In this paper, we have modeled a business process which starts with shortage of deteriorating items. After a duration managers have freedom to order the stock of assurance of committed customers. There are many products that follow logarithmic demand pattern, so in this paper we incorporate it with the shortage of items at the beginning. A new model is developed to obtain the optimal solution for such type of market situation and have obtained some valuable results. | Yugoslav Journal of Operations Research 23 (2013) Number 3, 431-440 DOI: LOGARITHMIC INVENTORY MODEL WITH SHORTAGE FOR DETERIORATING ITEMS Uttam Kumar KHEDLEKAR and Diwakar SHUKLA Department of Mathematics and Statistics Dr. Hari Singh Gour Vishwavidyalaya Sagar, Madhya Pradesh, India uvkkcm@ diwakarshukla@ Raghovendra Pratap Singh CHANDEL Department of Mathematics and Statistics, Government Vivekananda Collage Lakhnadon, ., India fengshui1011@ Received: September 2012 / Accepted: February 2013 Abstract: In this paper, we have modeled a business process which starts with shortage of deteriorating items. After a duration managers have freedom to order the stock of assurance of committed customers. There are many products that follow logarithmic demand pattern, so in this paper we incorporate it with the shortage of items at the beginning. A new model is developed to obtain the optimal solution for such type of market situation and have obtained some valuable results. Numerical examples and simulation study is appended along with managerial insights. Keywords: Inventory, cycle time, optimality, deterioration, shortage, logarithmic demand. MSC: 90B05, 90B30, 90B50. 1. INTRODUCTION A business could start with shortages, like advance booking of LPG gas, electricity supply, and pre-public offer of equity share of company before properly functioning it. In the proposed model, we incorporate two objects, where one is logarithmic demand and the other is the business started with shortages. Few items in the market are of high need for people, like sugar, wheat, oil, whose shortage break the customer’s faith and arrival pattern. This motivates retailers to order an excessive quantity of units of an item, in spite of deterioration. Therefore, the loss due to damage, 432 . Khedlekar , D. Shukla & RPS Chandel / Logarithmic Inventory Model decaying, spoilage or due to deterioration can not be negligible. As .
