Determination of Economic Lot Size between Suppliers and Manufacturers for Imperfect Production System with Probabilistic Demand

In this paper, we discussed the effects of discount price on demand and profit in a diminishing market. A production plan has been suggested for an imperfect production system. Here, demand is considered to be price sensitive and negative power function of the selling price. This problem is solved by optimization, using the Hessian matrix of order three. The main objective is to find the optimal expected average profit, optimal selling price, discount rate, backorder level, and lot-size. The recommendations are provided to offer a price discount for limited sale season on different occasions. A numerical example is presented to validate the model and is graphically illustrated accordingly.

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An economic production lot size model for randomly imperfect production system with stock-dependent demand and rework

International Journal of Operational Research ◽

10.1504/ijor.2018.10016676 ◽

2018 ◽

Vol 33 (3) ◽

pp. 315

Author(s):

Manoranjan Maiti ◽

Barun Das ◽

Manoranjan De

Keyword(s):

Production System ◽

Lot Size ◽

Imperfect Production ◽

Economic Production ◽

Stock Dependent Demand ◽

Size Model ◽

Production Lot Size ◽

Dependent Demand

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An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

Journal of Advances in Management Research ◽

10.1108/jamr-07-2019-0141 ◽

2019 ◽

Vol 17 (2) ◽

pp. 282-304

Author(s):

Katherinne Salas-Navarro ◽

Jaime Acevedo-Chedid ◽

Gina Mora Árquez ◽

Whady F. Florez ◽

Holman Ospina-Mateus ◽

...

Keyword(s):

Supply Chain ◽

Production System ◽

Inventory Model ◽

Collaborative Approach ◽

Lot Size ◽

Defective Items ◽

Content Type ◽

Imperfect Production ◽

Imperfect Items ◽

Exponential Probability

Purpose The purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team. Design/methodology/approach Two approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain. Findings A numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain. Originality/value The new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

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