In this paper, an inventory model with general ramp-type demand rate, partial backlogging of unsatisfied demand and time-varying holding cost is considered; where the “Time-varying holding cost” means that the holding cost is a function of time, . it is time dependent. The model is studied under the following different replenishment policies: (1) starting with no shortages (2) starting with shortages. | Yugoslav Journal of Operations Research 24 (2014) Number 2, 249 - 266 DOI: INVENTORY MODELS WITH RAMP-TYPE DEMAND FOR DETERIORATING ITEMS WITH PARTIAL BACKLOGGING AND TIME-VARING HOLDING COST Biplab KARMAKAR Department of Mathematics Assam University, Silchar-788011. India bipkar2011@ Karabi Dutta CHOUDHURY Department of Mathematics Assam University, Silchar-788011. India karabidc@ Received: February 2013 / Аccepted: June 2013 Abstract: In this paper, an inventory model with general ramp-type demand rate, partial backlogging of unsatisfied demand and time-varying holding cost is considered; where the “Time-varying holding cost” means that the holding cost is a function of time, . it is time dependent. The model is studied under the following different replenishment policies: (1) starting with no shortages (2) starting with shortages. Two component demand rate has been used. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy is derived for both the above mentioned policies. Keywords: Inventory, Ramp-type demand, Time-varying holding cost, Shortages. MSC: 90B05. 1. INTRODUCTION Inventory is an important part of our manufacturing, distribution and retail infrastructure where demand plays an important role in choosing the best inventory policy. Researchers were engaged to develop the inventory models assuming the demand 250 B. Karmakar, . Choudhury / Inventory Models With Ramp-Type Demand of the items to be constant, linearly increasing or decreasing, or exponential increasing or decreasing with time, stock-dependent etc. Later, it has been realized that the above demand patterns do not precisely depict the demand of certain items such as newly launched fashion items, garments, cosmetics, automobiles etc, for which the demand increases with time as they are launched into the market and after some time, it becomes constant. In order .
