An EOQ model for items with finite rate of production and variable rate of deterioration (Q1091252)

The differential equations describing the inventory process Q(t) in the interval [0,T] are given by d Q(t)/dt\(+atQ(t)=K-R\) \((0\leq t\leq t_ 1)\); \(dQ(t)/dt+atQ(t)=-R\) \((t_ 1\leq t\leq t_ 1+t_ 2)\); \(dQ(t)/dt=-R\) \((t_ 1+t_ 2\leq t\leq t_ 1+t_ 2+t_ 3)\); \(dQ(t)/dt=K-R\) \((t_ 1+t_ 2+t_ 3\leq t\leq t_ 1+t_ 2+t_ 3+t_ 4=T)\) with the conditions: \(Q(0)=0\), \(Q(t_ 1)=S\), \(Q(t_ 1+t_ 2)=0\), \(Q(t_ 1+t_ 2+t_ 3)=-P\) and \(Q(t_ 1+t_ 2+t_ 3+t_ 4)=0\) where a, K, R are given constants \((0<a<1\), \(K>R\). R denotes the demand rate and K the production rate). The constants S and P and the time points \(t_ i\), \(i=1,...,4\) are treated as the decision variables. The authors describe a method of minimizing the total average cost for a production cycle in a case when the unit carrying, shortage and production costs are expressed by some known constants.