In this article, we consider a two commodity continuous review perishable inventory system with a finite number of homogeneous sources of demands. The maximum storage capacity of Si units for the ith commodity (i=1,2). The life time of items of each commodity is assumed to be exponentially distributed with parameter gi (i=1,2). The time points of primary demand occurrences form independent quasi random distributions each with parameter li (i=1,2) A joint reordering policy is adopted with a random lead time for orders with exponential distribution. When the inventory position of both commodities are zero, any arriving primary demand enters into an orbit. The demands in the orbit send out signals to compete for their demand which is distributed as exponential. We assume that the two commodities are both way substitutable. The joint probability distribution for both commodities and number of demands in the orbit is obtained for the steady state case. Various system performance measures are derived, and the results are illustrated with numerical examples.

The carrier collaboration problem for logistic optimization is a fundamental part of the sustainable supply chain, and has increasingly been of concern in recent years. This study proposes a novel nonlinear mathematical model to address the carrier collaboration problem. It involves a set of heterogenous vehicles with specific capacities for serving perishable products to several pickup and delivery nodes. Products are corrupted at a constant rate. The purpose is simultaneously finding routes to maximize profits in order to enhance customer satisfaction which is dependent on the freshness of delivered products. There are various applications of the proposed model in the environment which can help reducing transportation emissions, eliminating empty back hauls. Further, the proposed model uses a Hybrid Genetic Algorithm (HGA) is proposed to solve this problem due to improve the quality of initial solutions Variable Neighborhood Search (VNS) method is developed. The obtained results demonstrate the efficiency of the proposed algorithm in providing reasonable solutions within an acceptable computational time.

Delivering perishable products to customers as soon as possible and with the minimum cost has been always a challenge for producers and has been emphasized over recent years asthe global market becoming more competitive. In this studya multi-objective mix integer non-linear programming model is proposed to maximize both profits of a distributer and the total freshness of the several products to be delivered to customers with respect to their demands and with consideration of different soft time windows for each customer, heterogeneous distribution fleet and customer selection option for the distributer. The proposed model is solved with TH method. The two genetic algorithm and simulated annealing algorithm are used to solve large-sized problems. Finally, their results are compared to each other when the optimization software becomes unable of solution representation.