In a JIT/Lean manufacturing environment, it is important to schedule production in such a way that units are manufactured in direct proportion to their demand. Otherwise, in-process inventories accumulate, throughput time increases, schedule compliance suffers, all resulting in sub-optimal performance [1] . Consider the simple example where four units of Item A are demanded, two units of Item B are demanded and one unit of Item C is demanded. One possible schedule is as follows: AAAABBC. While changeovers are minimized, units are not sequenced proportional to demand. The following schedule would be better in terms of “smoothing out” production in terms of demand: ABACABA [2] .

There are various strategies and algorithms used to find the “best” sequence in terms of smoothing out production. These sequencing algorithms vary in terms of details, but they all share the same intent of smoothing out sequencing as much as possible.

This paper explores four of the more common sequencing rules, uses them to sequence mixed-model production schedules, simulates production schedules under various conditions, and analyzes the performance of the various rules.

Four sequencing rules are investigated for this research effort. Prior to presenting the individual rules, a few definitions are needed.

As an example for the sequence: ABACABA, we have values of (2, 2, 2, 1) for (Item A), (4, 3) for (Item B), and (7) for (Item C). When we calculate these values, we assume that the sequence cycles over and over. For the values, we simply use, yielding values of for this particular problem.

To determine which of the sequencing rules is most effective in terms of the JIT/Lean objectives mentioned previously, experimentation is conducted. Several problem sets are simulated according to their best sequence in terms of the objectives described above, simulation is performed, data is collected from the simulation, and analysis is made in an attempt to differentiate performance among the four presented objectives [8] .

Tables 3-10 show the results of the experiments for each unique analysis, specifically including the mean for each factor level, along with the F-statistics and associated p-value for each experiment. These tables show that the sequencing rule has an effect on the performance measure of interest (26) times of the (120) experiments conducted, using an level of significance. Of these (26) times, USAGE is a superior performer compared to the other three (8) times, and is an inferior performer compared to the other three (17) times. There is one other occasion where the sequencing rule has an effect on a performance measure of interest, but the difference is not due to USAGE.

Table 11 shows the similarity between all four of the sequencing objectives, based upon the sequences obtained via complete enumeration of all possible sequences for all (120) problems.

As one can see, there is a great deal of similarity between the MRG, AGL and VAR objective functions, while the USAGE objective function is absolutely unique from the other three. This is a reasonable explanation as to why USAGE is the biggest contributor to the significance of the sequencing rule.

An experiment was conducted to see if four popular sequencing rules have any effect on performance measures important to JIT/Lean manufacturing systems. Eight different problems were investigated, each with three processing time arrangements, and five different JIT/Lean manufacturing performance measures to study. For each of the four sequencing rules, complete enumeration of all feasible permutations was generated to find the “best” sequence in terms of the objective function associated with each sequencing rule. This was done to show each sequencing rule in its “best possible light”.

Experimentation shows statistical significance of the sequencing rule (26) times out of a possible (120) times. The USAGE sequencing rule is the reason for the significant difference in means (25) of these (26) times?(17) of these (25) times USAGE provides inferior results than the other three sequencing rules. USAGE is the most unique of the other sequencing rules and provides less consistent results as compared to the other three. This should not come as a surprise because the USAGE objective function only looks at a single instance of the sequence, whereas the other three sequencing rules explore the cyclic nature of the sequence?multiple instances of the repeated sequence. The upshot of this is that USAGE is a higher risk strategy than the others.

Every research effort provides opportunities for further exploration. This is no exception. Longer production sequences would be helpful if there is some way around the combinatorial limitations that exist at present. Additionally, multiple-stage simulated production runs might also yield some interesting results.