Lead time replenishment

The only way to avoid this is by strict analysis of the supply chain from the customer order to final product delivery. Definition of the optimized (theoretical) process and sequential work towards a high service level approach allow the identification of gaps, and of opportunities which might not always be the cheapest (ship versus train versus plane) but could be the most effective way to reduce capital costs and shorten planning scope - an important aspect, especially in volatile customer markets with long production processes on the (chemical) supplier side. As in the case of CIP, this needs clear parameters, KPIs, commitment from all players, and regular tracking. The most important parameters are the lead time for all products, optimal lot sizes, replenishment points, and safety inventories. 

In considering kanban as a decentralized control system, the following control parameters are necessary number of kanbans in circulation number of units in the kanban standard container and kanban delivery cycle a-b-c (where b is number of deliveries per a days and c indicates the delivery delay factor as an indication of replenishment lead time). For example, 1-4-2 means that every 1 day the containers are delivered 4 times and that a new production order would be deUveted by the 2nd subsequent delivery (in this case, about a half-day later, given four deliveries per day). 

When demand is random, a standard model is to assume that the demand stream follows a renewal process, that is, D are independent and identically distributed (i.i.d.) random variables, where D denotes demand in period n. Suppose each production/replenishment order requires a lead time, denoted L, which can be constant or random. 

Next, suppose that due to limited production capacity, replenishment/production orders may have to wait in queue before they can be processed. In other words, in addition to the lead time (i.e.,... 

Let D(t) be the demand in period t, t = 1, 2,. . . Suppose demand (per period) over time is independent and identically distributed. Let L denote the lead time to flU each replenishment order. The number of outstanding orders, as explained in Section 2.1, is equal to the number of jobs, N, in an infinite-server queueing system. In particular, if the per-period demand follows a Poisson distribution, then N also follows a Poisson distribution with mean E(N) = E(D) E(L) (= p in Section 2.1 here D denotes the generic per-peiiod demand). Since N follows a Poisson distribution, we know Var(A0 = E(A0-... 

Suppose the lead time at each retailer i is periods, a deterministic constant, for i = 1,. . . , c. For instance, this can be the transportation time for a replenishment order to travel from the warehouse to the retailer or, in the case where stage i is a plant, the cycle time to build a customer order. Suppose the lead time at the warehouse is L . 

Thus, for the problem faced by Steco, a retailer of titanium rods. Weekly demand for these rods follows a normal distribution with a mean of 100 units and a standard deviation of 5 units per week. These rods cost 5 each and the cost of holding a rod in inventory for a year is 20% of its cost. The cost to Steco to place an order for replenishment is 25/order. Delivery lead time is one week. Management wants a less than 6% probability of stocking out. Assume 50 weeks per year. 

Note that supply chains are replenishment systems, thus the average amount shipped should match the average demand. If the transport lead time were L, the average in transit inventory is LD. Notice that this is just Little s law from queueing theory, which says that the average work in process inventory is equal to the demand rate times the average lead time through the system. 

Consider a supply chain with two spare-parts demand stations that face a daily demand for a part that follows a normal distribution with a mean (fx) of 50 and a standard deviation (cr) of 25. Assume that the parts stations face a replenishment cost (K) of 125, a holding cost (h) of 0.2/day/part, a backorder cost (h) of 5/day/part. Also, suppose each station faces a supply lead time (Z) of 3 days to be replenished by the... 

Sales forecasting, which projects point-of-sale consumer demand, is one of the collaboration tasks associated with this activity. The retailer task here is Point of Sale (POS) Forecasting and the manufacturer task is Market Data Analysis. The other collaboration task is Order Planning/Forecasting which uses factors, such as transit lead times, sales forecast, and inventory positions to determine future product ordering and requirements for delivery. The associated retailer task is Replenishment Planning, and Demand Planning is the associated manufacturer task. 

In the initial run of the game, each entity has a small stock of inventory, which is large enough to avoid any stock outs at the retailer assuming the forecast is correct and the lead times are met by each of the suppliers. Each entity is expected to receive orders from its customer and place orders for replenishment to its supplier. Other than receiving the orders, there is no communication allowed between the players. This is a simple, but realistic example of a supply chain. 

Fixed reorder quantity inventory model—A form of independent demand item management model in which an order for a fixed quantity, Q, is placed whenever stock on hand plus on order reaches a predetermined reorder level, R. The fixed order quantity Q may be determined by the economic order quantity, by a fixed order quantity (such as a carton or a truckload), or by another model yielding a fixed result. The reorder point R, may be deterministic or stochastic, and in either instance is large enough to cover the maximum expected demand during the replenishment lead time. Fixed reorder quantity models assume the existence of some form of a perpetual inventory record or some form of physical tracking, e.g., a two-bin system, that is able to determine when the reorder point is reached. These reorder systems are sometimes called fixed order quantity systems, lot-size systems, or order point-order quantity systems. 

Either type of inventory model will calculate a reorder point, which is the answer to the question of when to order. When calculating the reorder point, there are four factors to consider. The first is the length of time needed to replenish the order. The second is the average demand during the order replenishment lead time. And, the third is the variance in the demand pattern and the delivery time. Another piece of information is needed. That is, what is the level of customer demand that will be satisfied Do we want to carry enough inventory to meet the needs of 99% of our demand or just 80% of the demand This is a strategic decision that requires knowledge of the business and customer expectation to answer correctly. 

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. 

Material requirements planning (MRP)—A set of techniques that uses bill of material data, inventory data, and the master production schedule to calculate requirements for materials. It makes recommendations to release replenishment orders for material. Further, because it is time-phased, it makes recommendations to reschedule open orders when due dates and need dates are not in phase. Time-phased MRP begins with the items listed on the MPS and determines (1) the quantity of all components and materials required to fabricate those items and (2) the date that the components and material are required. Time-phased MRP is accomplished by exploding the bill of material, adjusting for inventory quantities on hand or on order, and offsetting the net requirements by the appropriate lead times. 

Tagaras, G., Cohen, M.A. (1992). Pooling in two-location inventory systems with non-neg-ligible replenishment lead times. Management Science, 55(8), 1067-1083. 

Replenishment cycle time The total time from the moment a need is identified until the product is available for use. The APICS Dictionary, lOth edition uses lead-time to define this. Here we refer to cycle time as a physical property and lead-time as a market-determined property, or expectation by customers for performance. (Adapted from APICS Dictionary, 10th edition )... 

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. 

The system still works in a periodic review fashion, and the order of events is such that the retailer places his order for period t before the supplier needs to determine his replenishment order (dealing with the opposite order of events requires some straightforward alterations to our models). Therefore, the supplier can make use of the information At when making his replenishment decision in period t. The supplier faces a fixed delivery lead-time of = r periods. We shall assume, again, that the retailer s inventory and forecasting process is in steady state. 

See Aviv (2002b) for more details and discussion. A different upper bound on p(7, 7 ) is based on a setting in which the retailer is responsible for forecasting the demand during a lead-time of L -f r periods, and the supplier s only role is to pass on the retailer s replenishment orders ... 

Thus, an important issue in our formulation will be how we specify the service constraint on our optimization problem. From our earlier discussion of in-stock probability and fill rate, recall that the probability distribution of demand figured prominently in measuring the service level. The most general case is the one in which both demand per unit time period (where the time period is typically specified as days or weeks) and replenishment lead time (correspondingly expressed in days or weeks) are random variables. Let us, therefore, assume that the lead time L follows a normal distribution with mean Pl variance al. Further, let us assume that the distribution of the demand also follows a normal distribution, such that its mean and variance, Po Od, are expressed in time units (i.e., demand per unit time) that are consistent with the time units used to express lead time L (e.g., days or weeks). 

A less rigorous approach to finding a (Q, R) solution would be to solve for Q and R separately. Note that z = R - MoltV dlt gives a fractile of the distribution of demand over the lead time. Thus, we could set R to achieve a desired in-stock probability, along the lines of the newsvendor problem solution discussed earlier (i.e., to accumulate a given amount of probability under the DLT distribution). In this setting, the in-stock probability is typically referred to as the cycle service level (CSL), or the expected in-stock probability in each replenishment cycle. Specifically, for normally distributed lead-time demand, DLT, we set... 

Again, the backlogging assumption is important. If unmet demand is lost as opposed to backlogged, then the replenishment quantity Q cannot be used to fulfill demand backlogged from previous cycles, and this inflates the expected total demand that is fulfilled in an average cycle from Q to Q + S R), such that, with normally distributed lead-time demand, we obtain P(R,Q) = 1 -... 

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... 

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