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                <term xml:lang="en">home health care</term>
                <term xml:lang="en">France</term>
                <term xml:lang="en">vehicle routes</term>
                <term xml:lang="en">minimal costs</term>
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              <p>The problem studied in our work arisen from a real application of home health care company in France. The home health care company must complete pickup and delivery tasks to satisfy the demands of customers (the patients receive home health care). The requirements can be partitioned into four types: delivering medicines from companys depot or hospital to patients home, and picking up materials from patients home to the lab or return to the companys depot. Each patient may require various pickup services and various delivery services, simultaneously. Meanwhile, there are time window constraints for lab, hospital and each patient. The objective of the company is to determine a set of vehicle routes with minimal costs, satisfying all the constraints. We build two mathematical formulations for this complex problem, and propose heuristic approaches to solve this problem. Computational experiments on some test instances are presented.</p>
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