Comprehending Weekly and Even Daily Demand Characteristics for Inventory Replenishment

Weekly Data vs. Monthly Generally monthly sales and demand history is more than adequate as the basis to drive the process of inventory management. Sufficient random fluctuations take place from day to day or week to week so that the monthly data actually provides some smoothing effect and yet very effectively indicates fundamental trends and direction of the product. Additionally, seasonality characteristics express themselves in terms of monthly shifts, without having to worry about any finer breakdown of the yearly pattern.

In some businesses, however, and particularly in the retail field, there can be predictable weekly events and even daily patterns within the week that are pertinent (e.g., demand for Easter related products that can shift within the month from one year to the next). The need to recognize these patterns is particularly pertinent if vendor lead times and reorder cycles are relatively short, since product can be ordered and arrive within a week or two thereby making it pertinent how demand falls within the month.

A capability to accept weekly sales data has been built into MARS to meet this particular need. The look and feel of the system is fundamentally the same as when running on monthly data except that weekly history is displayed and the formulas were modified to recognize the difference in the time interval of the data. Even the basic forecast will not change appreciably, since the very nature of the forecasting mechanism is to smooth out the period to period variability. This process takes place whether we are dealing with weekly data or monthly data. In fact, if the product has no seasonality or promotional characteristics, the two approaches will yield fundamentally similar result except that the user can view weekly history vs. monthly. The big difference relates to seasonality or predictable promotional programs.

The weekly version of MARS has 52 seasonal periods vs. the 12 for the monthly data. Consequently, it becomes possible to deal with week to week changes in future demand, which obviously is not possible in the monthly version. For example, assume that Easter fell in the 16th week of the year in the past year, but will fall in the 18th week for the coming year. In this situation, the seasonality index for the family of products impacted by Easter could be set to deseasonalize the spike in the 16th week of the past year, but also to set the spike of expected future demand into the 18th week. Note again, however, that this becomes pertinent only if the vendor lead times and order frequencies are relatively short. If the sum of the two is, for example, four months, it is a bit of overkill to worry about when product will arrive plus or minus a week.

Daily Variability Within the Week While monthly time buckets of history are normally adequate for most inventory planning, it is also true that it is rarely necessary to worry about variations of demand within the week. When weekly data is pertinent however, and particularly if vendor lead times are expressed in a few days, patterns of demand within the week become something to consider. For example, convenience stores will have vendors that ship within a few days and it is also possible to order every day or every other day. Additionally, demand for their product is very dependent on the day of the week (e.g., receipts of product on Friday may be needed to satisfy a surge of demand in anticipation of the weekend, where as mid-week demand is much lower.

The weekly data version of MARS has had a feature added that deals with this issue. It is possible to create a set of “indices”, similar to the seasonal index concept for monthly or weekly data that express the 7 days of the week. The indices are 7 two-digit numbers that vary around the index of “1”, similar to the way the seasonal indices operate for monthly data. The sum of the seven indices must add to 7, but each index will express the nature of that day of the week. MARS then will use these indices to determine the demand expected during the “exposure period” which is the sum of the lead time plus order frequency. In other words, it will temper the forecast by the index number for each day as it steps forward through the exposure period (e.g., let’s say the weekly forecast is for 490 units. That means that on the average day we expect to sell 70 units (490 divided by 7days). But when MARS looks at a given day of the week that has an index number of .8 for example, then it expects only 56 units of demand (70 times .8). Specifically MARS divides the forecast of each week or part of week in the exposure period by 7 to obtain a daily forecast and multiplies the daily forecast by the daily index for that day of the week to obtain the daily weighted forecast. The total of all the daily weighted forecast in the exposure period is the forecast used by the ROT calculation).

Typical sets of numbers could appear as follows:

Case A	Case B

Monday 1.00 1.20 Tuesday .80 .70 Wednesday .75 1.00 Thursday .80 1.10 Friday 1.50 3.00 Saturday 1.15 .00 Sunday 1.00 .00

In case A we have a classic case of deliveries that are made every day, and each day of the week expresses the typical demand for that day with a slump in the middle of the week and a surge in demand on Friday.

Case B expresses the same type of situation, but with the added issue that there are no deliveries on Saturday or Sunday. Friday therefore has the full demand of the weekend plus its own demand. As MARS tracks the demand expected during the exposure period, which includes a Friday, it will comprehend that it needs to anticipate large deliveries for the weekend coming up. Note, incidentally if the user wants to even-out the delivery loads between Thursday and Friday it is a simple matter of adjusting the two index numbers accordingly (This could be 1.8 for Thursday and 2.3 for Friday - which still add to 4.1 the sum of 1.1. and 3.0).

The creation of the indices themselves is aided by a subroutine into which you can place some historic daily sales data from which MARS will calculate the indices. These indices can then be adjusted manually to further refine the user’s objectives. (As in our example of the non-delivery on the weekend.) The indices can be tied to the entire sales of the location, or to individual vendors, or even finally down to individual high volume items.

The combination of introducing weekly history with its weekly “seasonality Indices” and the daily “seasonality indices” makes MARS a very powerful short interval inventory management tool. Note that the two indices will operate in combination. That is, MARS will first adjust the week to reflect the seasonality characteristics and then again the day-of-the-week to express what goes on within the week.

The default parameters for Daily Indices (all days have the same weight) require no entries. Any more detailed definitions of these parameters defined in this table will be used to modify the forecast. The order of priority and the additional levels of detail are as follows:

Priority Fields in the definition First ITEM and LOCATION Second LOCATION, VENDOR and Group1 Third LOCATION, VENDOR and Group2 Fourth LOCATION, VENDOR Fifth VENDOR

As an example: If a vendor is entered with specific parameters any of the above would override it and an item entered with a location would override any of the other levels. If no entries are made the default values from the System Parameters are used.

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