Abstract
This paper presents three approaches to support decision-making for production planning, sales and inventory problems. They work in a situation with: non-stationary probabilistic demand; production capacity in regular hours and overtime; shortage leads to lost sales; limited internal storage space; and ordering costs resulting from machine preparation are negligible. In the first approach, we consider the problem as linear and deterministic. In the second, safety inventories are used to fill a probabilistic demand, but the possibility of stockout is not considered. The third approach estimates shortage resulting from demand uncertainty. The last two approaches use iterative processes to re-estimate unit holding cost, which is the basis to calculate safety inventories in each period of the horizon. Using Microsoft Excel Solver, with linear programming and nonlinear search functions, a hypothetical example (but strongly based on real-life companies) and some scenarios permit concluding that developing more realistic and complex models may not provide significant benefits.
Highlights
Aggregate Production Planning, or Sales and Operations Planning, represents an intermediary level of planning in companies, between strategic, in which the company defines its production structure for future years, and operational, which defines the processing sequence of production orders based on the resources available. Buffa and Sarin (1987) present the main concepts about this subject
The first approach results from the arbitrary definition of a proportion of replenishment cycles without shortage or a demand proportion to be met without shortage, which leads to the identification of a safety coefficient to meet demand
This paper addresses a problem not addressed elsewhere in the literature: due to storage constraints in the company’s own facilities, unit holding costs depend on making seasonal and safety inventories for periods of high demand, which would require an iterative planning process, as the safety inventory is defined by the relationship between holding costs and shortage costs
Summary
The analysis of the related literature mentioned in the references of books about operations and papers found after search in databases (Science Direct, Scopus and Web of Science, among others) provided the approaches that could be useful to deal with the problem addressed . A decrease of 50% was made to original value of internal storage capacity; an increase of ten times was made to unit labor cost in overtime; a greater variation of demand along horizon, with same average, was applied in the last scenario
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