8

Only the EOQB approximation (approximation 2) has a fixed worst-case error bound. Zheng (1992) proved an error bound of $\frac18$, and Axsäter (1996) proved a stronger bound of $(\sqrt{5}-2)/2 \approx 0.118$, which is tight. The EOQ+SS approximation (approximation 1) does not have a fixed worst-case error bound; for any $m$, we can find a problem instance ...


6

To calculate the base-stock to meet a 99% type-1 service level, we need the 0.99 fractile of the demand distribution. The safety stock level is the base-stock level minus the mean demand. For the lognormal case, the author has fit a lognormal distribution and found that the parameters are $\mu=2.645$ and $\sigma=0.83255$. (Note that for a lognormal ...


4

Yes, there are such models. On (Q,R) specifically, see Gupta (1996), Parlar (1997), Mohebbi (2003), and others. There are many papers on other inventory models (not necessarily (Q,R)) under disruptions. My students and I wrote a literature review paper on these and other supply chain models with disruptions; see Snyder, et al. (2016). Note that these "...


4

Here's an approach that might be close to what you are looking for. Suppose that we have $n$ products, and for each product $i$ we know: $c_i$ = purchase cost per unit (i.e., cost to order inventory from the supplier) $\pi_i$ = profit margin per unit sold $f_i$, $F_i$ = probability distribution (pdf, cdf) of demand per period If there is only 1 product, ...


2

I think the two ways of phrasing it are slightly different: prevent a shortage before the delivery arrives during 95 percent of the order cycles means that in the long run, there will be a stockout in 5% of the order cycles, whereas meet demand 95% of the time is a little ambiguous, but to me it suggests you want to meet 95% of the demands, i.e., ...


2

There is no contradiction or inconsistency in having the lead time be longer than the time unit* for the model. The important thing to remember here is that the reorder point $r$ refers to the inventory position (IP), not the inventory level (L). The inventory position equals the on-hand inventory plus the on-order inventory (minus backorders, if any). So, ...


1

I think you could use a simple continuous-review base-stock policy, as @LarrySnyder610 mentioned too. About the inventorying each product to minimize the lost sales, first of all, you will need to forecast demand for each product in a specific time bucket, (e.g. weekly sales). Based on, further, you would be able to calculate the inventory level and ...


1

It sounds like you have a problem that involves three types of uncertainty: Demand uncertainty Lead time uncertainty Yield uncertainty Yield uncertainty is a somewhat general term that refers to uncertainty in the amount of supply available. (Related terms include capacity uncertainty and supply disruptions.) With uncertainty sources #1 and 2, you can use ...


1

You seem to be conflating two ordering systems. You say you will be receiving an order every 1.5 months on average. The only way that could happen with a lead time of 10 months would be if you had more than one order outstanding at a time. This ties to your use of $Q=6,000$ in the second paragraph. That's the order quantity when $L=3$, not when $L=10$. So if ...


1

Yes, I believe you can interpret it like this. The term service level describes it well: Service level is the probability that the amount of inventory on hand during the lead time is sufficient to meet expected demand – that is, the probability that a stockout will not occur. Service Level Assuming we want to be able to meet 99.9% of the demand would ...


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