Cal Poly Chocolates

Our design for this project began with building a strong understanding of the current production process. A meeting with the manager, Anna Nakayama, provided a detailed overview of the entire process and outlined some areas of concern. In addition, she provided us with access to critical data such as standard operating procedures and inventory spreadsheets. From there, time studies were conducted for each of the 8 types of chocolate. These time studies helped identify three main issues facing Cal Poly Chocolates. The first issue is in the packaging area of production. The process is entirely manual and has become a large bottleneck. Secondly, there is a need for a reordering system due to packaging supplies frequently being unavailable. And lastly, Cal Poly Chocolates recently faced the challenge of changing facilities and they have yet to find an efficient layout to optimize their process flow. In an attempt to eliminate the bottleneck in production, research into a packaging machine was conducted. From there, the total cost of ownership was calculated as well as a return on investment to determine if the purchase was feasible. We discovered the machine will dramatically cut the packaging process times and provide a greater production capacity. To solve the issue of unavailable material, three different reorder systems were developed. There was a need for three different systems due to the variation in demand and order sizes. Assuming the employees are well trained and the demand is monitored correctly, these systems should solve Cal Poly Chocolate’s stockout issues. Finally, to aid Cal Poly Chocolates in their facility change we developed a proposed layout that saved thirty feet in excess travel distance

Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s, S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted