Uncertainty lead time

Explanation of time uncertainty (lead time and delay) and quantity uncertainty in the model... 

Under the best of circumstances, none of these synthetic fuels could become significant commercial realities until the mid- or late-1980 s, because of technological and regulatory uncertainties, plus long lead times. But of more fundamental... 

In addition to studies examining cancers, many researchers have also sought to examine the possibility that living near landfill sites/contaminated land can have reproductive effects. Studies into the potential effects of contaminated sites on reproductive health tend to be inherently stronger than cancer studies because they avoid the uncertainty associated with long lead times between exposure and the onset of disease. The latency period for many reproductive effects is short (weeks or months) when compared with cancers, which can take years or even decades to appear. While some studies have been inconclusive or shown no reproductive effects,23-25 the larger and better conducted studies generally have identified some cause for concern. 

In this section we return to making decisions over continuous time. Demands each period ace modeled as following a distribution. We first consider the case where we can only mtike decisions once each period. The costs consist of the costs of holding inventory each period and the costs of shortage each period. We include the case where there may be a fixed lead time L for the supplier to deliver an order. The basic idea is that in the presence of uncertainty and lead time for delivery, orders have to be placed well in advance of inventory nmning out in order to guarantee a high level of availability. 

In the presence of lead time and demand uncertainty, the reorder level requires us to decide how much of the demand should be satisfied from stock. This factor can be expressed as service level. We express service level as the probability of being in stock. This probability is a number that the customers (generating the demand) can use to do their own planning. This probability will depend (intuitively) on the industry and on the extent of competition faced by the company. 

In this chapter we have provided a quick review of four possible approaches to forecast demand and its use in planning. The constant demand model allows for a quick analysis of the effect of ordering costs in a system. The models of demand as a distribution permit details of lead time and demand uncertainty to be included. The modeling of demands as a mixture of distributions enables us to consider the role of information acquired over time. Finally, the exponential smoothing model shows how demand forecast updating can create large swings upstream in a supply chain. 

Lot size re-order systems reviews the system continuously. The system has two variables R and Q. When inventory level hits R, Q units are ordered. As we assume a lead time L, demand during the lead time becomes the source of uncertainty. S is the set-up cost, p is the penalty cost per unit for unsatisfied demand. Then the following equations are solved back and forth iteratively [3] ... 

This example shows the close interaction between information, lead time, and capacity choice in the presence of demand uncertainty. In the absence of information, capacity buffers are optimal. However, lower lead times may permit better demand information, thus leading to a better match between demand levels and capacity. This enables additional capacity to be planned when there is an upside potential associated with high demand and simultaneously lower capacity when demand levels are anticipated to be low. The net result is a higgler profitability with lowered average capacity levels. 

Safety stock costs If the demand time, the transit time, or both are uncertain, it may be necessary to carry inventory as a buffer against demand uncertainty. As discussed earlier, the extent of this inventory buffer depends on the magnitude of the demand uncertainty during the supply lead time and the planned in-stock service level. If the planned in-stock probability is expressed as service and the demand over lead time has a standard deviation of ct i, then the safety stock level is expressed as (Note that we assume that... 

How do apparel supply chains compete One approach is to compete on cost, an approach used by Walmart and other department stores. This strategy focuses on developing a cost-efficient supply chain that may require global sourcing with low costs but long lead times. Such supply chains then require large buffer stocks to compensate for demand uncertainty or a focus on predictable demand for basic products with low demand uncertainty But there are many other dimensions of competition in the apparel industry. 

Second, company can avoid uncertainty by cutting lead times and increasing the supply chains flexibility so that it can product to order or at least manufacture the product at a time closer to when demand materializes and can be accurately forecast. 

Cycle stock—One of the two main conceptual components of any item in inventory, the cycle stock is the most active component, i.e., that which depletes gradually as customer orders are received and is replenished cyclically when supplier orders are received. The other conceptual component of the item inventory is the safety stock, which is a cushion of protection against uncertainty in the demand or in the replenishment lead time. 

Safety stock A quantity of stock planned to be in inventory to protect against demand fluctuations. The level of safety stock is a function of the uncertainty of the demand forecast during the replenishment period and uncertainties in the length of time required for replenishment. High uncertainty (such as for an innovative product) and longer lead times increase the need for safety stock. Also referred to as buffer stock. 

Chayet, S., W.J. Hopp. 2002. Lead Time Competition under Uncertainty. Working Paper, Graduate School of Business, University of Chicago, Chicago, IL. 

The value of 7 is interpreted as a fixed safety-stock level set for the endpoint. Thus, although the long-run optimal base-stock level P Xt) can take any functional form, we restrict ourselves to a target level (i which is a very specific linear function of the vector-estimate Xt. The reason we use a fixed safety-stock in (10.14) is that the level of uncertainty surrounding the lead-time demands is constant over time. 

Uncertainty in demand over lead time in a (Q, R) inventory system. 

Let us return to the problem stated in Example 3.5, the WallShaker speakers at J M Distributors. As we computed in this example, Qeoq = 189.7units, such that, if this value were feasible, we would set Q = 190. Now, assume that J M has collected additional information regarding demand and replenishment lead time. First, note that Pd = 18,000/365 = 49.32 units/day. J M has measured the uncertainty in daily demand to be Oq = 15 units/day. The company s data indicate, however, that the replenishment lead time is remarkably consistent at L = 4 days, such that they are willing to assume that Ol = 0- Thus, we can... 

For ease of discussion, let us consider only five items, as specified in Table 3.12. Since sales are concentrated in the relatively temperate Southeastern United States, we can assume that aggregate demand for tractors and accessories is reasonably steady across the year. Daily demand, however, exhibits some imcertainty. Although detailed standard deviation data for demand is currently not available, Milo s has historically used a coefficient of variation (standard deviation divided by mean) of 0.3 to estimate the uncertainty in daily demand in its past inventory planning. The order fulfillment lead time from the manufacturer DC (DJC) to the retailer DC (Milo s) is a fairly consistent 3 days. Both DCs operate 365 days per year. 

As companies turn to global suppliers, they must be aware of both the opportunities and the threats present. Understanding world markets can be extremely difficult since each country is unique and complex. Therefore, global operations increase uncertainty and reduce control capabilities. Problems might arise from the number of intermediaries, customs requirements as well as trade restrictions. In addition, uncertainty could result from greater distances, longer lead times, and less knowledge of the market conditions. 

Modelling of uncertainties in supply chains has become important with the proliferation of product varieties and the increased volatility of the global market places of the contemporary business environment. For instance, product range and product style in a fashion industry are renewed constandy while in the basic apparel industry, long production and distribution lead times still prevail. Managing business environment dynamics in an uncertain and competitive market is a challenging task and forced many organizations to reform their operational processes. 

Constraint (6)-(8) represents the dilferent situation of demand of the customer and production amount supplier can make available. In constraint (6), inventory is built up if production amount exceeds the demand and lost inventory situation is represented by constraint (7). Lost inventory situation leads to penalty which shows uncertainty in lead time. There is no inventory in case if demand is equal to the production amount which is embodied by constraint (8). Constraints (9)-(12) stipulate the non-negativity and discrete requirements for the variables. 

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