Inventory is the stock of the raw materials, products, and commodities that are considered to be the portion of business’s assets that are ready to use or will be ready to use. Inventory control is very important for any type of business. Inventory control becomes a huge task when the materials are perishable and space is limited for the materials. For this, we have to use inventory control policies for minimizing the ‘total inventory cost’ or maximizing the ‘total profit’.
It is expected that all systems in which controlling and managing inventory is an important factor, can greatly benefit from research results so as to minimize their relevant inventory cost operations. For example, according to Nahmias (2004), the investment in inventories in the US held in the manufacturing, wholesale and retail sectors during the first quarter of 1995 was estimated to be $1.25 tn. Therefore, there is a great need to perform special research on inventory management for those giant systems. Indeed many classical inventory models dealt with single item. Hong et al. (1990) developed an inventory model with uniform and finite production rate. Balkhi and Benkherouf (1996) developed models for perishable items. In this model optimal production policy for minimizing total inventory cost was developed. They (Balkhi, 1996, 1998, 2000, 2001 and 2003, and Balkhi et al., 2003) established sequentially, many inventory models. Those models considered the demand, production and deterioration rates as random function of time, and backlogged shortages were allowed.
Recently, Alamri and Balkhi (2007) and Balkhi (2009a and 2009b) introduced more advanced inventory models with similar but more relaxed and general assumptions.
Several papers have considered single-item inventory systems, and less work has been done on multi-item systems. So it is required to analyze the multi-item optimal inventory policies.
Hadley and Whitin (1963) and Nador (1996) dealt with the model under the resource constraints. Bhattacharya (2005) developed a model for two perishable items. Balkhi and Foul (2009a and 2009b) developed multi-item inventory model without considering resource constraints. More information about inventory systems for multi-items is available in the survey of Yasemin and Erenguc (1981) and in the reference within.
In this paper, a multi-item inventory control model is developed for perishable items in which production (or supply) is instantaneous with no lead time. Demand is uniform and deterministic and shortages are not allowed. The model is solved analytically for minimizing the total inventory cost, using Kuhn-Tucker theorem.
The results are also illustrated numerically.
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