Question

Consider a packaging/warehousing process with the following steps:

1. The product is filled and sealed.

2. Sealed units are placed into boxes and stickers are placed on the boxes.

3. Boxes are transported to the warehouse to fulfill customer demand.

These steps can be combined into a single processing time, as depicted in the system schematic.

The system is subject to the following assumptions:

1. There is always sufficient raw material for the process never to starve.

2. Processing is carried out in batches, five units to a batch. Finished units are placed in the warehouse. Data collected indicate that unit-processing times are uniformly distributed between 10 and 20 minutes.

3. The process experiences random failures, which may occur at any point in time. Times between failures are exponentially distributed with a mean of 200 minutes. Data collection also showed that repair times are normally distributed, with a mean of 90 minutes and a standard deviation of 45 minutes.

4. The warehouse has a capacity (target level) of R = 500 units. Processing stops when the inventory in the warehouse reaches the target level. From this point on, the production process becomes blocked and remains inactive until the inventory level drops to the reorder point, which is assumed to be r = 150 units. The process restarts with a instance, when our process becomes blocked, it may actually be assigned to another task or product that is not part of our model.

5. Data collection shows that interarrival times between successive customers are uniformly distributed between 3 and 7 hours, and that individual demand sizes are distributed uniformly between 50 and 100 units. On customer arrival, the inventory is immediately checked. If there is sufficient stock on hand, that demand is promptly satisfied; otherwise, customer demand is either partially satisfied and the rest is lost (that is, the unsatisfied portion represents lost business), or the entire demand is lost, depending on the availability of finished units and the loss policy employed.

Suppose the system produces and stores multiple products.

a. List the main components of the system and its transactions.

b. What are the transactions and events of the system?

c. Which performance measures might be of interest to customers, and which to owners?

d. What data would you collect and why?

Answer 1

a) The main components of the system are -

• Raw material processing
• Packing the product - Filling and sealing
• Warehousing - Finished product
• Customer demand - Partial, full, or lost

b) Main transactions in the system are -

• Transaction between production and packaging ---> Work-in-Process (WIP)
• Packaging and Warehouse ----> Finished goods
• Wahehouse and Customer ------> Final product

c) Customers need fullfilment of their complete demand and Owners need ROI, and satisfied customers will fulfilment of their complete demand.

When customer has a demand, it is either fulfilled completely if the number of units of inventory is available, or fulfilled partially if customer accepts, or customer is lost.

For owners, they need the returns on the investment, and complete fullfilment of customer demand. Also, no customer is lost in the system.

d) I would collect the data of the periodic and seasonal demands of the customer based on the past data. Based on that data, we can know the trend of the demand and based on the trend, production schedule can be made based on the priority.