An application of newsboy problem for determining policies for optimal stocking of textbooks

Some colleges, especially in the Middle East, maintain an exclusive textbook centre for the benefit of students. The centre procures textbooks for the courses offered by the college, circulates free of charge to students at the beginning of a semester and collects back at the end of the semester. This paper discusses an optimisation problem faced by the management of the textbook centre in deciding the optimal number of textbooks to be stocked. A cost function is developed and minimised using Lagrangian multipliers to identify optimal stocking quantities of the textbooks. An iterative procedure is suggested for the complicated problem involving textbooks of many courses. The procedure is illustrated to estimate optimal stocking quantities that minimise the total costs of overstocking and under stocking both for the simple case in which only one course is considered and for the more complex case involving multiple courses