Selected deterministic models for lot sizing of growing items inventory

Abstract

One of the more recent advances in inventory management is the modelling of inventory systems consisting of items which are capable of growing during the course of the replen- ishment cycle. These items, such as livestock, are a vital part of life because most of them serve as saleable food items downstream in supply chains. In the context of this study, growth is de ned as achieving an increase in weight. This increase in weight is what di erentiates growing items from conventional items. A typical inventory system for growing items has two distinct periods, namely growing and consumption periods. The growth period starts when a shipment of live newborn arrives. The live items are fed so that they can grow. All the items in each lot are assumed to grow at the same rate. Once the weight of the items reaches a speci c target, they are slaughtered. This marks the end of the growth period and thus the start of the consumption period. The slaughtered items are kept in stock and consumed continuously at a given demand rate. At the instant that the consumption period ends, items in the next cycle would have completed their growth period and they will be ready for slaughter and consumption. A feeding cost is incurred for feeding the live items during the growth period whereas holding costs are incurred for keeping the slaughtered items in stock during the consumption period. This study is aimed at developing lot sizing models for growing items under three di erent conditions which might occur in food supply chains. These selected conditions are used to develop three Economic Order Quantity (EOQ) models for growing items. In addition to item growth, these three models assume, respectively, that a certain fraction of the items is of imperfect quality due to errors in one of the processing stages; the available growing and storage facilities have limited capacities; and the vendor of the items o ers incremental quantity discounts. These models are aimed at answering two of the most important questions facing inventory managers, namely \how much to order?" and \when to place order?". A third question, which is speci c to growing items, arises, namely \when should the items be slaughtered?". In the imperfect quality model, it is assumed that the poor quality items are also sold, but at a discounted price. Furthermore, there is a screening process, conducted on all the items before they are sold, to separate the poor quality items from those of good quality. For the limited capacity model, it is assumed that if the order quantity exceeds the available capacity, additional growing and storage capacities are rented from an external service provider, but this comes at a cost as the rented warehouse has higher holding costs. The nal model assumes that the supplier of the newborn items o ers the purchasing company incremental quantity discounts. For all three model presented in this study, the proposed inventory systems are given vivid descriptions which are used to formulate corresponding mathematical models. So- lution procedures for solving the proposed mathematical models are also presented. Nu- merical examples are provided to demonstrate the solution procedures and to conduct sensitivity analyses on the major input parameters. The presence of poor quality items means that more items need to be ordered in or- der to meet a speci c demand for good quality items. The e ect worsens as the fraction of imperfect quality items increases. Having capacity constraints on the growing and storage facilities increases total costs mainly because of the higher holding costs in the rented facility. As the capacity increases, the total costs decrease, but increasing capacity is capital intensive and poses nancial risks if market conditions change for the worst. Quantity discounts were shown to reduce the purchasing cost of the newborn items, how- ever ordering very large quantities has downsides as well. The biggest downsides are the risk of running out of storage capacity, the increased holding costs and item deterioration since larger order quantities result in increased cycle times. Through sensitivity analyses conducted for all three models, the target slaughter weight was shown to have the greatest e ect on the EOQ than any other input parameter. The inventory models presented in this study can be used by procurement and in- ventory managers, working in industries which stock growing items, as a guideline when making purchasing decisions. This can result in sizable reductions in inventory-related costs. Seeing that growing items are an integral part of food supply chains, the result- ing cost savings can be used to cushion consumers against rising food prices or from a nancial stand point, the savings can be used to boost pro t margins.