Tabu Search Heuristic for Joint Location-Inventory Problem with Stochastic Inventory Capacity and Practicality Constraints

This paper studies the joint location-inventory on a two-level supply chain where a single plant supplies a single commodity to a set of facilities which serve a set of customers with stochastic demands. The proposed model accounts for the probability of unfulfilled demand during the lead time, the probability of inventory capacity violation, and practicality constraints to eliminate impractical solutions including reorder points close to or higher than inventory capacity and order quantities close to zero. An iterative-nested tabu search heuristic with 100 possible parameter combinations is performed on test problems to identify the best parameter combination. The parameter combination of the least-transport-cost customer assignment rule, the complex facility swap type, the random open facility selection rule and the least-estimated-cost close facility selection rule is ranked highest with up to 73.33%, 60% and 50% chance yielding best, second-best or third-best solutions on respective clustered, random and random-clustered customer configuration. The average computational time of each run is less than two seconds on each problem instance. The sensitivity analysis of demand standard deviation, unit transportation cost and unit holding cost is also performed. On a small problem where a commercial solver can solve the proposed formulation, the tabu search heuristic yields a better solution with the much shorter CPU time of 0.148 s and the tighter upper bound of optimality gap of 15.07% than the solution from the commercial solver (the CPU time of 55.05 h and the upper bound of optimality gap of 16.98%).