Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach

A multi-item inventory model with constant demand and infinite replenishmen t is developed under the restrictions on storage area, total average shorta ge cost and total average inventory investment cost. These restrictions may be precise or imprecise. Here, it is assumed that inventory costs are dire ctly proportional to the respective quantities, and unit purchase/productio n cost is inversely related to the demand. Restricted shortages are allowed but fully backlogged. First, the problem is formulated in crisp environmen t taking the deterministic and precise inventory parameters. It is solved b y both geometric programming (GP) and gradient-based non-linear programming (NLP) methods. Later, the problem is formulated with fuzzy goals on constr aints and objectives where impreciseness is introduced through linear membe rship functions. It is solved using the fuzzy geometric programming (FGP) m ethod. The inventory models are illustrated with numerical values and compa red with the crisp results. A sensitivity analysis on the optimum order qua ntity and average cost is also presented due to the variation in the tolera nce of total average inventory investment cost and total average shortage c ost following Dutta et al., 1993, Fuzzy Sets and Systems, 55, 133-142.