Stokastik Süreler İçeren Kapasite Kısıtlı Parti Büyüklüğü Belirleme Problemi

Abstract

Bu makalede üretim ve kurulum süreleri stokastik olan kapasite kısıtlı çok ürünlü dinamik parti büyüklüğü belirleme problemi ele alınmıştır. Bu problemde tüm sürelerin stokastik olduğu durum göz önünde bulundurularak hem verimli hem de güvenilir üretim planları elde edilmektedir. Ele alınan problemin amacı klasik üretim maliyetleri ve ek mesai maliyetlerinden oluşan toplam maliyeti en küçüklemektir. Klasik maliyetler, üretim, kurulum ve envanter tutmaktan kaynaklanmaktadır. Ek mesai maliyetleri ise makinenin zaman kapasitesini aşacak şekilde kullanılmasından dolayı ortaya çıkmaktadır. Öncelikle, belirli bir üretim ve kurulum planı için beklenen ek mesai süresini kesin olarak hesaplayan bir prosedür önerilmiştir. Problemi etkin bir şekilde çözmek için tabu algoritmasına dayanan bir çözüm yaklaşımı geliştirilmiştir. Bu yaklaşım üç aşamadan oluşmaktadır: Başlangıç, iyileştirme ve planlama. Algoritmanın ilk aşamasında olurlu planlar üreten bir başlangıç metodu önerilmiştir. Bulunan planlar makalede önerilen tabu arama metoduyla iyileştirilmektedir. Planlama aşamasında, yerel arama metodunun bulduğu çözümleri iyileştirmek için bir doğrusal programlama modeli geliştirilmiştir. Çözüm yöntemimizin performansı literatürde yayınlanmış alt sınırlar kullanılarak onaylanmıştır.  Ayrıca, sonuçlar tabu arama yöntemimizin makul sürelerde çok iyi çözümler elde ederek iyi performans sergilediğini göstermektedir.

Keywords

• Parti büyüklüğü belirleme,Stokastik üretim zamanları,Stokastik kurulum zamanları,Ek mesai maliyetleri

Capacitated Lot Sizing Problem with Stochastic Times

Abstract

In this paper, we study a capacitated multi-item dynamic lot sizing problem with stochastic production and setup times. In this problem, we consider stochastic times to obtain production plans that are both efficient and reliable. The objective of the considered problem is to minimize the total cost including regular production costs and expected overtime costs. The regular costs result from production, setup and inventory holding. The expected overtime costs are incurred due to the excess usage of the machine capacity. First, a procedure that exactly computes the expected overtime for a given production and setup plan is developed. A solution procedure based on tabu search algorithm is proposed to effectively solve the problem. This procedure includes three main phases: initialization, improving, and scheduling. In the first phase of the algorithm, an initialization method is developed to construct feasible production plans. These plans are then improved by the proposed tabu search method. In the scheduling phase, a linear programming model is developed to further improve the solutions obtained by the local search method. The performance of our solution procedure is validated by the lower bounds reported in the literature. Moreover, results show that our tabu search method performs well by obtaining very good solutions in reasonable amount of times.

Keywords

• Lot sizing problem,Stochastic production times,Stochastic setup times,Overtime costs

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