Logistics is defined in the Concise Oxford Dictionary as "the art of moving and quartering troops, and supplying and maintaining a fleet". While this definition is rather narrow, it nevertheless gives a general guide to the broad military support field known as logistics. This thesis is concerned with one of the more complex military logistics problems - namely the allocation of men, equipment and materiel to the engineer tasks associated with the movement, maintenance and support of military forces in a theatre of operations. The major factors are: a. tasks to be carried out by engineers; b. the number and type of available engineer construction units. c. stores and transport constraints imposed by other agencies in the Defence logistics system; d. deadlines imposed by the Commander and his staff; e. efficiency and proficiency of engineer constructions units in carrying out particular tasks; f. risk, including (1) possible enemy action (both directly against units, or indirectly against other elements in the logistics system) (2) adverse weather (both direct and indirect) Current military procedures for solving this type of problem are based on practices developed during World War II, and rely heavily on support from external sources (this was the case throughout the conflicts in Korea, Malaya and Vietnam). The recent change in Government defence policy requiring greater reliance on our own resources has meant that new solutions have had to be found to old problems. The aim of this thesis is therefore three-fold: a. to analyse the problem in terms of its various components; b. to develop a method whereby the problem can be solved manually in an efficient manner (but still considering all the relevant factors); and c. to develop a method whereby the solution to the problem can be optimized, using computers where necessary. Mathematical equations are developed for all factors in the engineer logistics planning problem, and a graphical technique is developed which enables a solution to the problem to be found quickly using manual methods. The approach to-the development of the graphical technique is based on some ideas presented by V.V. Kolbin in his book "Stochastic Programming".