Military logistics
History: The history of military logistics goes back to Neolithic times. The most basic requirements of an army were food and water. Early armies were equipped with weapons used for hunting like spears, knives, axes and bows and arrows, and rarely exceeded 20,000 men due to the practical difficulty of supplying a large number of soldiers. Large armies began to appear in the Iron Age. Animals such as horses, oxen, camels and elephants were used as beasts of burden to carry supplies.
Food, water and fodder for the animals could usually be found or purchased in the field.
The Roman Empire and Maurya Empire in India built networks of roads, but it was far less expensive to transport a ton of grain from Egypt to Rome by sea than 80 kilometres (50 mi) by road. After the fall of the Roman Empire in the fifth century there was the shift from a centrally organised army to a combination of military forces made up of local troops. Feudalism was a distributed military logistics system where magnates of the households drew upon their own resources for men and equipment.
When operating in enemy territory an army was forced to plunder the local countryside for supplies, which allowed war to be conducted at the enemy's expense. However, with the increase in army sizes from the late sixteenth century onward, this reliance on pillage and plunder became problematic, as decisions regarding where and when an army could move or fight became based not on strategic objectives but on whether a given area was capable of supporting the soldiers' needs. Sieges in particular were affected by this, both for an army attempting to lay siege to a town and one coming to its relief. Unless a commander was able to arrange a form of regular resupply, a fortress or town with a devastated countryside could become immune to either operation.
Napoleon made logistics a major part of his strategy. He dispersed his corps along a broad front to maximise the area from which supplies could be drawn. Each day forage parties brought in supplies. This differed from earlier operations living off the land in the size of the forces involved, and because the primary motivation was the emperor's desire for mobility. Ammunition could not as a rule be obtained locally, but it was still possible to carry sufficient ammunition for an entire campaign.

The nineteenth century witnessed technological developments that facilitated immense improvements to the storage, handling and transportation of supplies which made it easier to support and army from the rear. Canning simplified storage and distribution of foods, and reduced waste and the incidence of food-related illness. Refrigeration allowed frozen meat and fresh produce to be stored and shipped. Steamships made water transports faster and more reliable. Railways were  a more economical form of transport than animal-drawn carts and wagons, although they were limited to tracks, and therefore could not support an advancing army unless its advance was along existing railway lines. At the same time, the advent of industrial warfare in the form of bolt-action rifles, machine guns and quick-firing artillery sent ammunition consumption soaring during the First World War.
In the twentieth century the advent of motor vehicles powered by internal combustion engines offered an alternative to animal transport for moving supplies forward of the railhead, although many armies still used animals during the Second World War. The development of air transport provided an alternative to both land and sea transport, but with limited tonnage and at high cost. An airlift over "the Hump" helped supply the Chinese war effort, and after the war the 1948 Berlin Air Lift was successful in supplying half of the city. With the subsequent development of large jets, aircraft became the preferred method of moving personnel over long distances, although it was still more economical to move cargo by sea and land. In forward areas, the helicopter was well-suited to moving troops and supplies, especially over rugged terrain.

Models: 

Levels: Akin to the three levels of war, there can be considered to be three levels of logistics. Although modern communications and information technology may have blurred the distinction between them, the three-level hierarchy is deeply embedded in the organisational structure of military forces. 

Strategic logistics involves logistical activities that are conducted at national and international levels. It includes defining requirements, and arranging for the production and distribution of materiel to operational forces.
Operational logistics involves logistical activities within the theatre of operations. It includes the reception, storage, and distribution of supplies and personnel, the hospitalisation of casualties, the maintenance and repair of equipment, and the operation of the intra-theatre transportation system. The operational level of war can be defined by the amount of logistical independence a formation has. For this reason logistics is most often discussed at the operational level.
Tactical logistics involves the logistical activities of units engaged in combat.
Unlike business logistics, the objective of military logistics is not cost effectiveness of the supply chain, but maximum sustained combat effectiveness. At the tactical level, efficiency is the overriding consideration, whereas at the strategic level effectiveness is the dominant concern.

Analytical tools: The development of computers facilitated the use of analytic tools. Multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making. The location of a supply depot could involve multiple considerations and constraints, such as the access to road, rail and sea transport, and travel times to desired delivery destinations. Sometimes the number of alternatives is small and they can be considered individually, but they can also be too large for this to be possible. The consideration of constraints simplifies the decision making. These constraints could be economic, such as cost, but might also be less easily quantified, such as political, strategic or operational considerations. The United States Office of Management and Budget and the Department of Defense call this methodology the Analysis of Alternatives, and require it for military acquisitions.
Logistical planning requires forecasting of future consumption and attrition. There are two types of attrition: material attrition and personnel attrition. The former relates to the loss of equipment through combat, accidents and ordinary wear and tear through usage. Reliability theory can be used to forecast the mean time between failures of equipment and parts. This can be used to develop replacement factors, on which manufacturing and stock levels can be based. In the case of items like subsistence and soap, where demand is highly predictable, it is more convenient to use consumption factors instead.  Forecasting of casualties in combat is more difficult, as past experience may not be a reliable guide to future losses, but is required for planning by the medical services. Mathematical models of combat have been developed for this purpose. Lanchester's laws are differential equations that describe the time dependence of two armies' strengths as a function of time.
Mathematical models exist for scheduling of convoys to ensure that vehicles and the goods they carry arrive in time. Vehicle routing models can be used to select routes for timely delivery with minimum exposure to enemy action and without overloading the capacity of transportation networks. Scheduling models can be used to coordinate convoys the share the same routes. There are also models for inventory management that can be used to scheduling and quantity of orders, and stock levels, taking into account factors such as storage capacity, demand rates and delivery lead times.

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External links:  Media related to Military logistics at Wikimedia Commons