The choice of the model in inventory control and the cost of sophistication

• Martin O. Omorodion

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

This thesis is concerned with the inventory control of items that can be
considered independent of one another. The decisions when to order and in
what quantity, are the controllable or independent variables in cost expressions
which are minimised.
The four systems considered are referred to as (Q, R), (nQ,R,T), (M,T) and (M,R,T). Wiith ((Q,R) a fixed quantity Q is ordered each time the order cover (i.e. stock in hand plus on order ) equals or falls below R, the re-order level. With the other three systems reviews are made only at intervals of T. With (nQ,R,T) an order for nQ is placed if on review the inventory cover is less than or equal to R, where n, which is an integer, is chosen at the time so that the new order cover just exceeds R. In (M, T) each order increases the order cover to M. Fnally in (M, R, T) when on review, order cover does not exceed R, enough is ordered to increase it to M. The (Q, R) system is examined at several levels of complexity, so that the theoretical savings in inventory costs obtained with more exact models could be compared with the increases in computational costs. Since the exact model was preferable for the (Q,R) system only exact models were derived for theoretical systems for the other three.
Several methods of optimization were tried, but most were found
inappropriate for the exact models because of non-convergence. However one
method did work for each of the exact models.
Demand is considered continuous, and with one exception, the
distribution assumed is the normal distribution truncated so that demand is
never less than zero. Shortages are assumed to result in backorders, not lost
sales. However, the shortage cost is a function of three items, one of which,
the backorder cost, may be either a linear, quadratic or an exponential
function of the length of time of a backorder, with or without period of grace.
Lead times are assumed constant or gamma distributed. Lastly, the actual supply quantity is allowed to be distributed. All the sets of equations were programmed for a KDF 9 computer and the computed performances of the four inventory control procedures are compared under each assurnption.
Date of Award Jan 1974 English T.B. Tate (Supervisor)

Keywords

• model
• inventory control
• cost

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