# Inventory Control

 Question 1
With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?

 A Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost. B Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost. C Curve P1: Production cost, Curve P2: Holding cost, Curve P3: Total cost, and Curve P4: Setup cost. D Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.
GATE ME 2023   Industrial Engineering
Question 1 Explanation:

 Question 2
The demand of a certain part is 1000 parts/year and its cost is Rs. 1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is Rs. 100/order and the lead time for receiving the orders is 5 days. If the holding cost is Rs. 20/part/year, the inventory level for placing the orders is ________ parts (round off to the nearest integer).
 A 14 B 8 C 18 D 22
GATE ME 2022 SET-2   Industrial Engineering
Question 2 Explanation:
Inventory control:
Annual demand (D) = 1000 units
Lead time (LT) = 5 days
Inventory level for placing the order = Re-order level (ROL)
Rate of consumption (d) =D/365
$ROL=d \times LT=\frac{1000}{365} \times 5=13.69 \approx 14 \; units$

 Question 3
The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on-hand inventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).

 A 160 B 50 C 110 D 170
GATE ME 2022 SET-1   Industrial Engineering
Question 3 Explanation:

To produce 10 units of 'P'
No. of units of 'A' required = (4x10)+(2x3x2x10) = 160 units
Net requirement of 'A' = 160 - 50 = 110 units
 Question 4
Which one of the following is NOT a form of inventory?
 A Raw materials B Work-in-process materials C Finished goods D CNC Milling Machines
GATE ME 2022 SET-1   Industrial Engineering
Question 4 Explanation:

CNC milling machines will not be treated as inventory.
 Question 5
A factory produces $m(i=1,2,...m)$ products, each of which requires processing on $n(j=1,2,...n)$ workstations. Let $a_{ij}$ be the amount of processing time that one unit of the $i^{th}$ product requires on the $j^{th}$ workstation. Let the revenue from selling one unit of the $i^{th}$ product be $r_i$ and $h_i$ be the holding cost per unit per time period for the $i^{th}$ product. The planning horizon consists of $T \;(t=1,2,...T)$ time periods. The minimum demand that must be satisfied in time period $t$ is $d_{it}$, and the capacity of the $j^{th}$ workstation in time period $t$ is $c_{jt}$. Consider the aggregate planning formulation below, with decision variables $S_{it}$ (amount of product $i$ sold in time period $t$ ), $X_{it}$ (amount of product $i$ manufactured in time period $t$ ) and $I_{it}$ (amount of product $i$ held in inventory at the end of time period $t$.

$max\sum_{t=1}^{T}\sum_{i=1}^{m}(r_iS_{it}-h_iI_{it})$
subject to
$S_{it}\geq d_{it}\;\;\forall i,t$
< capacity constraint >
< inventory balance constraint >
$X_{it},S_{it}, I_{it} \geq 0;\; I_{i0}=0$

The capacity constraints and inventory balance constraints for this formulation are
 A $\sum_{j}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t$ B $\sum_{i}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t$ C $\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-S_{it}\; \forall \;i,t$ D $\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i ,t\text{ and }I_{it}=I_{i,t-1}+S_{it}-X_{it}\; \forall \;i,t$
GATE ME 2021 SET-2   Industrial Engineering
Question 5 Explanation:
\begin{aligned} m & \rightarrow i \ldots m \leftarrow \text { product } \\ n & \rightarrow i \ldots n \leftarrow \text { workstation } \\ a_{\bar{j}} & \rightarrow \text { time } \end{aligned}
$r_{i} \rightarrow$ selling price
$h_{i} \rightarrow$ holding cost
$T \rightarrow t=1,2, \ldots T$
$d_{i t} \rightarrow$demand of product in time t
$c_{j t} \rightarrow$capacity of workstation in time t
$S_{i t} \rightarrow$Number of product sold in time t
$x_{i t} \rightarrow$Number of product produced in time t
$I_{i t} \rightarrow$Number of product i hold in inventory at end of period t
Capacity constraint
$a_{i j} x_{i t} \leq c_{j t}$
Inventory constraint
$l_{i t}=I_{i, t-1}+x_{i t}-S_{i t}$

There are 5 questions to complete.