M♮-Convexity and Its Applications in Operations

A new approach for structural analysis of operations models with substitutability structures. In many operations models with substitutability structures, one often ends up with parametric optimization models that maximize submodular objective functions, and it is desirable to derive structural properties including monotone comparative statics of the optimal solutions or preservation of submodularity under the optimization operations. Yet, this task is challenging because the classical and commonly used results in lattice programming, applicable to optimization models with supermodular objective function maximization, do not apply. Using a key concept in discrete convex analysis, M♮-convexity, Chen and Li establish conditions under which the optimal solutions are nonincreasing in the parameters and the preservation property holds for parametric maximization models with submodular objectives, together with the development of several new fundamental properties of M♮-convexity. Their approach is powerful as demonstrated by applications in a classical multiproduct stochastic inventory model and a portfolio contract model.

Stochastic Inventory System With Different Rates of Production

This article analyzes a solitary item stochastic inventory model with two distinctive generation rates where a request pursues Poisson distribution and an item has a limited lifetime which is level dependent. It is expected that the framework be on a foreordained level and the framework is changed over to ON mode from OFF mode with a noteworthy exchanging time with exponential parameter α. During the switching time, no interest will be served, the interest during the exchange time is lost. Here, excesses are permitted and during accumulations, the production rate is higher than that of ordinary generation time. Some framework attributes are shown with time variety.

IMPLEMENTASI MODEL STOKASTIK PADA PERMASALAHAN OPTIMASI PERSEDIAAN KELAPA PADA TINGKAT DISTRIBUTOR

In the inventory system is given operational policies relating to product inventory control, such as how much is ordered, when to order with the aim of minimizing storage and ordering costs. Customer demand and lead time affect the inventory system. This study aims to determine the densitas distribution of demand data, total inventory costs and optimal coconut supply for the two order periods using the stochastic inventory model. Stochastic inventory models can be used if there is variable uncertainty. This paper discusses the optimization of coconut inventories using a stochastic model with uncertainty about demand and lead time. It is known that demand data is uniformly distributed, based on the realization value of random variable requests can be formed in 49 scenarios. Obtained an optimal total inventory cost for the two planning periods is Rp. 45,672,910, optimal supply for period one was 26031 coconuts. Inventory levels in two period for any scenarios are