# TAILIEUCHUNG - Manufacturer-supplier cooperative inventory model for deteriorating item with trapezoidal type demand

## This paper investigates a Supply Chain System for deteriorating items in which a supplier supplies a manufacturer with raw material, and the manufacturer produces the finished goods. Demand rate is assumed to be time-sensitive in nature (Trapezoidal type), which allows three-phase variation in demand, and production rate is demand dependent. Our adoption of trapezoidal type demand reflects a real market demand for newly launched product. | Yugoslav Journal of Operations Research 26 (2016) Number 1, 103-120 DOI: MANUFACTURER-SUPPLIER COOPERATIVE INVENTORY MODEL FOR DETERIORATING ITEM WITH TRAPEZOIDAL TYPE DEMAND Narayan SINGH Department of Mathematics . () College, Meerut (), India narayansingh1980@ Bindu VAISH Department of Mathematics . () College, Meerut (), India bindu58@ S. R. SINGH Department of Mathematics . () College, Meerut (), India shivrajpundir@ Received: January 2014 / Accepted: June 2014 Abstract: This paper investigates a Supply Chain System for deteriorating items in which a supplier supplies a manufacturer with raw material, and the manufacturer produces the finished goods. Demand rate is assumed to be time-sensitive in nature (Trapezoidal type), which allows three-phase variation in demand, and production rate is demand dependent. Our adoption of trapezoidal type demand reflects a real market demand for newly launched product. We show that the total cost function is convex. With the convexity, a simple solution algorithm is presented to determine the optimal order quantity and optimal cycle time of the total cost function. Numerical examples are given and the results are discussed. Keywords: Supply chain, Trapezoidal type demand, Deterioration. MSC: 90B05. 104 , , / Manufacturer-Supplier 1. INTRODUCTION There has been a growing interest in supply chain management in recent years. The supply chain, which is also referred to as the logistic network, consists of supplier distribution centres and retailer outlets, as well as raw material, work in process inventory and finished goods that flow between the facilities. Quite a lot of researchers and enterprises have shown a growing interest for efficient supply chain management. This is due to the rising cost of manufacturing, transportation, the globalization of market economies and the customer demand for diverse products of

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