称号及び氏名

博士（工学）ＫＵＮＣＯＲＯ ＨＡＲＴＯ ＷＩＤＯＤＯ

学位授与の日付

平成 17 年 9 月 30 日論

「Optimal Supply Chain for Harvesting andDelivering Fresh Agricultural Products

文

名（生鮮農産物の最適な収穫・配送サプライチェーン）」論文審査委員

主査

長澤啓行

副査

市橋秀友

副査

辻洋

副査

森澤和子

副査

太田雅晴

論文要旨
Supply chain models for fresh agricultural products are more complicated than thesupply chain models for usual industrial products with no deterioration because of somespecial properties such that (1) the plant flowering and growing process depends on theclimate in farmland; (2) the amount of fresh products to be harvested is restricted by thegrowing process which is hardly controllable; (3) the loss process of any fresh products
begins just after harvested and depends on the handling process; and (4) all fresh products
should be consumed directly by customers or used as fresh materials in food and beverageindustries before they become rotten. It is regrettable that the total loss of fresh agricultural
products can be up to 20-60% of the amount of harvested products in any country. A major
cause of this large loss may be a mismatch between harvesting and delivery processes interms of timing and quantity. Therefore, an optimal supply chain model for harvesting anddelivery in agro-industries should be constructed to reduce the total loss and to maximize
the total consumer satisfaction.

This thesis formulates basic agricultural models, especially a growing process of therelated plant on farmland and a loss process of fresh products after harvested. The former
process is identified as a maturing curve expressing the maximum amount of harvestablefresh products after flowering on the farmland. Successive multiple flowering and growing
processes are also formulated to express the maximum amount of harvestable freshproducts, provided that any requirements for harvesting fresh products should be satisfied
through the earliest possible flowering. The loss process is identified by a loss function
expressing the amount of available fresh products whose quality is good enough toconsume. Successive multiple deliveries to multiple markets are also formulated to express
the maximum amount of available fresh products, provided that any requirements forsatisfying demand should be satisfied through the earliest possible delivery. Decision
problems based on these models are formulated to find an optimal harvesting pattern offresh agricultural products for maximizing a demand level to be satisfied in the market
under the condition of periodical flowering. Two cases, a restricted inventory case and anunrestricted inventory case, are discussed separately, and two kinds of problems, asingle-market problem and a multiple-market problem, are constructed for each case. The
multiple-market problems are finally extended into decisions problems for selecting
optimal combination of transportation methods to deliver the fresh products from farmlandto the markets.
The thesis is organized as follows.
In Chapter 1, the introduction of the thesis is described.
In Chapter 2, three basic agricultural models are formulated in mathematical form to beapplied or extended in the remaining chapters. The first model, flowering-harvesting model,
is formulated to express the relationships between flowering-growing process andharvesting activity. The bound for fresh agricultural products to be harvested at any period
is given by a combination of plant maturing curves in multiple flowering of agriculturalplants. In this bound, the remaining amount of harvestable fresh products in any maturing
curve was appropriately assessed by considering the remaining growing process on thefarmland. The second model, harvesting-delivering model, is formulated to explain therelationships between harvesting and delivery of fresh products for consumption in eachmarket. The bound for demand of fresh agricultural products in each market at any period
is given by a sum of fresh products delivered with a given lead time and carried as on-handinventory. In this bound, the loss process inevitable for delivery and carrying inventory is
considered to obtain the amount of available fresh products in each market. The thirdmodel, periodical flowering model, is formulated to describe the process of
harvesting-delivering through periodical flowering, provided that harvesting pattern foreach flowering is all the same and is repeated periodically, and that any requirement for
harvesting fresh products should be satisfied through the earliest possible plant maturing.
The relationships between an effective harvesting pattern and a maturing curve inperiodical flowering is expressed in mathematical form, and effective bounds for a demandlevel to be satisfied constantly at any period are derived by eliminating a wasteful on-handinventory from the primary model.
In Chapter 3, decision problems based on the models provided in Chapter 2 areformulated to maximize a demand level to be satisfied constantly every period by
periodical harvesting-delivery process of fresh agricultural products in a “single market” or“multiple markets” under the condition that inventory can be carried as on-hand inventory
in the market for at most one period. In the multiple-market problem, demand in eachmarket is assumed to be satisfied in proportion to each market size so that the original
problem is converted to a “two-stage” optimization problem by decomposing it into a main
problem and a set of subproblems related to each market. An optimization algorithm isproposed and applied to each decision problem to find an optimal harvesting pattern. The
proof is given in an analytical manner to show that the proposed algorithms provide anoptimal harvesting pattern to each problem. Numerical examples are demonstrated to show
how the proposed optimization algorithm works well. From the computational results, wefound that the optimal harvesting pattern is affected by a change in an interval of flowering
cycle and in a delivery lead time, and that fresh products can be harvested only for carrying
them as on-hand inventory as long as the loss of fresh products is less than the loss causedby the deterioration on farmland in case of harvesting the products later.
In Chapter 4, the periodical flowering-harvesting problems discussed in Chapter 3 areextended to more general cases, where fresh products are delivered to a single market or
multiple markets immediately after harvested and on-hand inventory in the market can becarried for more than one period. In the multiple-market problem, the original problem isdecomposed into a main problem and a set of subproblems in the same way as in Chapter 3.
An optimal harvesting pattern to a single-market problem is derived analytically and anoptimization algorithm to solve a multiple-market problem is developed by exploiting theoptimal algorithm for the single-market problem. The proof is also given to show that thesolution obtained through the proposed algorithm is optimal. Numerical examples for thetwo models are demonstrated to show the effectiveness of the proposed algorithm. It ismade clear that harvesting fresh products at any period just after multiple harvest assigned
to use only for carrying them as on-hand inventory is possible as long as the loss of fresh
products is less than the loss caused by the deterioration on farmland in case of harvesting
the products later.
In Chapter 5, the two-stage decision problems for multiple markets discussed inChapters 3 and 4 are finally extended into a “two-phase, two-stage” periodical
flowering-harvesting-transportation problem for selecting a best combination oftransportation methods from a single farmland to multiple markets to maximize the total
gross revenue obtained from the harvesting-delivery process of fresh agricultural products,
provided that the delivery lead time from farmland to the markets can be changed throughselecting one of available transportation methods. The restricted inventory case and theunrestricted inventory case are dealt with separately in formulating the related optimization
problem, and in developing the optimization algorithm. A graphical method on atwo-objective space, to maximize the total relative sales and to minimize the totaltransportation cost, is proposed for selecting the optimal combination of transportation
methods to maximize the total revenue under a given set of prices in multiple markets.
Sensitivity analyses are implemented to provide a range of prices so that the combinationof transportation methods remains optimal. Numerical examples with real data on
transportation costs available in Indonesia are demonstrated to show the effectiveness ofthe proposed method for providing an optimal combination of transportation methods andan optimal harvesting pattern.
In Chapter 6, the results obtained in this thesis are summarized and some perspectives
for the future work are given.

List of Publications
No.

Title of the Article

Author(s)1Basic Supply Chain Management
Models in Harvesting andDelivering Agricultural Fresh
Products

K.H. Widodo
H. Nagasawa
K. Morizawa
M. Ota2

A Periodical Flowering-Harvesting
Model for Delivering Agricultural
Fresh Products

3

A Periodical Flowering-Harvesting
Model for Delivering Agricultural
Fresh Products to Multiple
Markets
A Periodical Flowering-Harvesting
Model for Delivering Fresh
Agricultural Products to Multiple
Markets with Inventory
Optimal Harvesting-Delivering
Pattern of Agricultural Fresh
Products to Multiple Markets in
Periodical Flowering

K.H. Widodo
H. Nagasawa
K. Morizawa
M. OtaK.H. Widodo
H. Nagasawa
K. Morizawa
M. OtaK.H. Widodo
H. Nagasawa
K. Morizawa
M. OtaK.H. Widodo
H. Nagasawa
K. Morizawa
M. Ota4567

Two-Phase Optimization Methodfor Harvesting and Delivering
Agricultural Fresh Products with
Periodical Flowering to Multiple
Markets
Optimal Harvesting-Delivery
Pattern of Fresh Agricultural
Products to Multiple Marketswith Inventory under PeriodicalFlowering

K.H. Widodo
H. Nagasawa
K. Morizawa
M. OtaK.H. Widodo
H. Nagasawa
K. Morizawa
M. OtaJournal’s/Conference’s Name,

CorrespondingVol., Pages (Year)

Chapter(s)Proc. of the 17th International
Conference on Production
Research, Blacksburg, Virginia,
USA. ISBN 0-9721257-3-6,#0171, pp.1-18 (2003)
European Journal of Operational
Research(in press)

Chapter 2
Chapter 3

Chapter 2
Chapter 3

Journal of Japan Industrial
Management Association(accepted for publication)

Chapter 3

European Journal of Operational
Research(submitted for publication)

Chapter 4

Proc. of the 8th International
Conference on Manufacturingand Management, Gold Coast,
Queensland, Australia.
ISBN 0-9578296-1-2,pp.731-738 (2004)
Journal of Japan Industrial
Management Association
Vol. 55, No. 6, pp.334-340(2005)

Chapter 5International Journal of Logistics(submitted for publication)

Chapter 5

Chapter 5審査結果の要旨
本論文は、生鮮農産物のサプライチェーンにおいて、農産物の成熟・劣化過程を考慮しながら、農地での収穫と市場への配送を最適に計画するための基本モデルを定式化し、その解法を提案したものであり、次のような成果を得ている。

(1) 農産物の開花・成熟過程および損失過程を数学モデルで定式化し、農産物の基本的なサプライチェーン・モデルを構築している。これに基づき、パパイヤのように連続的に開花・成熟して日常的に消費される農産物のサプライチェーンをモデル化し、市場規模に応じて各期で常に一定水準の農産物が供給されるという条件下で、その水準を最大にするための連続開花・収穫・配送問題を定式化している。
(2) 各市場における生鮮農産物の手持ち在庫が１期しか許されない場合と２期以上許される場合のそれぞれについて、単一市場および複数市場への連続開花・収穫・配送問題を定式化し、解析的に最適収穫・配送パターンを求め、最適性の証明を与えている。複数市場の場合には主問題と副問題からなる２段階意思決定問題に分割できることを示し、単一市場問題の解法を副問題へ適用し、システマティックに解いている。
(3) 数値例により、(a)成熟ピーク期までの最適収穫・配送パターンは単期分連続収穫になるが、ピーク期以降は複数期分収穫と無収穫が混在すること、(b)成熟ピーク期以降の最適収穫・配送パターンは開花周期が長いほど複雑になること、(c)複数期分収穫を行った次の期においても在庫のための単期収穫または複数期収穫が生じうること、(d)農地から市場までの配送リードタイムが長いほど最適収穫・配送パターンが一層複雑になることを明らかにしている。
(4) トラック輸送、貨車輸送、海上輸送、空輸など輸送手段を選択することによって配送リードタイムが変えられる場合を取りあげ、最適配送手段の選択問題を定式化している。この意
思決定問題に対し、生鮮農産物価格が全市場で同じである場合(均一価格)と市場によって比例的に変わる場合(相対価格)の２通りについて、相対的総販売量最大化と総配送費最小化の２目的空間上で図式的に解く方法を提案し、数値例を示している。

以上の研究成果は、経営工学分野におけるサプライチェーン最適化手法の発展に貢献するところ大である。また、申請者が自立して研究活動を行うに必要な能力と学識を有することを証したものである。