Fully loaded barges arrive at night in New Orleans following their long trips down the Mississippi River from industrial midwestern cities. The number of barges docking on any given night ranges from 0 to 5. The probability of 0, 1, 2, 3, 4, or 5 arrivals is displayed in Table 13.9. In the same table, we establish cumulative probabilities and corresponding random number intervals for each possible value.

A study by the dock superintendent reveals that because of the nature of their cargo, the number of barges unloaded also tends to vary from day to day. The superintendent provides information from which we can create a probability distribution for the variable daily unloading rate (see Table 13.10). As we just did for the arrival variable, we can set up an interval of random numbers for the unloading rates.

Barges are unloaded on a first-in, first-out basis. Any barges that are not unloaded the day of arrival must wait until the following day. Tying up a barge in dock is an expensive proposition, and the superintendent cannot ignore the angry phone calls from barge line owners reminding him that “Time is money!” He decides that before going to the Port of New Orleans’s controller to request additional unloading crews, a simulation study of arrivals, unloadings, and delays should be conducted. A 100-day simulation would be ideal, but for purposes of illustration, the superintendent begins with a shorter 15-day analysis. Random numbers are drawn from the top row of Table 13.4 to generate daily arrival rates. They are drawn from the second row of Table 13.4 to create daily unloading rates. Table 13.11 shows the day-by-day port simulation.

(1) DAY	(2) NUMBER DELAYED FROM PREVIOUS DAY	(3) RANDOM NUMBER	(4) NUMBER NIGHTLY ARRIVALS	(5) TOTAL TO BE UNLOADED	(6) RANDOM NUMBER	(7) NUMBER UNLOADED
1	a	52	3	3	37	3
2	0	06	0	0	63	b
3	0	50	3	3	28	3
4	0	88	4	4	02	1
5	3	53	3	6	74	4
6	2	30	1	3	35	3
7	0	10	0	0	24	c
8	0	47	3	3	03	1
9	2	99	5	7	29	3
10	4	37	2	6	60	3
11	3	66	3	6	74	4
12	2	91	5	7	85	4
13	3	35	2	5	90	4
14	1	32	2	3	73	d
$\underset{\_}{15}$	$\underset{\_}{0}$	00	$\underset{\_}{5}$	5	59	$\underset{\_}{3}$
	20		41			39
	Total delays		Total arrivals			Total unloadings
aWe can begin with no delays from the previous day. In a long simulation, even if we started with 5 overnight delays, that initial condition would be averaged out. bThree barges could have been unloaded on day 2. But because there were no arrivals and no backlog existed, zero unloadings took place. cThe same situation as noted in footnote b takes place. dThis time 4 barges could have been unloaded, but since only 3 were in the queue, the number unloaded is recorded as 3.

The superintendent will probably be interested in at least three useful and important pieces of information:

When these data are analyzed in the context of delay costs, idle labor costs, and the cost of hiring extra unloading crews, it will be possible for the dock superintendent and port controller to make a better staffing decision. They may even elect to resimulate the process assuming different unloading rates that would correspond to increased crew sizes. Although simulation is a tool that cannot guarantee an optimal solution to problems such as this, it can be helpful in recreating a process and identifying good decision alternatives.

Excel has been used to simulate the Port of New Orleans example, and the results are shown in Program 13.5. The VLOOKUP function is used as it was used in previous Excel simulations. Ten days of operation were simulated, and the results are displayed in rows 4 to 13 of the spreadsheet.

KEY FORMULAS
Copy C18:D18 to C19:D22 13.4-16 Full Alternative Text	Copy I18:J18 to I19:J21 13.4-17 Full Alternative Text
Copy B5:H5 to B6:H13 13.4-18 Full Alternative Text