Inventory of differential units of a deteriorating item purchased in a lot and sold separately from two shops under a single management is considered. Here deterioration increases with time and demands are time- and price-dependent for fresh and deteriorated units respectively. For the fresh units, shortages are allowed and later partially-backlogged. For the deteriorated units, there are two scenarios depending upon whether initial rate of replenishment of deteriorated units is less or more than the demand of these items. Under each scenario, five sub-scenarios are depicted depending upon the time periods of the two-shops. For each sub scenarios, profit maximization problem has been formulated and solved for optimum order quantity and corresponding time period using genetic Algorithm (GA) with Roulette wheel selection, arithmetic crossover and uniform mutation and Generalized Reduced Gradient method (GRG). All sub-scenarios are illustrated numerically and results from two methods are compared.