A mathematical model for an optimal appointed delivery date on a home delivery market

Hidefumi Kawakatsu; Hiroaki Sandoh

RAIRO - Operations Research - Recherche Opérationnelle (2005)

  • Volume: 39, Issue: 1, page 3-12
  • ISSN: 0399-0559

Abstract

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In recent years, the home delivery market has rapidly been growing since customers can purchase a variety of products very easily via Internet. At the same time, however, customers tend to switch from a supplier to another seeking for better service for them. For this reason, it is necessary for suppliers to enclose their customers by means of various kinds of service and strategy. An appointed delivery date of a product ordered by a customer is one of important factors of supplier’s services. From the suppliers’ point of view, they hope to make the period from the order date to the delivery date as short as possible to increase their customers, but at the same time they prefer to make this period as long as possible since the risk becomes higher that they cannot deliver products to their consumer by the appointed date under the short period appointed date. This study proposes a stochastic model to determine an optimal appointed delivery date for a supplier. For small values of an appointed delivery date L , the probability that a customer purchases the product becomes larger, but the probability of tardiness increases. In contrast, the purchase probability as well as the penalty of tardiness decreases with L . From this point of view, this study formulates the expected profit for a supplier, which is to be maximized as an objective function. Clarified are the conditions under which an optimal appointed delivery date exists for the case where the purchase probability is expressed by a multinomial logit model. Numerical examples are also presented.

How to cite

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Kawakatsu, Hidefumi, and Sandoh, Hiroaki. "A mathematical model for an optimal appointed delivery date on a home delivery market." RAIRO - Operations Research - Recherche Opérationnelle 39.1 (2005): 3-12. <http://eudml.org/doc/245703>.

@article{Kawakatsu2005,
abstract = {In recent years, the home delivery market has rapidly been growing since customers can purchase a variety of products very easily via Internet. At the same time, however, customers tend to switch from a supplier to another seeking for better service for them. For this reason, it is necessary for suppliers to enclose their customers by means of various kinds of service and strategy. An appointed delivery date of a product ordered by a customer is one of important factors of supplier’s services. From the suppliers’ point of view, they hope to make the period from the order date to the delivery date as short as possible to increase their customers, but at the same time they prefer to make this period as long as possible since the risk becomes higher that they cannot deliver products to their consumer by the appointed date under the short period appointed date. This study proposes a stochastic model to determine an optimal appointed delivery date for a supplier. For small values of an appointed delivery date $L$, the probability that a customer purchases the product becomes larger, but the probability of tardiness increases. In contrast, the purchase probability as well as the penalty of tardiness decreases with $L$. From this point of view, this study formulates the expected profit for a supplier, which is to be maximized as an objective function. Clarified are the conditions under which an optimal appointed delivery date exists for the case where the purchase probability is expressed by a multinomial logit model. Numerical examples are also presented.},
author = {Kawakatsu, Hidefumi, Sandoh, Hiroaki},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {home delivery service; expected profit per customer; optimal appointed delivery date; multinomial logit model; Home delivery service},
language = {eng},
number = {1},
pages = {3-12},
publisher = {EDP-Sciences},
title = {A mathematical model for an optimal appointed delivery date on a home delivery market},
url = {http://eudml.org/doc/245703},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Kawakatsu, Hidefumi
AU - Sandoh, Hiroaki
TI - A mathematical model for an optimal appointed delivery date on a home delivery market
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 3
EP - 12
AB - In recent years, the home delivery market has rapidly been growing since customers can purchase a variety of products very easily via Internet. At the same time, however, customers tend to switch from a supplier to another seeking for better service for them. For this reason, it is necessary for suppliers to enclose their customers by means of various kinds of service and strategy. An appointed delivery date of a product ordered by a customer is one of important factors of supplier’s services. From the suppliers’ point of view, they hope to make the period from the order date to the delivery date as short as possible to increase their customers, but at the same time they prefer to make this period as long as possible since the risk becomes higher that they cannot deliver products to their consumer by the appointed date under the short period appointed date. This study proposes a stochastic model to determine an optimal appointed delivery date for a supplier. For small values of an appointed delivery date $L$, the probability that a customer purchases the product becomes larger, but the probability of tardiness increases. In contrast, the purchase probability as well as the penalty of tardiness decreases with $L$. From this point of view, this study formulates the expected profit for a supplier, which is to be maximized as an objective function. Clarified are the conditions under which an optimal appointed delivery date exists for the case where the purchase probability is expressed by a multinomial logit model. Numerical examples are also presented.
LA - eng
KW - home delivery service; expected profit per customer; optimal appointed delivery date; multinomial logit model; Home delivery service
UR - http://eudml.org/doc/245703
ER -

References

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