In the present article, a production-inventory model is developed over a finite planning horizon where the demand varies linearly with time. The machine production rate is assumed to be finite and constant. Shortages in inventory are allowed and are completely backlogged. The associated constrained minimization problem is numerically solved. Sensitivity analysis is also presented for the given model. | Yugoslav Journal of Operations Research 21 (2011), Number 1, 29-45 DOI: A PRODUCTION-INVENTORY MODEL FOR A DETERIORATING ITEM WITH SHORTAGE AND TIMEDEPENDENT DEMAND S. KHANRA Department of Mathematics, Tamralipta Mahavidyalaya, Purba Medinipur-721636, India. sudhansu_khanra@ K. S. CHAUDHURI Department of Mathematics, Jadavpur University, Kolkata-700 032, India chaudhuriks@ Received: December 2007 / Accepted: January 2011 Abstract: In the present article, a production-inventory model is developed over a finite planning horizon where the demand varies linearly with time. The machine production rate is assumed to be finite and constant. Shortages in inventory are allowed and are completely backlogged. The associated constrained minimization problem is numerically solved. Sensitivity analysis is also presented for the given model. Keywords: Production inventory model, time-dependent demand, deteriorating item. MSC: 90B05. 1. INTRODUCTION The classical EOQ (Economic Order Quantity) model assumes that the demand rate is constant. However, in the real market, the demand for any product cannot be constant. Reaserchers have paid much attention to inventory modelling with timedependent demand. Silver and Meal [1] developed a heuristic approach to determine EOQ in the general case of a deterministic time-varying demand pattern. Donaldson [2] discussed the classical no-shortage inventory policy for the case of a linear, timedependent demand. His treatment was fully analytical and much computational effort was needed in order to get the optimal solution. Silver [3], using Silver-Meal heuristic, 30 S. Khanra, . Chaudhuri / A Production-Inventory Model obtained an appropriate solution procedure for the case of a positive linear trend in demand to reduce the computational effort needed in Donaldson [2]. Subsequent contributions in this type of modelling came from researchers such as Ritchie ([4],[5],[6]), Kicks and Donaldson .
