This paper considers a manufacturing system that procures raw materials and converts them to a finished product. The life cycle of the product usually has three distinct phases: increasing (inception), level (maturity) and declining (phasing out) demand. The finished products are supplied to the consumer at a fixed interval of deliveries with trend delivery quantities following the demand pattern, composed of piece-wise linear functions. This paper developed a decision rule for the manufacturer to determine the delivery quantities, the production start time and batch sizes with trend demands during increasing, level and declining phases of the life cycle of a product. It is found that when the demand is constant, the cost model becomes convex and a simple closed form solution can be obtained, but an algorithm is employed here under other cases to find a minimal cost of maintaining the system.

Raw material ordering policy and the manufacturing batch size for frequent deliveries of finished goods for a finite horizon plays a significant role in managing the supply chain logistics economically. This research develops an ordering policy for raw materials and determines an economic batch size for a product in a manufacturing system that supplies finished products to customers for a finite planning horizon. Fixed quantities of finished products are delivered to customers frequently at a fixed interval of time. In this model, an optimal multi-ordering policy for procurement of raw materials and production cycle time for a two-stage production and supply system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. The problem is then extended to compensate for the lost sales of finished products. A closed-form solution to the problem is obtained for the minimal total cost. A lower bound on the optimal solution is also developed for problem with lost sale. It is shown that the solution and the lower bound are consistently tight.

A group of M machines for processing a set of jobs in a manufacturing system is often located in a serial line. An efficient strategy for locating these machines is desired such that the total travel distance or the cost of transporting the jobs is minimized. If an application requires more than one identical machine, the cost is minimized by flow distributions between the machines. The problem of minimizing the travel distance that involves sets of identical machines is often formulated as a tertiary assignment problem. Finding an optimal solution for such a problem can be very complicated due to its combinatorial nature. This research proposes a two-stage solution methodology to ease the computation and to obtain a better solution. First, the problem of sets of identical machines is decomposed into sets of unique machines to find the machine assignment. Second, the task is to find the flow assignment by holding the machine assignment found in the previous stage. Results are encouraging and they are demonstrated through numerical examples and a set of test problems.

The ordering policy of raw materials and the manufacturing batch size for frequent deliveries of finished goods over a finite horizon play a significant role in managing the supply chain logistics economically. This research develops an ordering policy for raw materials and determines an economic batch size in a manufacturing system that supplies finished products to customers over a finite planning horizon. Fixed quantities of finished products are delivered to customers at a fixed interval of time. In this model, an optimal multi-ordering policy for procurement of raw materials and production cycle time for a production and supply system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. A closed-form solution to the problem is obtained for the minimal total cost. A lower bound on the optimal solution is developed for the problem and the empirical tests indicate that the lower bounds are very close to the solution.

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.