L6116 Inventory buildup diagram PDF

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Inventory Buildup Diagram
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L6116

Inventory Buildup Diagram Operations Management

[Adopted from MIT Sloan Open courseware]

Introduction This note discusses a simple but general model of a production process, often referred as a “ work station” as shown in fig 1. This model consists of a server (this could be a machine, a doctor at a clinic or a factory) and a holding or waiting area where waiting or queuing to be processed at the server (this could be Patients waiting in a clinic, arriving jobs, material, orders etc).

Customers Arrive

λ

Queue

i

Server μ

Customers exit

i

Figure 1 General model of a single server process Many Manufacturing processes or service operations can be usefully represented by this model: almost all are subject to variability of one kind or other; e.g. Patient arrival to clinic, job arrival to a machine, process time of a machine etc. Classifying sources of variability by unpredictable or predictable is often a useful first step to analyzing processes subject to variability. Predictable is often referred as seasonal e.g. demand for a mobile phone, air conditioners, or demand for passenger cars, customer arrivals at a restaurant, airline reservations etc. these are predictable but highly variable. In other processes the unpredictable component of the variability will dominate e.g. arrival at an accident and emergency or arrival of high mix jobs from a complex machine centre or breakdown of a machining centre or volume of stock trading at SGX; these are modeled as stochastic. In modeling we need assumptions and the analyst must consider the manufacturing or service environment as well as the purpose of the analysis to guide the choice of modeling assumptions.

Predictable (seasonal) variability In this section we discuss simplest analysis where the system variability is predominantly predictable. For a manufacturing or service firm the most important kind of seasonal variability is that associated with demand for finished goods or service. In this section concerning a plant with seasonal variation in its input is intended to introduce inventory buildup and throughput calculations in the simplest possible setting. Consider a firm that operates both a fleet of fishing boats and a factory to process the fish. All fish brought in by the firm’s fleet are processed at its factory and the factory only processes its own catch. In this context arriving fish plays the role of customers waiting in the queue and the factory plays the role of the server. 1.

When the fleet of ships operated at full capacity, the input to the factory follows the annual pattern as shown in figure 2 due to ocean currents /monsoon and Fish migration; 3,600 tons per month during first 4 months, 4,800 tons per month for the next 4 months and 600 tons per month for the last 4 months in a year (shown in Figure 2).

2.

Thus full time fleet operation throughout the year yields an annualized average rate of 3,000 tons of fish per month.

3.

Arriving fish is stored in a freezer if it is not immediately processed.

4.

The processing capacity of the factory is 3000 tons per month. Input rate tons per month 4800 t/mth

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3600 t/mth

600 t/mth Time (Months) 4 8 Figure 2 Annual pattern of fish arrival to factory

12

Inventory buildup diagram with unlimited incoming queue capacity If there is unlimited freezer capacity for unprocessed fish and if the firm decides to operate both, the ship fleet and factory at full capacity, then the inventory pattern is that shown in figure 3. The area under the inventory curve and dividing by 12 months gives average inventory over the year as 4,000 tons of unprocessed fish inventory. Inventory (tons) 9600 Increase at 1800 t/mth

Decrease at 2400 t/mth

Increase at 600 t/mth 2400

Time (Months) 4

8

12

Figure 3 Annual inventory pattern with 3,000 ton/mth processing capacity and unlimited freezing capacity (incoming queue size)

Inventory buildup diagram with controlled incoming queue capacity Suppose that management is concerned on the cost of 4,000 tons of average unprocessed fish inventory and decided to control accumulation beyond 2,400 tons of fish. The operating policy will be changed for full time fleet operation up until this limit is reached and after which the fishing activity must be reduced to keep the catch rate at 3,000tons or less to match with factory processing capacity. This is equivalent to constraining the queue size of the factory (freezer capacity) to be 2,400 tons. This will result in inventory build up as shown in figure 4. Inventory (tons)

Increase at 600 t/mth

Decrease at 2400 t/mth

2400

Time (Months) 4

8

12

Figure 4 Annual inventory pattern with 3,000 ton/mth processing capacity & incoming queue to 2,400 tons

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•

The average inventory over the year reduces to 1,300 tons (area under graph divided by 12). The actual catch rate during the middle 4 months is 3000 tons /mth compared to actual capacity of 4,800 tons /mth

•

Thus 4 x (4,800-3000) = 7,200 tons of potential catch is foregone each year due to inventory constraint and as such 7,200 tons of processing capacity during the last 4 months goes unused because of input shortage.

•

Total processing is reduced from 36,000 tons per year to 36,000-7200 = 28,800, a reduction of 20% throughput

•

On the other hand the inventory has reduced from average of 4,000 tons to 1,300 tons a reduction of 68%.

Inventory buildup diagram with an alternative strategy Suppose that management is considered to reduce the inventory by increasing the processing capacity. The factory processing capacity is increased to 3,300 tons per month and inventory or the queue size of the factory (freezer capacity) is again constraint at 2,400 tons. This will result in inventory build up as shown in figure 5. Inventory hits 2,400 tons after 4.8 months and hits zero after 8.89 months Inventory (tons)

Decrease at 2700 t/mth 2400 Increase at 300 t/mth 1200

Time (Months) 4

8

12

Figure 5 Annual inventory pattern with 3,300 ton/mth processing capacity & incoming queue to 2,400 tons

It is clear that average inventory is lower and system throughput is higher in this scenario.

The numerical example illustrates two important points about the economic impact of predictable seasonal variability (a) If the flow rate is variable at some process stage, then system throughput can typically be improved by allowing buffer inventories between the relevant stages. i.e 3000 tons/mth production capacity vs ; fishing capacity of 3,600 tons/mth or, 4,800 tons/mth or 600 tons/mth. The amount of inventory buffer size is another important consideration and will be covered at a future class on inventory theory!! (b) In the presence of variability, optimal capacity levels may be quite different from those suggested by naïve analysis based on average flow rates. In particular, it is usually best to build excess capacity at those process stages where capacity is relatively low cost.

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