Planning and inventories
Ordering lots of 400 or 1500 units instead of the optimal 775 costs the same: 23 % more per year. Near the optimum, the total cost curve is flat, and a 20 % error in the lot size adds only 2.5 %.
01The planning hierarchy
Planning production means deciding what, how much and when to manufacture with the available resources. It is done in levels, from the general to the particular:
| Level | Horizon | What it decides |
|---|---|---|
| Aggregate plan | Months to a year | Total output by family, staffing, shifts, subcontracting and inventory |
| Master production schedule | Weeks to months | How many units of each finished product and in which week |
| Material requirements planning (MRP) | Weeks | Which components to order or make, how many and when |
| Shop scheduling | Days and hours | Which order goes to which machine and in what sequence |
MRP starts from the master schedule and the bill of materials —each unit takes so many boards, each board so many components— and, subtracting inventory and adding lead times, calculates the necessary orders: this is the explosion of the bill. Integrated with purchasing, finance and sales, it became the ERP systems. Shop scheduling uses Gantt charts and priority rules, such as serving first the order with the shortest processing time or the one with the nearest due date. Just in time, by contrast, does not push production from a plan but pulls it from demand, with kanban.
02Inventories
Inventories —raw materials, work in process and finished goods— buffer the differences between the pace of purchasing, of production and of sales, but they tie up money, take up space, deteriorate or become obsolete, and hide problems. In electronics the risk of obsolescence is high: a discontinued component can stop a line. ABC classification ranks items by their annual value: typically 20 % of them, the A items, account for about 80 % of the value and deserve the strictest control.
03The economic order quantity and the reorder point
With a constant annual demand \( D \), a cost \( S \) for each order and a cost \( H \) of holding one unit in inventory for a year, the total annual cost as a function of the lot size \( Q \) and its minimum, Harris’s economic order quantity (1913), are:
The curves are the annual ordering cost (violet), holding cost (green) and total cost (blue) as a function of the lot size. The yellow dot is the chosen lot. For the reorder point, 250 working days, a lead time of 10 days, a standard deviation of daily demand of 20 % and a service level of 95 % (z = 1.645) are assumed.
04In the laboratory
Build the multilevel bill of materials of a laboratory unit and carry out the explosion for one hundred units.
With the laboratory component inventory and its prices, classify the items and plot the Pareto curve.
Schedule five orders on two machines with different priority rules and compare the delays on a Gantt chart.
05Common mistakes
- Forgetting the safety stock. With variable demand, ordering exactly at the expected demand leaves you out of stock half of the time.
- Applying the economic order quantity with highly irregular demand. The model assumes constant demand.
- Controlling all items equally. ABC classification concentrates the effort where the money is.
- Planning materials without considering capacity. An MRP can order more than the machines can make.
06Self-assessment
What is the economic order quantity with D = 12,000, S = 100 and H = 4?
\( \sqrt{2 \cdot 12\,000 \cdot 100 / 4} \approx 775 \) units.
How many orders per year does that imply?
About 15.5.
What happens to the economic order quantity if demand quadruples?
It doubles, because it depends on the square root of demand.
What is the explosion of the bill of materials?
The calculation of the quantities of each component needed to produce the master schedule.
07Further reading
- Jay Heizer and Barry Render. Principles of Operations Management. Pearson. (Spanish edition: “Principios de administración de operaciones”.) Planning, MRP and inventory models.
- Richard B. Chase, F. Robert Jacobs and Nicholas J. Aquilano. Operations and Supply Chain Management. McGraw-Hill. (Spanish edition: “Administración de operaciones: producción y cadena de suministros”.) Production and inventory planning with cases.
- Steven Nahmias. Production and Operations Analysis. McGraw-Hill. (Spanish edition: “Análisis de la producción y las operaciones”.) The mathematical models of inventory and planning.