MAP/PH/1 Üretim Envanter Modeli

Year 2023, Volume: 28 Issue: 1, 89 - 106, 30.04.2023

Şerife Özkar

https://doi.org/10.17482/uumfd.1171281

Abstract

Bu çalışmada, müşterilerin Markovian varış sürecine göre sisteme katıldığı faz-tipi hizmet sürelerine sahip bir üretim envanter modeli tartışılmaktadır. Envanter seviyesi pozitif olduğunda, gelen bir müşteri hizmet biriminin boş olduğunu tespit ederse hemen hizmete girer. Hizmet verilen müşteri sistemden ayrılır ve eldeki stok, hizmet tamamlanma anında bir birim azalır. Aksi takdirde müşteri sonsuz büyüklükte bir bekleme alanına (kuyruğa) girer ve hizmet almayı bekler. Üretim tesisi, ürünleri (𝑠, 𝑆) politikasına göre üretir. Envanter seviyesi 𝑠'ye düştüğünde üretim açılır ve envanter seviyesi maksimum 𝑆 seviyesine ulaşana kadar üretim açık kalır. Envanter seviyesi 𝑆 olduğu anda, üretim süreci kapatılır. Matris-geometrik yöntemi uygulayarak, üretim envanter modelinin kararlı durum analizini gerçekleştiriyoruz ve parametrelerin sistem performans ölçüleri üzerindeki etkisini ve envanter politikası için bir optimizasyon çalışmasını içeren birkaç açıklayıcı sayısal örnek gerçekleştiriyoruz.

Keywords

Üretim envanteri, Faz-tipi dağılım, Markovian varış süreci, Matris-geometrik yöntem, Yerel satın alma, Optimizasyon

A MAP/PH/1 PRODUCTION INVENTORY MODEL

Abstract

In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (𝑠,𝑆) policy. The production is switched on when the inventory level depletes to 𝑠 and the production remains on until the inventory level reaches to the maximum level 𝑆. Once the inventory level becomes 𝑆, the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory policy

Keywords

Production inventory, Phase-type distribution, Markovian arrival process, Matrix-geometric method, Local purchase, Optimization

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