Abstract-Research on procurement-production systems for deteriorating items has been done. The majority of studies assume that the perishable characteristics affect only the quantity of inventoried items. For food products, however, their quantity remains constant during their shelf life period, but the quality deteriorates over time. This paper proposes a new procurement-production model incorporating this situation. The quality change behavior of food products is approached differently depending on their forms either as raw materials or finished goods. As raw materials, the kinetic model is used to represent the quality degradation during storage time, while as finished goods the shelf-life dependent pricing is utilized to describe the value loss due to the quality perception of customers. A mathematical model representing the integrated procurement-production of raw materials and finished goods at a manufacturer is established in this research. The objective is to maximize the total profit per unit time of the system by controlling a number of variables, namely the production cycle (T), the number of raw materials' procurement over one production cycle (m) and the number of finished goods delivery over one production cycle (n).Index Terms-Deteriorating items, food inventory, procurement-production system, quality loss, value loss.
I. INTRODUCTIONEver since EOQ (Economic of Quantity) inventory control has been introduced, many researchers still develop it to solve various inventory problems. Conventionally, economic lot-size of raw materials was decided separately from finished product and this may lead to sub-optimization. It is because demand for raw materials depends on production schedule of finished products. Later, Goyal [1] developed an integrated inventory model for raw material and finished product. This research gave the first contribution in the field of integrated procurement-production (IPP) systems.Recently, research in the field of IPP system receives significant attention from scholars and many inventory models has been developed to accommodate this issue [2]. Goyal and Deshmukh [3] developed a model for IPP systems in just in time JIT environment to minimize set up time. And later, Lee [4] extend the IPP to an integrated supply chain problem by integrating the economic lot size of raw material, manufacturing set up and finished products. However, those studies assume that items can be stored infinitely, while in Manuscript received November 5, 2012; revised January 10, 2013. Gusti Fauza is with the School of Engineering, University of South Australia and Food Science and Technology Department, Sebelas Maret University, Indonesia (email: faugy001@mymail.unisa.edu.au).Yousef Amer and Sang Heon Lee are with the School of Engineering, University of South Australia. fact, some items have limited life time.In reality, it is often found that some particular items deteriorate over the storage period, for instance food products. For such items, the quality degradation during the storage time can lead ...