Language:

1. Python: Determine reorder point and order quantity to minimize expected cost per year

Situation

Suppose now that the rate at which the plant uses power-lock mechanisms is stochastic and normally distributed, with a mean of 192 per day (8 per hour) and a standard deviation of 17.4 per day. Replenishment orders for power-lock mechanisms incur a lead time of 3 days. If the plant runs out of power locks, it must expedite them from the supplier at a cost of $40 each.

1. Find r and Q using each of the methods below.

2. Also report the expected total cost per week.

Solution Approach

1. Expected-Inventory-Level Approximation:

   The first approximation we discuss is probably the best known and most widely covered approximation to find r and Q. We call this the expected-inventory-level (EIL) approximation, for reasons that will become clear shortly.

   

   • Demo
   • Code

2. EOQB Approximation:

   There are important connections between the EOQ problem with planned backorders and (r, Q) policies with continuous demand distributions. We explore these connections further in Section 5.4. The EOQB approximation for finding near-optimal r and Q makes use of the EOQB, setting Q using (3.27) and r using Lemma 5.2. This approach has a fixed worst-case error bound of 0.125.

   • Demo
   • Code

3. EOQB + SS Approximation:

   Another common approximation for r and Q is to convert the inventory-cost parameters into a service level and then to use the approach described for type-1 service level constraints. The safety stock is given by s = r − µ = zασ. The expected inventory process can be thought of as being decomposed into two parts, a “top” part that looks like an EOQ curve and a “bottom” part that is flat, with a height of s, the safety stock.

   We therefore refer to this as the EOQ+SS approximation.

   • Demo
   • Code

Comparasion