" (Bienstock, 1996) Simulation is stated to offer an alternative "for understanding these systems, since experimenting with the actual systems would be too costly." (Bienstock, 1996) Furthermore, simulation is stated to facilitate the "examination of dynamic processes or systems over time by allowing the compression of real time." (Bienstock, 1996) Bienstock states that the methods for adjusting the sample size 'n' in simulation studies are as follows: (1) simulation runs for each experimental condition (each cell) may be replicated 'n' times;

(2) observation of 'n' subintervals of the simulation of an experimental condition may be increased by decreasing the length of the subintervals; or (3) the simulation of an experimental condition may be continued for a longer period of time, thereby increasing the number of subintervals (i.e. The sample size). (Bienstock, 1996)

The technique described by Bienstock (1996) is one that "...enables a logistics researcher to determine the number of replications necessary to achieve a relative degree of precision. A relative precision goal for a logistics/distribution experiment ensures a reasonable degree of precision within the context of the system being investigated. Use of this technique will provide a researcher with the number of replications which will yield the degree of precision necessary for drawing conclusions about the behavior of the system under the various experimental conditions." (Bienstock, 1996) This technique is stated as appropriate for "simulation modeling that employs successive independent replications of simulation runs; it is not appropriate for determination of achieved relative precision on subintervals of a single simulation run." (Bienstock, 1996) Furthermore, Bienstock states that this technique "...cannot be used in experimental designs that utilize VRT." (1996)

V. Appraisal of existing Simulation Models in Logistics

The work of Rosenfield, Copacino, Little and Payne (nd) entitled: "Logistics Planning and Evaluation Using 'What-if' Simulation" states that the planning for the configuration of "large, complex distribution systems for optimal balance of cost and service can be best accomplished through use of sophisticated computerized models. The use of such models of all types has gained attention in the solution of large scale logistics problems." (Rosenfield, Copacino, Little and Payne) One such model is that developed by Geoffrion and Graves which was a large-scale logistics planning and optimization model for a major large food company introduced in the early 1970s. Another was developed by Bender, Northrup and Shapiro and Klingman, Napier and Stutz which were mathematical approaches for logistics planning and optimization models. Other models have focused on simulation of the wide range of "costs and activities in the logistics system." (Rosenfield, Copacino, Little and Payne)

Rosenfield, Copacino, Little and Payne state that the various approaches of computerized and manual evaluations are inclusive of those as follows:

(1) Manual evaluation of alternatives;

(2) What-if simulation modeling;

(3) Optimization modeling; and (4) Heuristic modeling. (Rosenfield, Copacino, Little and Payne, nd)

It is related that in problems that are 'small-scale' or in which the number of shipment alternatives is limited, the analysis can be performed "manually and alternative scenarios can be explicitly evaluated." (Rosenfield, Copacino, Little and Payne, nd) the manual approach is stated to have been used "historically" although "the power and availability of computers have made other approaches more desirable." (Rosenfield, Copacino, Little and Payne, nd)

What-if simulation modeling is one of the two most widely used approaches and the other is optimization modeling. Rosenfield, Copacino, Little and Payne state that 'What-if' simulation modeling "generally connotes scenario evaluation, while optimization involves a determination of the optimal or best solution." (Rosenfield, Copacino, Little and Payne, nd) a third stated approach is that of "heuristic modeling" which is defined as a "trial and error process to reduce the multitude of possible problem solutions to a small, manageable number of feasible solutions." (Rosenfield, Copacino, Little and Payne, nd) the heuristic approach is one that is based most often upon "a criterion which managers seek to optimize. Hence heuristic modeling in this case is really a form of optimization modeling." (Rosenfield, Copacino, Little and Payne, nd) the What-if approach is stated to be feasible only when there are a limited number of alternatives for consideration. It is also related that the optimization approach is generally necessary when there are "significant (typically resource allocation) constraints in the logistics system activities." (Rosenfield, Copacino, Little and Payne, nd) What-if simulation is stated to be "cumbersome to apply" when "systems alternatives are restricted, the complexities of considering many policy variables" exists. (Rosenfield,...

(Rosenfield, Copacino, Little and Payne, nd) Rosenfield, Copacino, Little and Payne state that the optimization approach and the 'What-if' simulation modeling are "not necessarily mutually exclusive, and indeed, often overlap." (Rosenfield, Copacino, Little and Payne, nd) Rosenfield, Copacino, Little and Payne report that three separate sets of computer programs used in the model reported in their work were those of:
(1) Data-base management programs;

(2) Freight and lead time analysis models; and (3) the What-if scenario evaluator. (Rosenfield, Copacino, Little and Payne, nd)

The data-base management programs are stated to have processed and converted the data into files. These programs then converted the supply/demand data into a set of demands by product class broken down by combination of origin node and destination node. (Rosenfield, Copacino, Little and Payne, nd) While the actual part-by-part modeling is stated to have not been performed due to limitations of a practical nature related to computer storage and time it is stated that the "aggregation of each suppliers parts into a part class provided a reasonable estimate for individual parts." (Rosenfield, Copacino, Little and Payne, nd)

A detailed account of the number of parts each supplier shipped and for each model year was contained in the corporate data base including information of the piece weight, dollar value, quantity of each part, assigned shipping class, and destination. Large amounts of freight cost and lead time data were processed by freight and lead time analysis models into functional regression relationships between costs and lead times distances, weights per shipment and other factors. (Rosenfield, Copacino, Little and Payne, nd) System mileages are stated to have been determined "on the basis of the latitude and longitude specifications for each of the nodes." (Rosenfield, Copacino, Little and Payne, nd)

Therefore, "any two nodes could be assigned locations and hence a mileage fro lead time and freight rate calculations." (Rosenfield, Copacino, Little and Payne, nd) Important to the model was the use of arbitrary locations with the model's key part of the software being the 'what-if' simulator based on the supply/demand data" which made determination of the overall system costs. The software implemented in this analysis had the capacity to trace a part from the supplier across the entire supply network and to the part's final destination.

The what-if scenario evaluator was designed to determine total system costs given:

(1) the supply/demand matrix as a function of the origin/destination pair and part class; and (2) the specific scenario. (Rosenfield, Copacino, Little and Payne, nd)

Rosenfield, Copacino, Little and Payne state that in broad terms "the scenario was a specification of a path for each element of demand." (nd)

Rosenfield, Copacino, Little and Payne state that they created a module that: (1) recalculated all system mileages; (2) recomputed all freight rates and lead times; (3) updated arc costs to reflect modifications; and Updated all paths to reflect new arcs. (Rosenfield, Copacino, Little and Payne, nd) Therefore, the arcs and paths were "identified in the same way, all paths and arcs were modified." (Rosenfield, Copacino, Little and Payne, nd) the model is reported to have been implemented "...in two separate sets of runs." (Rosenfield, Copacino, Little and Payne, nd)

The appropriate broad alternatives and specific candidate scenarios were identified but only following much analysis and scenario evaluation. The majority of the lead times underwent regression calculation and the majority of the freight rates on arcs that originated at the suppliers were based on formulas for calculation as well. The primary strategic question was related to the issue of the facility and the actual freight rates were utilized for "all of the paths in the system in the second set of runs." (Rosenfield, Copacino, Little and Payne, nd)

It is reported that in the runs, and where "specific freight rates were used to verify the final decisions, shipment sizes were calculated and used to determine the appropriate input freight rate over a selection of weight breaks." (Rosenfield, Copacino, Little and Payne, nd) the savings that were identified in this model were comprised by…