Analysis of a production inventory system with MAP arrivals, phase-type services and vacation to production facility

Şerife Özkar

Makale detayları

Analysis of a production inventory system with MAP arrivals, phase-type services and vacation to production facility

Yazarlar:

Şerife Özkar

Yayıncı:

Ankara University

Ana Başlıklar:

Applied Mathematics

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 2, pp.286-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001289292

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 In this paper, we discuss a production inventory system with service times. Customers arrive in the system according to a Markovian arrival process. The service times follow a phase-type distribution. We assume that there is an infinite waiting space for customers. Arriving customers demand only one unit of item from the inventory. The production facility produces items according to an s, S-policy. Once the inventory level becomes the maximum level S, the production facility goes on a vacation of random duration. When the production facility returns from the vacation, if the inventory level depletes to the fixed level s, it is immediately switched on and starts production until the inventory level becomes S. Otherwise, if the inventory level is greater than s on return from the vacation, it takes another vacation. The vacation times are exponentially distributed. The production inventory system in the steady-state is analyzed by using the matrix-geometric method. A numerical study is performed on the system performance measures. Besides, an optimization study is discussed for the inventory policy.

 In this paper, we discuss a production inventory system with service times. Customers arrive in the system according to a Markovian arrival process. The service times follow a phase-type distribution. We assume that there is an infinite waiting space for customers. Arriving customers demand only one unit of item from the inventory. The production facility produces items according to an s, S-policy. Once the inventory level becomes the maximum level S, the production facility goes on a vacation of random duration. When the production facility returns from the vacation, if the inventory level depletes to the fixed level s, it is immediately switched on and starts production until the inventory level becomes S. Otherwise, if the inventory level is greater than s on return from the vacation, it takes another vacation. The vacation times are exponentially distributed. The production inventory system in the steady-state is analyzed by using the matrix-geometric method. A numerical study is performed on the system performance measures. Besides, an optimization study is discussed for the inventory policy.

 In this paper, we discuss a production inventory system with service times. Customers arrive in the system according to a Markovian arrival process. The service times follow a phase-type distribution. We assume that there is an infinite waiting space for customers. Arriving customers demand only one unit of item from the inventory. The production facility produces items according to an s, S-policy. Once the inventory level becomes the maximum level S, the production facility goes on a vacation of random duration. When the production facility returns from the vacation, if the inventory level depletes to the fixed level s, it is immediately switched on and starts production until the inventory level becomes S. Otherwise, if the inventory level is greater than s on return from the vacation, it takes another vacation. The vacation times are exponentially distributed. The production inventory system in the steady-state is analyzed by using the matrix-geometric method. A numerical study is performed on the system performance measures. Besides, an optimization study is discussed for the inventory policy.

 In this paper, we discuss a production inventory system with service times. Customers arrive in the system according to a Markovian arrival process. The service times follow a phase-type distribution. We assume that there is an infinite waiting space for customers. Arriving customers demand only one unit of item from the inventory. The production facility produces items according to an s, S-policy. Once the inventory level becomes the maximum level S, the production facility goes on a vacation of random duration. When the production facility returns from the vacation, if the inventory level depletes to the fixed level s, it is immediately switched on and starts production until the inventory level becomes S. Otherwise, if the inventory level is greater than s on return from the vacation, it takes another vacation. The vacation times are exponentially distributed. The production inventory system in the steady-state is analyzed by using the matrix-geometric method. A numerical study is performed on the system performance measures. Besides, an optimization study is discussed for the inventory policy.

Makale detayları

Analysis of a production inventory system with MAP arrivals, phase-type services and vacation to production facility

Yazarlar:

Şerife Özkar

Yayıncı:

Ankara University

Ana Başlıklar:

Applied Mathematics

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 2, pp.286-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001289292

pISSN:

1303-5991

Production inventory system

vacation

phase-type distribution

Markovian arrival process

matrix geometric method

Sayı

Makale detayları

Analysis of a production inventory system with MAP arrivals, phase-type services and vacation to production facility

Yazarlar: Şerife Özkar

Yayıncı: Ankara University

Ana Başlıklar: Applied Mathematics

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 2, pp.286-306

Belge Tipi: Makale

Yayın Tarihi: 6/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001289292

pISSN: 1303-5991

Production inventory system

vacation

phase-type distribution

Markovian arrival process

matrix geometric method

Sayı

Yazarlar:

Şerife Özkar

Yayıncı:

Ankara University

Ana Başlıklar:

Applied Mathematics

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 2, pp.286-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001289292

pISSN:

1303-5991