Operations Management: Processes and Supply Chains, 12th Edition

Key Equations

Noninstantaneous Replenishment

1. 1. Maximum cycle inventory: $I_{\text{max}}=Q\left(\frac{p-d}{p}\right)$

2. 2. $\text{Total annual cost}=\text{Annual holding cost}+\text{Annual ordering or setup cost}$

   $$C=\frac{Q}{2}\left(\frac{p-d}{p}\right)\left(H\right)+\frac{D}{Q}\left(S\right)$$

3. 3. Economic production lot size: $\text{ELS}=\sqrt{\frac{2DS}{H}}\sqrt{\frac{p}{p-d}}$

4. 4. Time between orders, expressed in years: ${\text{TBO}}_{\text{ELS}}=\frac{\text{ELS}}{D}$

Quantity Discounts

1. 5. $\text{ Total annual cost}=\text{Annual holding cost}+\text{Annual ordering or setup cost}$

   $+\text{Annual cost of material}$

   $$C=\frac{Q}{2}\left(H\right)+\frac{D}{Q}\left(S\right)+PD$$

One-Period Decisions

1. 6. Payoff matrix: $\text{ Payoff}=\{\begin{array}{cc}pQ\hfill & ifQ\le D\hfill \\ \hfill pD-\ell \left(Q-D\right)& ifQ>D\hfill \end{array}$