Decision support for the single‐period inventory problem

Publication Date01 Mar 2000
AuthorJohn Walker
SubjectEconomics,Information & knowledge management,Management science & operations
Decision support for the single-period inventory
John Walker
Nanyang Business School, Nanyang Technological University, Singapore
The single-period inventory problem can be
summarised as follows. A single order
quantity can be made for delivery of an item
before the beginning of a period representing
the duration of some planning horizon. There
is uncertainty regarding the total demand for
the item over the period. There is no
opportunity of placing any subsequent orders
during the period. Units remaining at the end
of the period are disposed of at some (possibly
negative) value, and unsatisfied demand
results in a shortage cost. Such problems are
associated with the inventory of an item
having one or more of the following
.becomes obsolete quickly, e.g.
newspapers, fashion goods, etc.;
.spoils quickly, e.g. fruit, vegetables, etc.;
.seasonal goods where a second order
during the season is difficult;
.is stocked only once, e.g. spare parts for a
single production run of products;
.has a future that is uncertain beyond the
planning horizon.
Some problems owing to the very large cost
of setting up an order have the
characteristics of the single-period inventory
problem. Thus, the design decision on the
capacity of, say, manufacturing plants, and
the lot size decision for items produced to
tight quality control specifications can be
considered as single-period inventory
problems. For multi-period periodic-review
inventory problems, the single period model
is sometimes used in a ``myopic'' policy for
determining whether or not an order should
be placed, and if so, how large it should be to
meet an uncertain demand over each period.
A myopic policy is one that selects the order
quantity for the current period to optimise
the selected performance measure in the
current period alone.
Development of the support tool
Specification of the order quantity
In many cases reported in the literature, the
specification of the order quantity for the
single-period inventory problem has been
characterised by the development of a
mathematical model and the subsequent
determination of an ``optimal order
quantity''. The mathematical models
employed usually make specific assumptions
regarding the demand distribution, the cost
functions and the performance measure. The
mathematical models require
mathematically-sophisticated analysis and
are, therefore, difficult for managers to
understand, accept and implement.
The motivation for the development of the
support tool follows a suggestion by Ward et
al. (1991) that a more transparent and
managerially-acceptable approachwould be to
simply enumerate various performance
measures on a managerial-defined grid of
order quantities. A manager can then select a
preferred order quantity or a preferred range
of order quantities based on an examination
of the various performance measures. If a
preferred range is selected, the support tool
quantities. Transparency and constructive
simplicity are requiredif the support tool is to
be understood, ``owned'' and implemented by
managers in a direct and practical manner.
The support tool utilises the Visual IFPS/
Plus package, Gray (1996). Visual IFPS/Plus
is a financial modelling package that uses
English-like syntax and a spreadsheet format
to perform Monte Carlo simulations. The
package has the distinct advantage that the
use of the English-like syntax allows the
immediate identification of the purpose of
the support tool rather than the confusion
caused by the ``row-column'' references of
conventional spreadsheets. In keeping with
The current issue and full text archive of this journal is available
[ 61 ]
Industrial Management &
Data Systems
100/2 [2000] 61±66
#MCB University Press
[ISSN 0263-5577]
Inventory control,
Decision-support systems,
Problem solving,
Monte Carlo simulation
The development of a decision
support tool for the single-period
inventory problem is presented.
The support tool allows a consid-
eration of the following factors:
empirical frequency distributions,
theoretical probability distribution
functions and managerial prob-
ability estimates of total demand
over the period; piece-wise linear
(possibly discontinuous) cost
functions. Such functions allow for
the possibility of ``fixed cost''
elements and/or ``economies/dis-
economies'' of scale and account
for most, if not all, of the purchase
cost, holding cost, salvage reven-
ue and shortage cost functions
that arise in practice; choice of
performance measures; and
``what-if'' analysis on the problem
parameters. The support tool,
which uses the Monte Carlo simu-
lation option of Visual IFPS/Plus,
is transparent and constructively
simple and thus readily facilitates
understanding, acceptance and
implementation by management.
The support tool runs under the
Windows operating system and
has easy access to appropriate
spreadsheet and word-processing
packages for further processing
and report presentation.

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