportation network. As shown in Figure 1, the types of products for each market have different demands and they are produced in the plants, transported to the markets using multiple paths of transport.

For markets, demand quantities and selling prices are not fixed in this study. When prices of products are decided, the demand quantities are, too, using the demand curve function. For plants, production labor costs of each plant are different, it is possible that all types of products can be produced in each plant. However, each region may have a popular product and production capacity is limited in each plant. Finally, liners travel between plants and retail markets, for two liners or more, where doubling on a part of certain routes is allowed.

### 3.1 Definition of Route, Liner, and Path

Doubling a part of the routes of real maritime transportation networks is allowed. Thus, it is necessary to define the whole route, liner, and path to identify a doubled part for two liners or more. In this study, a route is the minimum distance unit of a liner linking one plant or market with another. Liner travel is between two fixed ports using a single track voyage. Each liner is built on one route (direct transportation) or multiple routes, which is advanced in a transportation network.

The path is the possible link between demand market and supply plant, which may be formed by a single route, or as part of multiple lines. For example, they are distinguished in Figure 2[a][b][c] below.

### 3.2 Problem Formulation

In this study, the objective function is profit maximization, and it is determined by sales revenues, sales costs, production costs, and transportation costs. Sales revenues are calculated from the price-quantity (PQ) curve in each market, while sales costs are inventory costs plus tariff costs. Production costs are divided into fixed and variable production costs, and transportation cost is the voyage cost from the plants to the markets with routing selection and discount policy. The formulation is as follows:

Indices

• j Market zones j∈J

• k Products k ∈ K

• i Plants i ∈ I

• v Nodes V∈{I ∪J}

• r Routes $r = ( i , j ) ∈ R = { ( i , a ) , ( a , b ) , … ( t , j ) }$

• p Paths p=(i,a,bt, j)∈P

• l liners l=(a,bt)∈L

Parameters

• αjk Scaling factor of customer preference in market j∈J for product $k ∈ K(α jk ≠ 0 )$

• n Industry exponent of PQ curve (n<0)

• $m ijk proc$ Markup coefficient of product k ∈ K from plant i ∈ I to market j∈J (%)

• $β ij duty$ Tax/tariff rate of market j∈J for importing goods from plant i ∈ I (%)

• $I j inve$ Unit inventory cost in market j∈J ($/piece) • PCapi Maximum production capacity of plant i ∈ I (piece) • $C i fix$ Fixed cost in each plant i ∈ I ($)

• $C ik prod$ Unit variable production cost of product k ∈ K in plant i ∈ I ($/piece) • $C r trans$ Unit voyage cost of route r ∈ R ($/piece)

• $P a t h p i j = ( i , a , b … t , j )$ Number sequence of routes r ∈ R from plant i ∈ I to market j∈J through path p∈P

• $L i n e r l = ( a , b … t )$ Number sequence of routes r ∈ R of liner l ∈ L

• $R ^ Cap r$ Maximum booking capacity in route r ∈ R (piece)

• γr Discount rate among liners of route r ∈ R (%)

• εr Load required rate of booking capacity corresponding to discount rate γr of route r ∈ R (%)

Decision Variables

• vjk Sales price of product k ∈ K in market j∈J ($/piece) • yjki 1 if plant i ∈ I is chosen to produce product k ∈ K of market j∈J or 0 otherwise • xjkp 1 if path p∈P is chosen to receive product k ∈ K of market j∈J or 0 otherwise • $RQ r j k i p$ The amount transportation quantity in route r ∈ R of product k ∈ K from plant i ∈ I to market j∈J using path p∈P • $RC r j k i p$ The amount of transportation cost in route r ∈ R of product k ∈ K from plant i ∈ I to market j∈J using path p∈P corresponding to discount rate γr In economics and marketing literature, the variations in sales quantities are usually described by demand curves. A general form of demand curves is the continuous function, the sales price is positive, then vjk > 0 which is shown as . Thus, it is clear that sales revenue is as The integrated production and sales planning model with a marine transportation problem is, therefore, Model I, which is formulated as if Then $RC r j k i p = ∑ j ∑ k ∑ i ∑ p T r a n C r RQ j k i p r γ r$ Else $RC r j k i p = ∑ j ∑ k ∑ i ∑ p T r a n C r RQ j k i p r$ (1) The objective is to maximize total profits. It is composed of sales revenues, sales, production and transportation costs. The first term in Eq. (1) defines sales revenues. Sales revenues of the sales process: $∑ j ∑ k α jk ( v jk ) n + 1$ (1.1) The second term defines the total average inventory costs. Inventory costs occur in sales bases of the demand market and the speed of outflow can be regarded as averaged. Inventory costs of the sales process: $∑ j ∑ k I j inve α jk ( v jk ) n 2$ (1.2) The third one presents import tariff costs, which are production costs multiplied by procurement rates (1 + markups) and tariff rates among plants and markets. Tariff costs of the sales process: $∑ j ∑ k ∑ i { ( C i fix ∑ j ∑ k α jk ( v jk ) n y jki + C ik prod ) α jk ( v jk ) n y jki } ( 1 + m ijk proc ) β ij duty$ (1.3) The fourth and fifth terms represent the fixed and variable production costs of each plant, respectively. Production costs of the manufacturing process: $∑ i C i fix + ∑ j ∑ k ∑ i C ik prod α jk ( v jk ) n y jki$ (1.4) Finally, the last term represents total costs of transportation (voyage), after considering transportation routing and discount policy. The decision of path selection results in cargo volume in each of selected path. Therefore, when the amount quantity $R Q r j k i p = ∑ j ∑ k ∑ i ∑ p α j k ( v j k ) n y j k i x j k p P a t h p i j$ is equal to or greater than the load required a rate of booking capacity $R ^ Cap r ε r$, there is a discount policy, then acquired mount transportation cost is $RC r j k i p = ∑ j ∑ k ∑ i ∑ p T r a n C r RQ j k i p r γ r$, otherwise, the cost is $RC r j k i p = ∑ j ∑ k ∑ i ∑ p T r a n C r RQ j k i p r$. Voyage costs of transportation process: $∑ r RC r j k i p$ (1.5) Production and transportation allocation constraints $∑ i y jki = 1 ( ∀ j , k )$ (2) Each product k in each market j must be produced in exactly one plant i. Each product k in each market j must be transported through exactly one path p. $∑ p x jkp = 1 ( ∀ j , k )$ (3) Production and transportation capacity constraints The total production quantity produced in plant i from each product k of each market j cannot exceed the total production capacity in each plant i. $α j k ( v j k ) n$ is a sales quantity related to the decision variable of the sales price of vjk. Moreover, $α j k ( v j k ) n y j k i$ is production quantity produced in plant i of product k of market j. It is related to another decision variable of production allocation of yjki. Thus, in order to aggregate the total production quantity in each plant i, multiplication of two decision variables appear in this constraint. $∑ j ∑ k α jk ( v jk ) n y jki ≤ P ^ Cap i ( ∀ i )$ (4) The total transportation quantity through route r of each path p from each plant i to each market j of each product k cannot exceed the total booking capacity of each route r. To obtain the total transportation quantity in each route r, multiplication of three decision variables appears in this constraint. (5) ## 4. SOLUTION APPROACH The model I (v, y, x) in Eq. (1), is a nonlinear programming model with a nonconvex objective function and nonlinear constraints. In this section, we want to emphasize the difficulties of the model I to be resolved in a pair of aspects. One is high-dimension, the other one is multivariable. Thus, we abbreviated “vjk” to “υ,” “yjki” to “y,” “xjkp” to “x,” to focus only on the degree and number of decision variables in Model I. Then, the model I can be linearized to $( v n + 1 − v n ) − ( 1 v y v n y ) − v n y − v n yx$. Moreover, it can be shortly represented to a highdimensional multivariable form as $v n + 1 − v n y − v n yx$. Meanwhile, the most important objective of this paper is to provide various production planning during management meetings. Many decision items need to be discussed during the meeting. For example, under different production, transportation environment, next year, each product type in each market should be sold in what quantity, in what price, and which product should be produced in what plant, using which transportation route, etc. Therefore, as the first step, we try to propose a method that can provide a feasible plan for managers to discuss. Therefore, this section searches for approximations to Model I’s optimal solution and obtains MILP that can be solved with an optimization solver. ### 4.1 Descending Degree of Equation First, a high-dimensional equation is transformed into a linear equation by importing set P that is related to candidate sales prices and set D that is related to quantities for each product in each market, and binary variable z. As a result, the high-dimensional form is converted to PDz−Dzy−Dzyx . Set P, D are multiplying by binary variable z to choose a sales price and quantity from candidates, after which the high-dimensional equation disappears. This is reasonable since, in actual production planning problems, it is assumed that sales prices or quantities are forecasted or estimated by an expert’s judgment. In this regard, such values are not always continuous. New indices: Q Candidate indices q∈Q(q=1,2,…,Q) New parameters: • Pjkq The qth candidate sales price of product k ∈ K in market j∈J ($/piece)

• Djkq The qth candidate sales quantity of product k ∈ K in market j∈J (piece)

New decision variables:

• zjkq 1 if the qth sales quantity of product k ∈ K in market j∈J is chosen or 0 otherwise

### 4.2 Eliminating the amount of Variables

Second, a two-dimensional variable, u, is used to simplify the variables. Since the variable u is denoted as the combination of zy, the formulation turns into PDz − Du−Dux . In addition, since z represents the demand to choose and y represents the plant to produce, chosen demand can be simultaneously determined with production allocation. Thus, the combination of zy is also feasible.

From the formulation PDz−Du−Dux , it is possible to find that ux is also a quadratic equation, which is difficult in an optimization solver. Then, a three-dimensional variable is used to simplify the variables. The variable o is denoted as the combination of ux. Hence, the formulation changes to PDz−Du−Do .

New decision variables:

• ujkqi 1 if plant i ∈ I is chosen to produce a product k ∈ K of qth q ∈Q sales quantity in market j∈J or 0 otherwise

• ojkqip 1 if path p∈P is chosen to transport a product k ∈ K of qth q ∈Q sales quantity in market j∈J and produced in plant i ∈ I or 0 otherwise

In this study, each plant can be assumed to have maximum utilization. Therefore, the production quantity $∑ j ∑ k ∑ q D jkq u jkqi$ can be linearized to the production capacity PCapi of each plant. Through the conversion, Model I can be rewritten as Model I’:

if

$RQ r j k i p = ∑ j ∑ k ∑ i ∑ p D jkq o j k q i p P a t h p i j ≥ R ^ Cap r ε r$

Then

$RC r j k i p = ∑ j ∑ k ∑ i ∑ p T r a n C r RQ j k i p r γ r$

Else

(1′)

Subject to:

(2′)

$∑ q ∑ i u jkqi = 1 ( ∀ j , k )$
(3′)

$∑ q ∑ i ∑ p o jkqip = 1 ( ∀ j , k )$
(4′)

(5′)

$RQ r j k i p = ∑ j ∑ k ∑ i ∑ p D jkq o j k q i p P a t h p i j ≤ R ^ Cap r ( ∀ r )$
(6′)

By transforming the nonconvex nonlinear equation into a MILP problem, the resulting Model I’ can be solved by using standard mathematical programming software.

## 5. COMPUTATIONAL STUDY AND RESULTS

In this section, the computational experiments that are carried out on two different types of global production networks are presented. They are different in a number of markets, the number of plants and connection routes for transportation networks. The proposed multi-market, multi- product, multi-plant, and multi-path model is tested to find the effect of increasing total profits compared with a separated approach.

Recently, some of the marine shipping companies have been reporting to consolidate their container shipping business on various international liners. The transportation booking fee may drop because of large-scale vessel usage of combined transport. However, each liner has the same discount policy on different cargo volume, as 10% discount on liner 1 of cargo volume 1000~1500 piece, 10% discount on liner 2 of 1500~2000 piece. Therefore, the discount policy of each liner has been considered with production planning to find the changing of total profit and cost construction in production networks.

Discount policies of liners effect on not just transportation process but also the whole integrated production planning. Because the unit transportation costs vary with a discount policy on liners, and different unit transportation cost of each liner would change the supplying path of products. How to use limited information (with or without discount policy) from a transportation company to make profitable global production plan is a significant problem of manufacturing industries. We discuss the mentioned problem in the latter part of this section.

The linearized MILP model is implemented using modeling language OPL of ILOG CPLEX 12.6. The computational tests are performed on a Dell desktop with a 3.3GHz processor and 8GB of RAM.

### 5.1 Total Profits Increasing by Integrated Approach

The integrated approach proposed in this study is applied in different size of networks to confirm the effectiveness. The experiment aims to testify how much potential profit improvement rates can be increased under different network construction compared with a separated approach.

The separated approach means to decide production planning in two steps. The first step is to decide production and sales planning, then put the result of the first step as input into the second step that is to decide transportation planning. Meanwhile, the integrated approach that is proposed in this study is to decide production, transportation, and sales planning simultaneously (Figure 3).

Information regarding the size of the test problem is given in Table 1. The production data are modified from a household company in Japan, and the transportation data are collected form container line company as NYK Container Line of Japan. Main results of the problem are displayed in Figure 4.

Table 1 shows that two types of global production networks have been considered. Network 2 is a largerscale network compared with Network 1, especially in numbers of possible paths of product to be transported from plants to markets. According to Figure 4, since the complexed network that has a more selectable and flexible construction, it results in getting more potential profit. In other words, the integrated approach is an effect on increasing total profit in the different type of networks where the problem scale becomes larger, the increasing profit also becomes significantly higher.

Six cases have been conducted when percentage change (share rate of average route cost to the average sales price) from approximately 3%~15% sequentially. From the result, we can find that regardless of network construction, profit increasing from case 1 to case 3, because the share rate of transportation process becomes higher. It is indicated that the integrated approach proposed in this study is more preferable in a manufacturing industry whose transportation cost cannot be ignored and has a share rate in cost construction, like household appliances industry, automobile industry, etc.

### 5.2 Discount Policy on Different Liners Result in Total Profits Changing

Network 2 mentioned in Section 5.1 is used for the case in this Section. The information of plant, market, and the product is assumed to be in Asia-Oceania area (5 plants, 15 markets) and the information of transportation network is set in 10 liners by referring the data from Asia- Oceania marine alliance as follows in Table 2.

The discount policy has been simultaneously considered with production, transportation, and sales planning in this case. Discount policy here means when the quantity of shipping cargo in a liner reaches the level of discount quantity, the unit booking transportation cost decreases because of discount policy. The discount policy (if discount quantity = route capacity × a then discount rate = b or does not have a discount policy) is obtained for each liner. Figure 5 is the result of different discount policy (a=0.5 b=0.5; a=0.5 b=0.7; a=0.7 b=0.5) applied in each liner. Liner 2, 7, 8 are sensitive to various discount policy compared with others; Liner 3, 4, 5, 6 are not sensitive to discount policy because transportation flows in those lines are small and not the central lines in transportation networks.

Results are shown in Figure 6. The total profit of the network is greater when considered with a discount policy compared than without one. However, the same discount policy in each liner brings different total profit. When a discount policy obtained for liner 2 (0.5, 0.5), the profit of the production network is highest. Then are liner 7 and liner 8. The results indicate that the three liners mentioned before are sequentially important while contracting with the transportation booking company. Because Obtain a greater discount rate on those liners can lead to greater potential profit. The integrated approach proposed in this study can provide decision support advice for manufacturers not only on how to allocate demand to production plants, how many and how much for products to sell in a market, but also for the department of manufacturers who hesitate to how to deal with transportation booking companies.

A cost analysis has been conducted to analyze the reasons why total profit changes are influenced by the discount policy on each liner. Since sales cost is nearly unchanged in the ten scenarios (10 liners), production and transportation costs variances are summarized in Figure 7. The discount policy makes both production and transportation costs vary. In the integrated approach, transportation decisions also influence production decisions. As a result, both production and transportation costs vary with the discount rate. Consequently, when a discount policy is obtained on liner 2, the firm experiences both lower production and transportation costs than those of other liners. When the discount policy obtained in for liners 7 and 8 is realized, transportation cost is lowest but production costs increase. However, they cancel each other out, resulting in total profit increasing after the influence of liner 2.

### 5.3 Supply Path Changing with transportation planning

The activity of transportation process has a significant effect on total profit and cost construction of production network, which was proved in Section 5.2. And the transportation routing problem is considered simultaneously with production planning in this study. However, how about the supply path routing under the activity of transportation process still unknown. In this experiment, liners without a discount policy and liners with a discount policy (liner 2) have been conducted.

Then, under a discount policy (liner 2), the tonkilometer (TKM), which is a measure of freight carried (production quantity × travel distance), has been found increased over the entire network. However, there is no substantial change in production quantity which is one parameter of TKM, but total travel distance which is the other parameter of TKM has increased. Since some of the products are produced in a more distant plant while under a discount policy, which can generate economies of scale in transportation result in total transportation cost decreasing.

The supply path is changing under the discount policy (liner 2: if the discount quantity = route capacity × 0.5; discount rate = 0.5) compared to without one. The changing result of supply path is presented in Table 3.

The result indicates that, while market and plant are in the same place (as Shanghai is both a market and a plant), local production with local supplying is permitted. Therefore, when only focus on the node of Shanghai, local production with local supply is best. However, from a general perspective, products produced in Osaka would occur production costs but they could be turned into economies of scale in the case of using transportation with liner 2 in this case. The same supply path change logic works when using a discount policy of Yangon and Mundra. With those contributions, liner 2 reach economies of scale in transportation simultaneously with optimum production planning and sales planning, resulting in total profit increasing the global production network.

## 6. CONCLUSION

This paper proposed an integrated model for global production, transportation and sales planning including marine transportation routing considerations. Since the proposed model is a nonlinear problem with a nonconvex objective function and nonlinear constraints, the model was linearized into a mixed-integer linear problem, so that it could be solved with an optimization solver.

The paper makes three primary contributions. First, to prove why the integrated approach is better. The integrated approach is applied in different size of networks to confirm the effectiveness. Potential profits can be acquired under different construction of production networks compared with a separated approach. However, the adoption of some assumptions based on big gaps among the global business environment. For instance, different labor cost, different tariff rates, and many selectable paths. We think that when the global business environment is similar to each other, the potential profits acquired in the integrated approach would decrease.

Second, to emphasize why we should consider transportation routing in production planning and what can we do for manufacturers. The transportation process is always decided without relationship to the production process. Since the transportation network is becoming complex in international transportation, selectable cargo routing would influence not just transportation cost but also production profit. Therefore, the integrated approach proposed in this study can provide decision support advice for manufacturers not only on how to allocate demand to production plants, how many and how much for products to sell in a market, but also for the department of manufacturers who hesitate to how to deal with transportation booking companies. However, marine transportation was only considered in this study, it is suggested to consider international railway, airliner connection and also multi-mode transportation to find a further suggestion.

The integration of multi-decision generally leads to complex models that are difficult to solve. In this study, we linearized the model so that which could be solved with an optimization solver. A decision variable structure is developed to represent the quantity of product sold in each market produced in each plant and transported by what path. However, there is no comparison with the metaheuristic method as GA, SA, Tabu search and etc in both calculation accuracy and time. Clearly, there is a need of developing a metaheuristic method for further study.

By extension, cost functions as setup costs for a plant, transship cost, and loading and unloading costs in marine transportation should be considered. Other global factors also should be considered in this model, e.g., exchange rates and local taxes. Moreover, the uncertainty of demand and exchange rate should be considered as well.

In conclusion, we hope that the proposed model will aid as a decision support tool, and thus, be used by global manufacturers that want to increase profits but so far have hesitated to do sales planning, production planning and contract with transportation booking companies.

## ACKNOWLEDGMENT

This work was supported by JSPS KAKENHI Grant Number JP20K14987.

## Figure

Example of global production network.

Example of route, liner, and path.

The separated and the integrated approach.

Profit improvement rates using the integrated approach.

Different discount policy obtained in each liner.

Total profit change influenced by the discount policy of each liner.

Production and transportation cost changes influenced by a discount policy for each liner.

## Table

The size of the two networks

Plants, markets, and liners in the object network

Supply change from plants to markets

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