An alternative optimal solution technique for a single-vendor single-buyer integrated production inventory model

A predetermined production rate in a supply chain model with economic production lot size is quite appropriate for this type of situations as production rate can be changed in some cases to fulfill demand of customers. This paper investigates an integrated production inventory model with variable production rate on quality of products involving probabilistic defective under variable setup cost. As a rate of production has a direct impact on system performance, the production rate is considered as a variable along with the production cost. This production process gone through a long run system as a result after some specific time the production gone out-of-control state due to different issues and produced defective items. In addition, we consider that the defective follows three types of probability distribution function such as, (i) uniform, (ii) triangular and (iii) beta distributions. Two types of lead time crashed concept considering in this model and also we consider three types of continuous probabilistic defective function to find the associated cost of the system. The main objective is to find an optimal solution for an order quantity, safety factor, production cost, setup cost and to analyze how the flexibility of the production rate affects the process quality. An efficient iterative algorithm is designed to obtain the optimal solution of the model numerically and sensitivity analysis table formulate to show the impact of different parameter.

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Designing a single-vendor and multiple-buyers' integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

RAIRO - Operations Research ◽

10.1051/ro/2021174 ◽

2021 ◽

Author(s):

Chayanika Rout ◽

Ravi Shankar Kumar ◽

Arjun Paul ◽

Debjani Chakraborty ◽

Adrijit Goswami

Keyword(s):

Fuzzy Rule ◽

Inventory Model ◽

Approximation Formula ◽

Integrated Production ◽

Single Vendor ◽

Production Inventory ◽

Integrated Cost ◽

Interval Type ◽

Multiple Buyers

In this paper, a single-vendor and multiple-buyers' integrated production inventory model is investigated where deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of interval type-2 fuzzy number (IT2FN) is developed. Its application in the proposed model is brought off by considering imprecise demand patterns at the buyers' locations which are in the form of IT2FNs. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. An optimization problem with interval objective function is formulated. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.

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