The commercial software used for the analysis is based on an optimization algorithm developed by Graves and Willems [6] (G&W2000}) and introduced in Chapter 3. Using existing optimization software allowed the focus of this research to be on the conceptual development and the empirical aspects of dynamic time- based postponement. Another reason for using commercial software was to use
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the same fools that were available to managemeni. In other words, dynamic time- based postponement should be an available solution fo management willing to coordinate activifies across the supply chain, rather than available only to those who understand complicated mathematics or those who have proprietary software.
Using the modeling approach of G&W2000, a supply chain is modeled as a cnain of stages. Each stage represents an activity or a set of activities after which inventory can be held unless otherwise specified, Therefore, a stage can be ail necessary activities to procure a raw material, to transport product between locations, or to serve demand. Two stages are connected by an arc, Stages and arcs have properties which determine the behavior of the model. The behavior of the model also depends on properties of the supply chain, such as the modeling horizon.
Table 4.7 summarizes the properties used for the supply chain, stages and arcs. Table 4.7.1 shows the inout oarameters for the supply chain, which are the modeling horizon, the base time unit, and whether review periods are used. Table 4.7.2 snows the input parameters for the stage. Inout parameters vary by the type of the stage; some parameiers apply to all siages, some are specific to demand stages, and others are particular fo internal stages. Internal stages are all stages other than demand stages. The input parameters are stage cost, holding cost, and stage time, which apply fo allstages, and are described in the column Description.
Time constraints also could apply to all stages, bul are activated where needed. The Service Time constraint refers jo the maximum and minimum replenisnment time quoted fo the nex?-tier customer. The maximum service time quoted io the customer is used to proteci the supplier stage; the minimum service time is used fo protect the next-tier customer. For example, stores need to have product available on-the-snelf, with no delay, when end-customers order meals.
Thus, the maximum service time at the stores is set to zero. The exposure time refers to the number of days for which safety stock has fo be held. Therefore, for example,
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since no safety stock is held in the transportation stages, their maximum exposure time parameter is set to zero. The concepts of service time and exposure time, and the optimization algorithm were explained in Chapter 3.
Table 4.7.2 also shows the parameters for demand stages. These are the average daily demand, the coefficient of variation of demand, the service level {measured as probability of no stockout), and a measure of autocorrelation of demand. The coefficient of variation of demand (COVd}) is preferable to the standard deviation of demand because it is a coefficient; that is, it has no unit of measure. Thus the same coefficient of variation for allrestauranis could be used for each phase while accounting for the size of the restaurant. The use of COVd faciitated data input and minimized errors.
Customer service level or product availability can be measured in several ways, each of which results in different inventory levels and has different managerial implications. As described in Chapter 3, the modeling approach assumes that ail demand below an upper bound will be filled; and that if demand is higher than this, managers will resort to other ways to fill demand. For instance, restaurant managers will fransship ingredients from another restaurant. Therefore, the measure of cusiomer service level used is probability of no stockout, which measures the number of times managers need to resort to exceptional actions fo avaid a stockout. This measure is appropriate in this setting because once a stockout occurs the effort (and cast) of the transshipment of one unit or a several units of ingredient was aimost the same.
Autocorrelation of demand describes the relationship of daily demand at each store over time. Demand variability is calculated from the standard deviation of the forecast errors and itis assumed that the forecast method used is regression- based. In this situation, the forecast error can be included as one regression term and demand considered to be independent over time. Because the franchisor was Implementing a forecasting system at the time this research was conducted, considering demand to be independent over time was appropriate.
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The other input parameter for internal stages is the pooling factor which is the extent to which demand streams from several locations served by the same stage are pooled. The concept of variance pooling was described in Chapter 2.
Finally, arcs have a single inout parameter, shown in Table 4.7.3. The value of an arc indicates how many units of supply are needed for each unit produced by the customer stage. For example, the unit for a manufacturer of an ingredient is a case, but restaurants produce 200 meals from a case of product; therefore, the value of the arc is 0.005 (1/200).
Parameter Description
Modeling Horizon The length of time that is modeled 1 year Ỉ Base Time Unit What is the unit of time modeled: day, week, etc. Day
| Review Periods Whether review periods are enabled Enabled
Table 4.7.1 — Inout Parameters of the Supply Chain
Stage Type Parameter Description Comments
Stage Cost The added cost to a unit of product Holding Cost Cost rate at which inventory is held Stage Time The time it takes to process one unit
Max and Min Constraint to the time quoted to the next-tier | Min=Planning and
All Stages Service Time customer Max=Promise
Max and Min Constraint to the exposure time of a stage. ventory levels during
Exposure Time .
Speculation Only if the review Review Period Length of the review period period is longer than
the base time unit
Demand Average demand per base time unit
The variability of Measure of demand variability forecast errors was
used.
Coefficient of Variation of Demand
Demand Stages
9 Service Level Measured as probability of no stockout Measure of correlation of demand over time (autocorrelation), The extent to which demand uncertainty accrues over time.
How demand uncertainty is pooled at a central location.
Autocorrelation of Demand
Internal Stages Pooling Factor
Table 4.7.2 — Inout Parameters of the Stages
Parameter | Description
Value Number of units of the supplier node that are needed per unit at the customer node
Table 4.7.3 — Inout Parameters of the Arcs Table 4.7
Supply Chain Modeling Input Parameters
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