TY - JOUR

T1 - DGAP- The Dynamic Generalized Assignment Problem

AU - Kogan, Konstantin

AU - Shtub, Avraham

AU - Levit, Vadim E.

PY - 1997

Y1 - 1997

N2 - The Generalized Assignment Problem (GAP) is a well-known operations research model. Given a set of tasks to be assigned to a group of agents and the cost of performing each task by each agent, the mode allocates tasks to agents to minimize the total cost subject to the availability of a single resource type. The single resource is consumed by the agents when performing these tasks. In this paper, we add the impact of time to the model assuming that each task has a due date, and inventory cost as well as shortage cost is incurred when a task is finished ahead or after its due date, respectively. We formulate the continuous-time optimal control mode of the problem where identical tasks are grouped into jobs (or batches), each job is performed by each agent with a fixed (production) rate, while due dates are transformed into demand. As a result, analytical properties of the optimal behavior of such a dynamic system are derived. Based on those properties, an efficient time-decomposition procedure is developed to solve the problem.

AB - The Generalized Assignment Problem (GAP) is a well-known operations research model. Given a set of tasks to be assigned to a group of agents and the cost of performing each task by each agent, the mode allocates tasks to agents to minimize the total cost subject to the availability of a single resource type. The single resource is consumed by the agents when performing these tasks. In this paper, we add the impact of time to the model assuming that each task has a due date, and inventory cost as well as shortage cost is incurred when a task is finished ahead or after its due date, respectively. We formulate the continuous-time optimal control mode of the problem where identical tasks are grouped into jobs (or batches), each job is performed by each agent with a fixed (production) rate, while due dates are transformed into demand. As a result, analytical properties of the optimal behavior of such a dynamic system are derived. Based on those properties, an efficient time-decomposition procedure is developed to solve the problem.

UR - http://www.scopus.com/inward/record.url?scp=2242451556&partnerID=8YFLogxK

U2 - 10.1023/a:1018933012422

DO - 10.1023/a:1018933012422

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AN - SCOPUS:2242451556

SN - 0254-5330

VL - 69

SP - 227

EP - 239

JO - Annals of Operations Research

JF - Annals of Operations Research

ER -