B Glossary of notation and technical terms
B.1 Modelling variables
| Term | Description |
|---|---|
| \(ns_t\) | Net stock at time \(t\). When \(ns_t>0\), inventory is held in stock. A backlog exists when \(ns_t<0\). |
| \(k\) | Lead-time. The time between placing an order and receiving it in stock. |
| \(\beta\) | Feedback parameter. |
| \(Q\) | An economic order quantity, a batch quantity. |
| \(d_t\) | Demand at time \(t\). |
| \(t\) | Time \(t\). Because time is operating on a periodic basis, the index \(t\) is an integer. |
| \(\hat{d}_{t,t+k}\) | A forecast made at time \(t\) of demand in period \(t+k\). |
| \(T_s\) | Your supplier’s lead-time. |
| \(T_p\) | Your production and distribution lead-time. |
| \(o_t\) | The order placed at time \(t\). |
| \(\hat{o}_{t,t+1}\) | A forecast of the order made at time t or the order in period \(t+1\). |
B.2 Mathematical operators
| Term | Description |
|---|---|
| \(min\{x,y\}\) | The minimum operator, pick the minimum of \(x\) or \(y\). |
| \((x)^+\) | The maximum operator, pick the maximum of \(x\) or \(0\). |
| \(!\) | Factorial number. For example, \(4!=1\times 2\times 3\times 4=24\). |
| \(\mathbb{E}[x]\) or \(\bar{x}\) | The expectation operator, the average of \(x\). |
| \(\mathbb{V}[x]\) or \(\sigma^2_x\) | The variance of \(x\). \(\sigma^2_x=\mathbb{E}[(x-\mathbb{E}[x])^2]\). |
| \(\sigma_x\) | The standard deviation of \(x\). \(\sigma_x=\sqrt{\mathbb{V}[x]}=\sqrt{\mathbb{E}[(x-\mathbb{E}[x])^2]}\). |
| \(\lim_{a \to b}\) | In the limit, as \(a\) approaches \(b\). |
| \(\approx\) | Approximately equal to. |
| \(\lfloor x \rfloor\) | The floor function; ``round \(x\) down to the nearest integer’’. |
B.3 Acronyms
| Term | Description |
|---|---|
| BOM | Bill of materials. |
| CSL | Customer Service Level. Availability or fill rate. |
| EDI | Electronic data interchange. Different standards exist, Rosetta, EDIFACT etc. |
| EDIFACT | Electronic data interchange for administration, commerce and transport |
| EOQ | Economic order quantity. |
| EPQ | Economic production quantity. |
| ERP | Enterprise resource planning. |
| FGI | Finished goods inventory. |
| IT | Information technology. |
| MPS | Master production schedule. |
| MRP | Materials requirement planning. |
| MRP II | Manufacturing resource planning. |
| MTS | Make to stock. |
| OEE | Overall equipment effectiveness. |
| OUT | Order up to policy. |
| PFG | Proportional future guidance. |
| PO | Purchase order. |
| POUT | Proportional order up to policy. |
| RMI | Raw materials inventory. |
| SKU | Stock keeping unit. |
| VMI | Vendor managed inventory. |
| VSM | Value stream map. |
| FIFO | First in, first out. |
| PMF | Probability mass function. |