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AN INVENTORY PROBLEM APPLIED TO A RENTAL SITUATION
Author(s) -
Jain H. C.
Publication year - 1966
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1966.tb00265.x
Subject(s) - renting , purchasing , inventory valuation , profit (economics) , stock (firearms) , business , inventory control , economic rent , perpetual inventory , truck , stockout , operations research , inventory theory , operations management , marketing , economics , microeconomics , finance , engineering , aerospace engineering , mechanical engineering , civil engineering
Summary An inventory problem, applied to a rental situation business, has been considered. If no item is in stock when a demand occurs, the company borrows the units from other concerns in the same line of business. The profit function has been calculated and it has been shown how the inventory level increases with penalty cost. A review of the literature on inventory control reveals that not much work has been done in holding inventories of rental items. In a recent paper, Tainiter (1964) considered the situation in which a company rents out items such as cars, trucks, farm equipment, books, furniture, etc., and obtained the profit function by taking “rental‐out” time as a negative exponential and demand as a general random variable. The model is equally applicable to companies which rent out “service personnel”, repair men, taxi cabs, etc. “We consider a company renting out items to customers. The company starts its business by purchasing a total number of M items in the inventory. The term inventory, defined by Arrow, Earlin and Scarf (1958) as the stock of goods which is kept for future sale or production, is applicable here. Whenever a demand occurs the item is rented out immediately, if it is available in the stock. But if the inventory is zero, i.e. all the items are rented out, the demand will be satisfied by borrowing items from other companies which are dealing in the same line of business. For example, a manufacturer of refrigerators maintains and repairs his product at the customer's house after sale. If a complaint arrives when no repairmen are available, the company will “borrow” repairmen from elsewhere and will attend to the complaint immediately. The borrowing cost may be negative or positive, representing a penalty or a profit. On the other hand if the company does not borrow and the customer has to wait (and such situations occur very often) the loss of the customer's goodwill may occur. It is also not possible to keep large numbers of items because of the storage costs and tied up capital. The problem is then to devise an optimal policy such that the profits of the company are maximized.