Lead Time in a Manufacturing System with Order Batches

7 Lead Time in a Manufacturing System with Order Batches 

Consider demand that consists of orders, where each order is for a batch of Q units. These orders are generated by the customer, for example, a retailer, either to (1) replenish manufacturer finished goods inventory or (2) represent an accumulation of customer demands for the product when the manufacturer carries no finished goods inventory. The main reason that manufacturing and ordering are done in batches is to optimize the impact of set-up times on the machine. 

Consider production in batches of size Q units, where it takes time units to set up a batch for production and tp time units to produce each unit in a batch. The production time for a batch of Q units is modeled as exponentially distributed with a mean production batch rate of 

Consider an example of the Instock store that sells ten different types of products. Demand for each product each day follows a normal distribution with a mean of 50 units and a standard deviation of 25 units. All these products are produced by a manufacturer who carries no finished goods inventory, i.e., operates a make-to-order system. 

The manufacturer has 3 machines working in parallel, and production of a product requires a set-up time of 30 minutes and a processing time of 2 minutes per unit. This implies a set-up cost of 50. The cost per unit of product charged by the manufacturer is 25/unit. Instocks holding and storage cost are estimated to be 10% of the cost per unit. Assume that production occurs 8 hours per day, 5 days per week, 50 weeks per year, and that Instocks service level is 95%. 

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