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Lanchester equations: a pair of differential equations that describe the losses incurred by two competitors or combat forces as a function of their sizes. In discrete time, if the size of the two forces in period t are At and Dt and K, r, and s are parameters, then: At+1 = At - KAt rDt s, and Dt+1 = Dt - KDt rAt s. Typical cases are a) r = s = 1, and b) r =0, s = 1. Parameter K corresponds approximately to a probability of success. Either case illustrates the importance of concentrating one’s efforts. The essence of these quations was given by F.W. Lanchester in 1916, and by M. Osipov in 1915. Lane: shipping along a specific origin-destination pair. Typically the origin-destinations are city to city, but they might also be state to state, city to state, etc. LASH (Lighter Aboard SHip): A multi-modal form of shipping in which small barges are carried on ocean going ships. A standard size of such barges is 44 feet by 26 feet with a capacity of 385 metric tons. A LASH ship may carry about 80 LASH barges. League: An ancient measure of distance equal to approximately three miles. Learning curve: A model of the time or cost to perform some task that quantifies the observation that time to perform the task decreases the more times the task is performed. This was first observed by T. P. Wright in the 1930’s with regard to the number of labor hours required to assemble aircraft. A typical observation was that each time the cumulative production doubled, the time per unit decreased to, say, 80% of its previous value. This leads to a mathematical form: T(v) = T(1)*v-b, where v = cumulative units produced, and T(v) =time or cost to produce unit number v. An 80% learning curve corresponds to b = 0.322. Letter of Credit: A document from a reputable bank to party A, saying that party B has a specified amount of money on deposit for the purpose of buying something from A. LIFO (Last In First Out): Inventory policy in which the last item added to inventory is the first one used. It is of interest for tax purposes in that in a time of rising raw material prices, taxable profits are postponed. See also FIFO. LIFR (Line Item Fill Rate): The fraction of line items that are filled. For example, if a line item in an order quests ten units, then the line item is defined as filled only if all ten units are shipped. If all line items request just one nit, then the line item fill rate is the same as the item fill rate. See also order fill rate and item fill rate. Linear programming: a mathematical procedure for maximizing a linear function subject to linear inequality constraints. George Dantzig gave a general statement of the problem and invented the Simplex method for solving linear programs. Line item: One line in a purchase order requesting a certain amount of one SKU. Linear loss function: = expected value of Max{0, X- S)}, where X is a random variable (e.g., demand) and S is a threshold (e.g., the stock level). Therefore, in an inventory setting, it is the expected amount of unsatisfied demand. In the LINGO modeling language, the linear loss function for the standard Normal distribution is given by the function @PSL( z). For a Poisson distribution with mean D, it is given by @PPL( D, S). If F(z) and f(z) are the c.d.f and p.d.f. of the standard Normal, then @PSL( z) = z*F(z) + f(z) – z. Little’s Flow Equation: states that (average inventory level) = (average throughput rate )* (average time in system). Load planning: The process of deciding which items get loaded where in a truck, airplane, container, or ship. For a LTL truck, you want to load items in the reverse order of which they will be removed (assuming unloading from the rear). For ships and airplanes, you want the center of gravity of the load to be close to the center of lift or support. You want the heaviest item to be closest to the center of support, so as to reduce the stress. For a truck, you want the load evenly distributed over the axles, so as to not violate axle weight limits. Logit model: A statistical technique frequently used in deciding whether to grant or deny credit to a prospective customer. Given various features of customer i, xi1, xi2, .. xin, the logit model determines weights w0, w1,… wn, to compute a score s(i) = w0 + w1* xi1 + … +wn*xin. Prospects with a high score are granted credit; prospects with a low score are denied credit. Probability of being bad (0) is based on the logistics distribution and is given by: Prob{ i is bad | s(i)} = 1/(1 + e-s(i)). See also Probit model. Lot-splitting: A manufacturing convention of splitting a final order size into smaller lots at some point in the production process. For example, suppose a customer orders 100 angle rings and producing angle rings requires two steps (rolling and welding). We lot split if after rolling the first ten rings, we ship this sub-lot of ten on ahead to begin the welding operation. The advantage is that for our little example, the lot splitting may allow the order to get through the factory in almost half the time. The disadvantage is that administrative costs may increase if we do not have a good way of keeping track of the status of all the sublots of a final lot. JIT is based in large part on lot-splitting. LP: see linear programming. LTL (Less Than Truckload): A shipment that shares space on the vehicle with shipments destined for other recipients. A vehicle that makes multiple stops, dropping off or picking up only a portion of its load at each stop. |
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