The　rapid　advancement　of　mobile　edge　computing　(MEC)　networks　has　enabled　the　augmentation　of　the　computational　power　of　mobile　devices　(MDs)　by　offloading　computationally　intensive　tasks　to　resource-rich　edge　nodes.　This　paper　discusses　the　decision-making　process　for　task　offloading　and　resource　allocation　among　multiple　mobile　devices　connected　to　a　base　station.　The　primary　objective　is　to　minimize　the　time　taken　to　complete　tasks　while　simultaneously　reducing　energy　consumption　on　the　device　under　a　time-varying　wireless　fading　channel.　This　objective　is　formulated　as　an　energy-efficiency　cost　(EEC)　minimization　problem,　which　cannot　be　solved　by　conventional　methods.　To　address　this　challenge,　we　propose　a　dynamic　offloading　decision　algorithm　of　dependent　tasks　(DODA-DT)　that　adjusts　local　task　execution　based　on　edge　node　status.　The　proposed　algorithm　facilitates　fair　competition　among　all　devices　for　edge　resources.　Additionally,　we　use　a　deep　reinforcement　learning　(DRL)　algorithm　based　on　an　actor-critic　learning　structure　to　train　the　system　to　quickly　identify　near-optimal　solutions.　Numerical　simulations　demonstrate　that　the　proposed　algorithm　effectively　reduces　the　total　cost　of　the　task　in　comparison　to　previous　algorithms.