Exact solutions to a class of stochastic generalized assignment problems

Abstract

This paper deals with a stochastic Generalized Assignment Problem with recourse. Only a random subset of the given set of jobs will require to be actually processed. An assignment of each job to an agent is decided a priori, and once the demands are known, reassignments can be performed if there are overloaded agents.We construct a convex approximation of the objective function that is sharp at all feasible solutions. We then present three versions of an exact algorithm to solve this problem, based on branch and bound techniques, optimality cuts, and a special purpose lower bound. Numerical results are reported.

The Million-Variable “March” for Stochastic Combinatorial Optimization

“…This problem appears in (Alonso-Ayuso et al 2003) as problem c5. SGAP 28 is an instance of a stochastic generalized assignment problem and is reported in (Albareda-Sambola et al 2002) as problem instance number 28. The reformulation of this problem has both continuous and binary variables.…”

A capacitated location-allocation problem with stochastic demands using sub-sources: An empirical study

“…In our work, demands are considered to be stochastic and the request vectors to be Bernoulli random variables. Considering the stochastic generalized assignment problem, Albareda-Sambola et al [26] proposed an exact algorithm to optimize the expected cost of a recourse function. Later, Albareda-Sambola et al [27] presented a location-routing problem with Bernoulli demands where several heuristics and lower bounds for minimizing the expected value of the recourse function were introduced.…”

The facility location problem with Bernoulli demands

“…Constraints (2) assure that all customers will be assigned to (exactly) one facility while constraints (3) assure that this assignments can only be done to operating facilities. Constraints (4) state the minimum number of customers that should be assigned to one operating facility.…”

“…The authors propose heuristics and lower bounds to minimize the expected value of the defined recourse function. AlbaredaSambola et al [2] propose an exact algorithm for minimizing the expectation of a recourse function for the Stochastic Generalized Assignment Problem, where it is assumed that the customers demands follow a Bernoulli distribution. To the best of our knowledge, no work exists in the literature that uses a similar methodology for discrete location problems with Bernoulli demands.…”